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PowerTeaching: i3 Level F/G Unit 1 Cycle 1 Lesson 3 © 2012 Success for All Foundation Homework Problems 1

Homework Problems

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Team Name Team Complete?

Team Did Not Agree On

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Today we learned more about working together as a team in math class, and practiced some challenging

problems to build up our brains. Recent research shows that exercising and challenging your brain, like

with difficult math problems, actually grows brain cells. It strengthens and multiplies the connection in

your brain, so tasks that were once difficult get easier.

Directions for questions 1–3: Write how many squares are shown.

1)

PowerTeaching: i3 Level F/G Unit 1 Cycle 1 Lesson 3 2 ©2012 Success for All Foundation Homework Problems

2)

3)

4) Write addition problems with a sum of 4.

5) Write addition problems with a sum of 10.


Mixed Practice

6) 15

8 –

15

2

7) 350 ÷ 7

8) 60.718 × 3

9) What is 3

1 of 240?

Word Problem

10) Marcus wanted to figure out how many steps he takes walking to and from school every day. This

morning, he counted 162 steps to walk to school. If he walks the same number of steps each day,

how many steps would he take walking to and from school during a 180-day school year?


Homework Problems

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Today your student learned about a simple problem-solving process that can be applied to any complex

word problem. It is a set of steps to break down the tasks into smaller chunks. Here is an example of

using this process to solve a problem.

I'm making a spaghetti dinner for 8 people. Each person needs 8 oz of spaghetti sauce. 28-oz jars of

spaghetti sauce are on sale. How many 28-oz jars will I need?


Directions for questions 1–6: Solve.

1) Aimee and Tanya baked 36 pretzels. Aimee made pretzels before, so she made more than Tanya.

Tanya made half as many pretzels as Aimee did. How many did Aimee make?

2) Angela and her aunt were looking into taking a cruise. Angela read that the top speed of the cruise

ship would be 28 knots per hour. If 1 knot per hour equals 1.151 miles per hour, how fast can the ship

go in miles per hour?

3) The students in Ms. Chong’s class are making paper pinwheels. Each pinwheel has 4 sides that can

be caught by the wind. There are 29 students in Ms. Chong’s class. How many pinwheel sides are

there for the wind to catch in all?

4) Jacqueline is making apple, cranberry, and grape frozen juice pops. Each pop is made with 6 ounces

of juice. She has 24 ounces of apple juice, 36 ounces of cranberry juice, and 30 ounces of grape

juice. How many juice pops could she make?

5) Lee is helping his parents plan a big family dinner. The recipe for roast turkey says that they should

bake the turkey at 475° Fahrenheit for 45 minutes. Then, they have to lower the oven temperature

to 375° Fahrenheit and bake it for 12

1 hours longer. Finally, they have to let the turkey cool for

15 minutes before serving it. If they want to have dinner at 6:30 p.m., what time do they need to put

the turkey in the oven?

6) Haley has enough film to take 108 pictures with her old SLR camera. She’s used three-quarters of the

film. How many pictures can she still take?

Mixed Practice

7) Estimate the product of 19 and 213.

8) 43

1 – 1

3

2


9) Find the perimeter of a rectangular yard that measures 332

1 feet in width and 12

6

5 in height.

10) What is the area of this plot of land?

Word Problem

11) Explain your thinking for question 10.


Homework Problems

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Quick Look

Today you and your team worked on problems that included extraneous data. That is, data that isn’t

needed to answer the math question. You practiced focusing on and picking out the data that is needed.

You also talked about other distractions that can get in the way of doing math, like loud noise, text

messages or email, trying to do many things at once, and even daydreaming or “going on vacation”

and thinking about stuff other than math. Here is an example of working through a problem that has

too much information.



1) Maggie picked 48 plums from the plum tree outside her house. 8

1 of the plums were not ready to be

eaten. Of the plums that were good to eat, Maggie gave 2

1 to her neighbor. Her neighbor ate

3

1 of

the plums after one week. How many plums did Maggie have for herself that were good to eat?

2) Donte ran a mile in 6 minutes flat. He also could do 12 pull-ups. It took Martha 2

3 as long as Donte to

finish her mile, and she did 10 pull-ups. Tony, who ran track, ran the mile in 2

1 the time it took

Martha, and did 2

1 the pull-ups that she did. How long did it take Martha and Tony to run the mile?

3) Oscar and Keisha take the bus home from school together. It leaves at 3:04 p.m. The bus makes 17

stops on its route. Each stop is 2.39 miles apart. Oscar gets off the bus at stop 6 and Keisha gets off

the bus at stop 12. The library is at stop 10. How far apart are Oscar’s and Keisha’s stops?

4) Last week, Christian made $90.73 working 2 days at a camp, and spent $19.50 on a new shirt. In the

same week, Devon earned $100.24 working for his parents, and he spent $30.10 on some new jeans.

Amber made $68.90 in a day at her job that week, and spent $4.50 on candy. All three friends plan to

spend $50.00 on a concert ticket next month. How much money does Devon have now?

5) Doug and Gary are goalies on the soccer team. They have to practice drop-kicking a soccer ball.

Doug kicked the ball 34 yards, and the ball was in the air for 3.78 seconds. Gary kicked it 43 yards,

and the ball stayed in the air for 4.19 seconds. On their second kick, Doug kicked it 7 yards farther,

and Gary kicked it 3 yards less. How much longer did Gary’s ball stay in the air in comparison to

Doug’s on their first attempt?

Mixed Practice

6) 179,845 + 476

7) 121 ÷ 11


8) Find 4

1 of 72.

9) Nick spends $2.15 on crickets for his pet lizard every week. How much will Nick spend on crickets in

a year?

Word Problem

10) Explain your thinking for question number 2.


Homework Problems

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Today you and your team completed problems that were missing parts. Every math word problem has three parts: the situation, the math data, and the question. You figured out which parts were missing and finished them in in a way that made sense given the information you had. You and your team also talked about times when you or a teammate is on a “bad vacation” and is angry or frustrated. You thought about ways to stop and stay cool and then come back to your team and math.

Here is an example of finishing a problem that is missing parts.


Directions for questions 1–5: Finish writing the problem. Do not solve.

1) Gary and Travis are collecting plastic bottles and aluminum cans from their neighbors to take to the

recycling center. At what time did they finish?

2) Serena is putting together a puzzle that has 300 pieces in all. She finds 82 pieces that have a flat

edge and so are on the border of the puzzle.

3) Oliver’s school is on a rectangular plot of land that is 62 yards by 35 yards. Just outside the fence

around the land is a small rectangular garden that also belongs to the school. The garden is 12 feet

by 21 feet.

4) Alicia has a dog named Chloe. Here is Chloe’s growth chart.

5) $45 the first week, $104 the second, $28 the third week, and $40 the last week. How much did she

deposit?


6) Sequoia trees grow in the western United States. They grow very tall. The “General Sherman” giant

sequoia tree has grown to be about 3,312 inches tall. How many feet tall is the tree?

7) Randy is a shareholder at an organic farm. He paid $425 to the farm in exchange for a box of

vegetables each week for 22 weeks during the summer. In addition, he spends an average of $35 per

week at a local farmers market to buy fruit. How much does Randy pay for vegetables per week?

8) Ellie’s town has an area of 14 square miles. The population is 39,201. There is one middle school,

and the enrollment is 2,055. What is the average population of Ellie’s town per square mile?


Mixed Practice

9) Convert 12

123 to a mixed number.

10) 6,004 × 9

11) 108 ÷ 9

12) Kevin left home at 3:12 p.m. on Saturday and biked 1.2 miles to the library. After 45 minutes there he

biked 3.45 miles to the mall. After spending $12.50 on a watch battery, he biked 3.6 miles back home.

How many miles did he bike in all?

Word Problem

13) Gina hit a softball 4

3 of the way to the fence in right field. Pete hit a ball half as far as Gina. Erich hit a

ball halfway between Gina’s and Pete’s ball. How far did Erich’s ball go?

PowerTeaching: i3 Level F Unit 2 Cycle 1 Lesson 1 © 2012 Success for All Foundation Homework Problems 1

Homework Problems

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Mental math is a way to think about parts of numbers to make it easier to add, subtract, multiply, and

divide in our heads.

We can use basic math facts to do problems in our heads.

4,000 ÷ 80 = ?

I know 40 ÷ 8 = 5, so 80

4,000the answer is 5 × 10 or 50.

We can also break apart numbers in a math problem and use the distributive property to find the product.

18 × 5 = ?

I can think of this problem as (10 + 8) × 5, so that is 10 × 5 + 8 × 5 or 90.

And if we have to divide by 5, we can think of it as dividing by 10 then multiplying by 2. It looks like this:

530 ÷ 5 = ?

I can think of ÷ 5 as ÷ 10 × 2. So, 530 ÷ 10 × 2 = 53 × 2 or 106.

Directions for questions 1–16: Use mental math to solve.

1) 8 × 6

2) 33 ÷ 3

3) 9 × 7

4) 81 ÷ 9

5) 9,900 ÷ 5

6) 46 × 5

7) 350 ÷ 5

8) 36,000 ÷ 120

PowerTeaching: i3 Level F Unit 2 Cycle 1 Lesson 1 2 ©2012 Success for All Foundation Homework Problems

9) 64 × 8

Explain your thinking.

10) 2,700 ÷ 5


11) 6,800 ÷ 10

12) 81 × 7

13) 800 ÷ 5

14) 5,600 ÷ 700

15) 34 × 6

16) 630 ÷ 5

Mixed Practice

17) Estimate the value of the dot on the number line below:

18) Find the missing number.

45 ÷ _____ = 5

19) Subtract.

10

7 –

10

2

20) What is 2

1of 650?

Word Problem

21) Use mental math to solve.

Jonas’ family is buying a new entertainment center. The unit they like best costs $4,060. If Jonas’

family pays the bill over 5 months, how much will they pay per month?


Homework Problems

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In everyday life, sometimes we need an exact answer and sometimes we can just estimate with an

informed guess. For example, figuring out how long two loads of laundry will take might only need an

estimate, but figuring out how much you owe for a phone bill might need to be exact.

In this lesson, you thought about different situations and decided where an estimated answer was good

enough, then practiced rounding and using compatible numbers when estimating.

For example, to estimate 5,793 × 23, you could round the numbers and get 6,000 × 20 = 12,000.

To estimate 4,326 ÷ 91, you could substitute compatible numbers and get 4,500 ÷ 90 = 50.

Directions for questions 1–3: Look at the following problems. Would you need an exact answer? Would

an estimate be enough? Explain.

1) The Brown’s have cats. They feed each cat about pound of food each day. About how much

cat food should the Brown’s purchase each month?

2) May-Lee and her friends compete in the 400-meter relay race. At their last track meet, the times for

each runner in the relay were minutes, minutes, minutes, and minutes. What was

their total time for the relay race?

3) The French club held an end of the year picnic. pizzas were ordered for students. If each

pizza is cut into 8 slices, can each student have at least three slices?


Directions for questions 4–9: Estimate. Show your work.

4) 3,497 ÷ 58

5) 7,341 × 64

6) 80,925 ÷ 93

7) 6,513 ÷ 82

8) 8,621 × 13

9) 4,794 × 42

10) A local business is mailing out flyers about an upcoming sale. There are 43,864 flyers to go out and

22 employees to deliver the flyers. About how many flyers will each employee deliver?

11) A town needs about 8,165 hot dog buns for their big summer barbeque. When purchased in bulk, the

buns come in packages of 12. About how many packages should the town purchase?

12) A concert is being held for a fundraiser. Approximately 14,975 guests will be attending. If each ticket

cost $27, about how much money was raised in ticket sales?

Mixed Practice

13) Use mental math to solve:

90 × 19

14) What is 2

1 of 180?

15) Add.

4.15 + 0.7

16) Multiply.

46 × 31

Word Problem

17) Isabella has to estimate 53,709 ÷ 63. Explain how she could do this.


Homework Problems

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In this lesson you practiced long division. Let’s take a look at the steps involved.

The new car Ms. Parsons likes costs $37,440. How much is the monthly payment if it is spread over

36 months?

Step 1: Estimate. 36,000 ÷ 36 = 1,000, so about $1,000.

Step 2: Rewrite the problem and divide into each place of the dividend.

Step 3: Multiply, subtract, and bring down.

Here is one place you may get stuck:

Here is what to do:


1) The side of a building is 2,460 inches tall. Each brick of the building is 4 inches tall. How many bricks

tall is the building?

2) 35,174 ÷ 86

3) 132,176 ÷ 88

4) There were 14,910 hits to a math tutoring website last month. If there were 30 days in the month,

what was the number of hits per day (assuming an equal number each day)?

5) 8,052 ÷ 132

6) 35,235 ÷ 87

7) A soccer league has $1,140 to buy new soccer balls. If each ball costs $12, how many soccer balls can

the league buy?

Mixed Practice

8) Solve with mental math:

4,620 ÷ 5

9) Solve with mental math:

39 × 9

10) Estimate:

44,892 ÷ 506

11) Estimate:

9,628 ÷ 18

Word Problem

12) Explain the steps you used to solve question 4 above.


Homework Problems

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In this lesson, you practiced long division with remainders. Remainders can be shown as a whole

number, a fraction, or a decimal. One of the three ways might be most appropriate for a particular

situation. Here is an example from class:

68 teams raised $526,004 for a charity walk. On average, how much money did each team raise?

Because this problem involves money amounts, using a decimal is the best way to show this quotient:

The average amount of money raised by each team was $7,735.35.


Directions for questions 1–5: Solve. Show your answer three ways.

1) 32,859 ÷ 54

2) 7,502 ÷ 18

3) 984,515 ÷ 25

4) 14,652 ÷ 32

5) 135,496 ÷ 320

Directions for questions 6–9: Solve. If your answer has a remainder, choose the best way to show it.

6) 3,406 guests attended the Morris family wedding. For the reception, each table can seat 12 guests.

How many tables will be needed for the reception?

7) Ahmed’s income is $52,533 per year. How much does Ahmed earn per week (1 year = 52 weeks)?

8) An aquarium moved 11,888 fish into 88 separate tanks for a new display. On average, how many fish

were in each tank?

9) Myra worked a lot of overtime last month. Her check showed $1,435 in overtime. If she makes $14

per hour, how many overtime hours did Myra work last month?


Mixed Practice

10) Estimate. Show your work.

89,452 ÷ 88

11) Divide.

22,256 ÷ 856

12) Multiply.

4,832 × 125

13) Write 4

3 as a decimal.

Word Problem

14) Explain the steps you took to solve question number 4 above.


Homework Problems

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Today we learned to estimate with decimals. For example:

Estimate 630.346 × 0.44685.

One possible estimate could be 600 × 0.5 = 300.

Even though 0.44685 rounds down to 0, it is closer to 0.5 than 0 on the number line. Rounding down to

0 would give a product of 0, which is not close to the answer. In this case, using a compatible number

gives a better estimate.

Directions for questions 1–8: Estimate to answer each question.

1) About what is the product of

522.85 and 3.985?

2) 13.4522 + 9.2671 + 2.1329

3) Estimate the quotient of 1,280.7853 and 0.8729. Explain your thinking.

4) 409.3548 + 589.2563

5) 0.7239 × 0.005921


6) Franny ran the 100 yard dash in 13.7785 seconds at the beginning of the track season. By the end,

she was running it in 11.2239 seconds. About how much time did she cut off her original time?


7) Principal McAfferty needs to buy a candy treat for all 463 students at his school to celebrate the

end of the year. Each piece of candy costs $0.85. About how much will Principal McAfferty spend

on the candy?

8) 4.88215 – 0.46871

Mixed Practice

9) Add:

4,580,234 + 2,796

10) Subtract:

87,232 – 19,091

11) Estimate:

The product of 297 and 6

12) Divide:

560 ÷ 16

Word Problem

13) Josephina sells supplies at her school bookstore. She collected $3.72 from selling erasers.

The erasers cost $0.11 each. About how many erasers did she sell today?


Homework Problems

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Today we learned to add and subtract decimals. Estimate the answer to make sure your answer makes

sense. You may need to convert fractions and decimals first to solve. For example:


1) 0.0572 + 0.04 + 48

1

2) Jim and Karen want to buy a cake that costs

$49.55. Together they have $83.81. How

much money will they have left over?

3) 1,097.45 – 289.943

4) 17.6 + 23.402 + 60

28

5) 8.90 – 4.218

6) 6

145 – 2.729

7) 11.862 + 82.4763


8) Alex grew 0.587 inch last month. This month he grew 0.25 inch. How many inches did Alex grow in

the last two months? Explain your thinking.

9) 35.42 – 0.999

10) 47.001 + 5

1 + 0.59

Mixed Practice

11) Multiply.

47,339 × 64

12) Rewrite 12.8 as a simplified mixed number.

13) Divide. Write remainder as a decimal.

2,584 ÷ 5

14) Estimate.

2,792 × 18.5

Word Problem

15) Baltimore had 3 days of rain in February. On February 2nd it rained 0.528 inch.

On February 3rd it rained 1.101 inches. On February 22nd it rained 0.97 inch.

How much did it rain in Baltimore in February?


Homework Problems

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Today we learned to multiply decimals. It is just like multiplying whole numbers except you need to figure

out how many decimal places are in the answer. For example:

3 3

0.134 3 decimal places (134 ÷ 1,000) × 2.09 + 2 decimal places (209 ÷ 100) 1206 + 16800 0.18006 5 decimal places in the product (18,006 ÷ 100,000)

Directions for questions 1–14: Solve. Round your answer to the nearest thousandth.

1) 0.0342 × 0.420

2) 1.9 × 4.721

3) 34

1 × 1.0512

4) 4.0555 × 2.2939

5) 0.592 × 0.09725

6) 20 × 8.9271

7) 8

3 × 0.2554

8) 16.999 × 0.5

9) 0.776 × 0.649

10) 3,050 × 0.1958


11) 10

7 × 0.25

12) 25.88 × 0.4531

13) Jake’s construction company is trying to

build a new office building. They need

to lay wood measuring 100.5921 ft2 on

each of the 4 sides of the building. How

many square feet of wood is needed in all?

14) Four explorers found 210.5 pounds of gold!

They want to split it all evenly, so each

explorer gets 4

1 of the total weight.

How much do they each get?

Mixed Practice

15) Divide. Write the remainder as a decimal.

7,421 ÷ 5

16) Estimate.

391 ÷ 4.43

17) Rewrite the fraction as a decimal.

50

17

18) Add.

0.5456 + 0.902 + 0.0029

Word Problem

19) Al bought 38 balloons for his friend’s birthday party. Each balloon costs $0.23. How much did the

balloons cost Al? Explain your thinking.


Homework Problems

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Today we learned to divide decimals. Before dividing by a decimal, multiply both the dividend and divisor

by the same power of 10 (10, 100, 1,000, etc.) so that the divisor is a whole number.

Directions for questions 1–10: Solve. Round your answer to the nearest hundredth.

1) 0.027 ÷ 0.97

2) 7.8922 ÷ 1.66

3) 2.53 ÷ 2.01

4) Silver costs $762.45 for each ounce.

Olivia spent $85,675.22 on the silver.

How many ounces did she buy?

5) 0.625 ÷ 1.7

6) 19.349 ÷ 11.88


7) Angela has 8.98 pounds of bird seed in all.

Bags can hold 1.23 pounds of bird seed

each. How many bags does she need to

bag all of the bird seed?

8) 0.0071 ÷ 0.0046

9) A group of coworkers raised $764.37 for a

crab feast for the entire office. A bushel of

crabs costs $55.89. How many full bushels

can they buy?

10) 800,294.59 ÷ 0.52

Mixed Practice

11) Find the difference.

0.872 – 0.016

13) Use mental math to divide.

5,600 ÷ 70

12) Estimate.

5.92 × 1.19

14) Find three factors of 42.

Word Problem

15) Josephina has $8.63. She wants to purchase jelly beans that cost $1.56 a pound. How many pounds

can she buy?


Homework Problems

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Today we learned to solve complex, real life problems involving decimals. It is helpful to make sense of

the problem, figure out what it is asking, and make a plan before solving the problem. For example:

Belinda is making granola bars for a group trip. She wants to make enough for the 62 people on the trip to

each have 1 bar. How many cups of oats does she need to make enough bars?

Granola Bar Recipe

34

1 cups of oats

14 ounces of condensed milk 1.5 tablespoons of butter 1.5 cups of chocolate chips makes 1 sheet of 24 bars

What’s going on in the problem?

Belinda is making granola bars for a certain number of people on a trip. She has a recipe for the bars.

What’s the question?

How many cups of oats does she need to make enough bars for the trip?

What do I need to do?

Divide the number of people by the amount 1 batch makes to find how many batches to make.

Multiply the amount of oats for 1 batch by the number of batches to find the total.

62 people/granola bars needed ÷ 24 bars per batch = 2.583 batches, or 3 batches needed.

3 batches × 3.25 cups of oats per batch = 9.75 cups of oats needed in all.


1) Solve.

Susie drives her little sister to and from school each day. It takes 4.67 miles to get to school in the

morning, but an extra 1.39 miles on the way back because they go a different route to avoid traffic.

Her car holds 10.3 gallons of gas and it takes her car 1 gallon of gas to go 13.2 miles. How much gas

does Susie need to take her sister to and from school for 5 days?

Mixed Practice

2) Estimate the difference.

46.79 – 3.92

3) Convert to a fraction.

0.043

4) Find 3 multiples of 18.

5) Divide. Round your answer to the nearest hundredth.

0.893 ÷ 0.34

Word Problem



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Today we found the greatest common factor (GCF) of two numbers. The GCF is the greatest number that

is a factor of two or more numbers. Here are three ways of finding the GCF of 24 and 16:

Area Model:

The largest possible squares that fit in this rectangle are 8 × 8.

Listing Factors: Prime Factorization:

24: 1, 2, 3, 4, 6, 8, 12, 24 24 = 2 × 2 × 2 × 3

16: 1, 2, 4, 8, 16 16 = 2 × 2 × 2 × 2

The largest factor in both 24 and 16 is 8. The prime factorizations have 2 × 2 × 2 or 8 in common.

Directions for questions 1–5: Find the greatest common factor (GCF) of each pair of numbers.

1) 36 and 90

2) 22 and 55

3) 15 and 75

4) 28 and 84

5) 8 and 12

PowerTeaching: i3 Level F Unit 3 Cycle 1 Lesson 1 2 © 2012 Success for All Foundation Homework Problems

6) Mr. Reynolds wants to divide a 25-foot × 50-foot garden into the largest possible squares that will

cover the garden without overlapping. Find the dimensions of each square.

7) Marie wants to divide a 12-foot × 16-foot quilt into the largest possible squares that will cover the quilt

without overlapping. Find the dimensions of each square.

8) Michael wants to divide a piece of paper that is 16 inches × 24 inches into the largest possible

squares that will cover the paper without overlapping. Find the dimensions of each square.

9) An aerobics instructor wants to cover a 10-meter × 40-meter room with the largest possible square

mats that will cover the floor without overlapping. What are the dimensions of the mats?

10) A gym teacher wants to divide a 35-foot × 60-foot field into the largest possible squares for different

activities. The squares will cover the field without overlapping. Find the dimensions of each square.

Mixed Practice

11) 2.015 × 5

1 =

12) 100 ÷ 10 =

13) 12,568 ÷ 2,403 =

14) Estimate the quotient.

6.35 ÷ 1.99

Word Problem

15) There are 100 sixth graders and 120 seventh graders. The principal wants to divide the students into

equal groups. If each group will have all sixth graders or all seventh graders, what is the greatest

number of students that can be placed in each group? Show your work.


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Today we learned how to find the least common multiple (LCM) of two numbers. The LCM is the smallest

number that is a multiple of two or more numbers. Here are two ways to find the LCM of 4 and 10:

Listing Multiples:

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

10: 10, 20, 30, 40

Some common multiples are 20 and 40. 20 is less than 40, so 20 is the LCM.

Prime Factorization:

4 = 2 × 2

10 = 2 × 5

LCM = 2 × 2 × 5 = 20

To find the LCM, multiply each factor the most times it appears in either 4 or 10. 2 appears twice at the

most and 5 appears once. So we multiply two 2s and one 5 to find the LCM.

Directions for questions 1–6: Find the least common multiple (LCM) for each pair of numbers.

1) 15 and 25

3) 3 and 12

5) 5 and 6

2) 9 and 4

4) 8 and 10

6) 6 and 10


7) Two runners start a race at the same time. One of the runners stops for a drink every 10 minutes. The

second runner stops for a drink every 12 minutes. How many minutes will it take for the runners to

stop at the same time?

8) Jacob attends soccer practice every 3 days. He attends swimming practice every 10 days. In how

many days will Jacob first have both soccer and swimming practice?

9) Starting at 8:00 a.m. a passenger plane leaves from an airport every 6 minutes and a cargo plane

leaves every 7 minutes. When is the next time they will leave at the same time?

10) A farmer feeds his cows every 5 hours and his pigs every 2 hours. In how many hours will he first

feed both the cows and the pigs?

Mixed Practice

11) Find the GCF of 16 and 56.

12) Convert a 0.36 to a fraction in simplest form.

13) 5,246 ÷ 232 =

14) 0.12 + 0.28 + 3

1 =

Word Problem

15) An express bus leaves every 8 minutes starting at 8:00 a.m. A local bus leaves every 20 minutes

starting at 8:00 a.m. When is the next time they will leave at the same time? Explain your thinking.


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Today we used multiples and factors to solve real-world math problems. For example, we can solve the

following problem.

Henry invited 20 of his classmates to his party. He wants to purchase bottles of water and can sodas. The

bottles of water are sold in cases of 18. The can sodas are sold in cases of 12. If Henry wants to buy the

same number of bottles of water and can sodas, what is the least number of cases of water and cases of

soda he can purchase?

1) Identify the useful information.

• 18 bottles of water per case

• 12 cans of soda per case

2) Do we need to find multiples or factors?

• Henry will buy multiple cases of water and soda to get equal amounts, that means we will find the

least common multiple, or LCM.

3) Finally, solve the problem.

• 18: 18, 36, 54, 72…

• 12: 12, 24, 36…

• Henry can buy 2 cases of water and 3 cases of soda to get 36 bottles of each.

1) A school has 91 sixth-graders. Of the sixth graders, 36 of the boys and 48 of the girls were present

for the class photo. The students were arranged in equal rows, with either all boys or all girls in each

row for the photo. What is the greatest number of students that was in each row?


2) Kendra baked 21 blueberry muffins and 28 banana-nut muffins in 3 hours. She placed the muffins

in small containers to sell at the spring fair. If she placed the same number of muffins in each

container and each container only has 1 type of muffin, what is the greatest number of muffins

in each container?

3) Mrs. Anderson has 45 math students in the 5 math classes that she teaches. She wants to purchase

pizza and juice boxes for the class that won the math challenge.

Large pizzas have 8 slices and the juice boxes are sold in packages of 6. Mrs. Anderson bought

enough large pizzas and packages of juice so the number of slices was equal to the number of juice

boxes. She bought the least number possible to stay within her class party budget. How many large

pizzas did she purchase? How many packages of juice?

Mrs. Anderson got a teacher’s discount of $1.50 for each pizza. What total amount did

Mrs. Anderson pay for the pizza and the juice? If her class party budget is $100, how

much remains for future class parties?

Mixed Practice

4) Find the difference.

20

13 – 0.64332

5) Multiply.

8.59 × 19.7

6) Estimate.

83.97 ÷ 7

7) Convert 46.6 to a fraction.


Homework Answers

1) The greatest number of students in each row is 12.

2) 7 is the greatest number of muffins per container.

3) Mrs. Anderson purchased 3 large pizzas and 4 packages of juice.

She paid $44.71 for the pizzas and juices.

There is $55.29 left in the class party budget.

Mixed Practice

4) 0.00668

5) 169.223

6) Possible estimate: 84 ÷ 7 = 12

7) 465

3

Word Problem

8) They could form 5 teams.

Possible explanation: I would use the GCF to help me solve the problem because I am dividing the 8

sprinters and 12 long-distance runners into smaller teams. I would list the prime factorization of each

number, then find the common numbers in each to find the GCF. The GCF of 8 and 12 is 4, so if

every team has 4 members, there are 8 ÷ 4 = 2 sprinter teams, and 12 ÷ 4 = 3 long distance teams.

That’s 5 teams in all.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to estimate fractions as closest to 0, 2

1, or 1. To estimate the value of a fraction, we

compare the numerator and denominator. For example, consider 102

7. 7 is such a small part of 102 the

fraction is close to 0. With 102

47, 47 is close to half of 102. So the fraction is close to

2

1. Finally with

102

89,

89 is much greater than half of 102, so the fraction is close to 1 whole.

1) Is 21

9closest to 0,

2

1, or 1? Explain your thinking.

2) Maria has read 199 pages of a 247-page book. Write the number of pages she read as a fraction of

the total pages of the book. Is the fraction closest to 0, 2

1, or 1?


3) Is 87

13closest to 0,

2

1, or 1?

4) Angelina collects coins. Of the 409 coins in her collection, 345 of them are dimes. Write the

fraction of coins that are dimes. Is this fraction closest to 0, 2

1, or 1?

5) Is 708,3

043,2 closest to 0,

2


6) Mrs. Patton has a total of 108 students. 59 of those students received an A on the last test that she

gave. Write the number of students that received an A as a fraction of the total number of students. Is

this fraction closest to 0, 2


7) Is 518,1

127closest to 0,

2


8) Is 55

11 closest to 0,

2

1, or 1?

9) Is 66

55 closest to 0,

2



10) Is 178

82 closest to 0,

2

1, or 1?

11) Aaron received $50 for his allowance. He spent $21 at the mall. Write the amount that Aaron spent as

a fraction of the amount he received. Is this fraction closest to 0, 2


12) Is 747

344 closest to 0,

2

1, or 1?

Mixed Practice

13) Convert to a fraction in simplest terms.

0.578

14) Write as an improper fraction.

58

3

15) Write as a mixed number.

9

48

16) Find the LCM of 9 and 14.

Word Problem

17) Grace drank 16

3 gallon of water. Did she drink closest to 0 gallons of water,

2

1 gallon of water, or

1 gallon of water? Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we ordered mixed numbers, fractions, and decimals. For example:

Write 1.9, 112

11, and

4

7 in order from least to greatest.

4

3 is exactly halfway between

2

1 and 1, but

10

9and

12

11 are close to 1. So

4

3 is the least.

60 is the LCM of 10 and 12. We can use that to compare the fractions: 10

9=

60

54and

12

11 =

60

55.

So the numbers in order from least to greatest are 4

7, 1.9, 1

12

11.

1) Write 612

5,

12

75, and 6.56 in order from least to greatest.

2) Tonya was measured at 58

3 inches, Sam was measured at 5.4 inches, and Meghan was measured

at 59

2 inches. Write the heights in order from least to greatest.

1.9 = 110

9

4

7= 1

4

3


3) Write 10

83, 8

40

11, 8.625 in order from least to greatest.

4) Write 0.59, 75

43, and

150

87in order from least to greatest.

5) Write 40

11,

18

7, and 0.375 in order from least to greatest.

6) Adrienne drove 43.72 miles. Laura drove 4323

20miles. Lawrence drove 43

45

35miles.

Write the distances in order from greatest to least.

7) Write 18

167, 9.35, and 9

10


8) Jackson caught a fish that weighed 77

1 pounds. Scotty caught one that weighed 7.09 pounds.

Annabel caught one that weighed 714

3 pounds. Write the weights in order from greatest

to least.

9) Write 11

1,

47

5, and 0.12 in order from greatest to least.

10) Write 34.98, 3

100, and

7


11) Write 22.8, 3

67, and 22

2

1in order from greatest to least.

12) Joel ran for 1.78 hours. Candace ran for 114

10 hours. Jason ran for 1

11

9hours. Write the times in order

from greatest to least.


Mixed Practice

13) Divide.

366 ÷ 6

14) Write as a mixed number.

12

23


89

5

16) Divide.

4,000 ÷ 80

Word Problem

17) The screen sizes of three laptops are 1745

11 inches, 17

75

22 inches, and 17.35 inches.

Write the screen sizes in order from least to greatest.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we multiplied with fractions and mixed numbers. Consider 23

1 ×

11

9.

• Estimate: 23

1 ×

11

9 2 × 1 = 2. The product is about 2.

• Rename the mixed number: 23

1 ×

11

9 =

3

7 ×

11

9.

• Divide out any GCFs of a numerator and denominator pair. 3

7 ×

11

9 =

33

7

÷

× 11

39 ÷.

• Multiply the numerators and multiply the denominators. Make sure the answer is in

simplest form: 1

7 ×

11

3 =

11

21 =

11

101

• 11

101 is close to the estimate of 2.

Directions for questions 1–12: Multiply.

1) 84 × 6

1

2) At a football game, 7

6 of the crowd in attendance were fans of the home team. Of these fans,

3

2

were wearing the home team’s jersey. There were 70,000 fans at the stadium. How many people in

the stadium had on the home team’s jersey?


3) 19

4 ×

100

57

4) Jenny lives 5 miles from her school. From her house, the library is 20

9 of that distance. How far is the

library from Jenny’s house?

5) 410

9 × 4

7

4

6) Joseph swims 312

1 miles 4 times per week. How far does he swim each week?

7) 154

1× 7

8) Angelina bought 232

1 gallons of iced tea at the grocery store. She and her friends drank

12

5 of it.

How many gallons did they drink?

9) Three friends rented out an apartment that cost $465 each month. As one of the 3 living there, Jamie

must pay 3

1 of that cost. How much does Jamie have to pay each month?

10) 35

2 ×

34

11

11) Amer’s cupcake recipe called for 313

9 cups of water. He decided to add

4

1 the amount of water for

milk. How much milk did Amer add?

12) 254

× 63

1


Mixed Practice

13) Order from greatest to least.

611

9,

13

87, 6.83

14) Find the GCF.

56 and 28

15) Is 698

123 closest to 0,

2

1, or 1?

16) 85 × 9

Word Problem

17) On Sunday, 25

14 of museum visitors were adults, and

7

3 of the adults were female. What fraction of

the visitors to the museum on Sunday were adult females?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we divided whole numbers by fractions and whole numbers by mixed numbers. We can think of

dividing by a fraction just like dividing by a whole number. For example, 20 ÷ 4 means the number of

groups of 4 that can be made from 20. So 20 ÷ 4

1

means the number of groups of 4

1 that can be made

from 20. You can draw a model and think: How many 4

1 pizzas are in 20 whole pizzas?

One way to divide a whole number by a fraction or mixed number is to use an algorithm. Consider 6 ÷6

4 .


Directions for questions 1–12: Divide.

1) 40 ÷ 29

2

2) 18 ÷ 35

3

3) 12 ÷ 63

2 . Explain your thinking.

4) Jim made 14 gallons of a sports drink for his teammates. Each teammate drank 15

7 of a gallon. How

many servings were there in all? Explain your thinking.

5) The office supply store received 29 pounds of recycled copy paper. They need to divide it into piles of

7

3of a pound. How many piles will they have in all?

6) Principal Berger ordered 72 pizzas for her school’s Pizza Celebration Day. Principal Berger figured

one serving would be 16

3 of a pizza. How many servings of pizza did Principal Berger order?

7) Noah’s rain barrel contains 65 gallons of rainwater. Each time Noah waters his garden, he uses

62

1 gallons of water. How many times can Noah water his garden from the water he has in his

rain barrel?

8) Elsie works as a dental hygienist. She spends 33 hours per week cleaning patients’ teeth. Each

cleaning she performs takes 4

3 of an hour. How many patients does Elsie see in a week? Explain

your thinking.


9) Martin has $39 in his account. The cereal bar he likes costs 5

3 of a dollar at the drug store. How many

cereal bars could Martin buy with the money in his account?

10) 4 ÷ 910

1

11) 64 ÷ 321

17

12) 3 ÷ 57

1. Explain your thinking.

Mixed Practice

13) Is 8

3

closest to 0,2

1 , or 1?

14) Multiply3

2 ×19

5

15) Divide 4,200 ÷ 5 using mental math.


Word Problem

17) Rochelle has 6 yards of fabric. She uses 4

3

yard to make one scarf. How many scarves can

she make?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we divided fractions by fractions using reciprocals. We used the same steps that we used to divide

a whole number by a fraction or mixed number. Take 9

8÷

7

2 as an example.

Show the Math

Shortcut

9

8 ÷

7

2 =

9

8

×

2

7 ÷

7

2 ×

2

7

= 18

56 ÷ 1

= 318

2

= 39

1

9

8 ÷

7

2 =

9

8

×

2

7

= 18

56

= 318

2

= 39

1

We also divided mixed numbers by mixed numbers. The same methods are used, but each mixed

number must be rewritten as an improper fraction first.

Directions for questions 1–4: Divide. Explain your thinking.

1) 10

3÷

4

2


2) 36

2÷ 5

3

1

3) Mr. Lock grew 284

3pounds of sweet corn. Each basket holds 2

8

7 pounds of sweet corn. How many

baskets does he have? Explain your thinking.

4) Anderson’s Furniture Factory has 15

12 of a load of lumber. If the factory uses

5

2 of a load to make a

wardrobe, how many wardrobes can be made? Explain your thinking.

Directions for questions 5–16: Divide.

5) 35

18÷

7

4

6) 30

13 ÷

19

12

7) 21

6 ÷

3

2

8) 211

7÷ 10

20

4

9) 514

5÷ 2

20

8

10) 109

5 ÷ 3

6

5


Mixed Practice

11) Multiply: 3

2×

5

2 12) Convert

5

79 to a mixed number.

_____________________________________ _____________________________________

13) Convert 211

6 to an improper fraction. 14) Divide: 15 ÷

6

1

_____________________________________ _____________________________________

Word Problem

15) Theodore has a 12

11 foot long board. He wants to cut the board into pieces that are

3

1foot long.

How many pieces can he cut from the board?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we solved complex problems by multiplying and dividing with whole numbers, fractions, and mixed

numbers. We continued using the reciprocal and the algorithm learned previously. For example:

Ricky is creating a game board. He is cutting square game pieces from a 98-square inch piece of

paper. If each game piece is 14

3inch on each side, what is the maximum number of game pieces

he can cut from the paper?

First, find the area of each piece: 14

3 in. × 1

4

3 in. =

4

7 ×

4

7 =

16

49= 3

16

1 sq in.

Then, find how many game pieces possible in the piece of paper:

98 sq in. ÷ 316

1 sq in. =

1

98 ÷

16

49 =

1

98 ×

49

16=

1

4998 ÷ ×

4949

16

÷

= 32 game pieces.

1) Jack enlarged a photo so that its area was 414

1 inches. If the area of the enlarged photo is

about 28

3times the area of the original photo, then what are some possible dimensions of the

original photo?


2) In the last basketball game, Rob scored 36 points. 9

1 of those points were from free throws.

During the next game, he scored 12

1 times the number of points from free throws as he did

from free throws in the last game, how many free throws did he make?

Mixed Practice

3) Multiply.

12

5×

10

7

4) Multiply.

8 × 6

5

5) Multiply.

107

5 × 2

25

6

6) Divide.

14 ÷ 28

5

Word Problem



Homework Problems

Name



Questions…

#’s

Quick Look

Today, we sorted and listed different options to solve problems. We organized the different options to find

all possible combinations and permutations. The options can be shown in an organized list or in a tree

diagram. Here’s some examples:

Example 1: Mrs. Evans asked Steven, Jill, Lily,

and Dexter to form partner pairs to work on an

assignment. How many ways can partner pairs

be made?

Use an organized list to find all combinations of

partners. Since order doesn’t matter, eliminate

the repeating items in the list.

SJ SL SD

JS JL JD

LS LJ LD

DS DJ DL

From the list, we can see that there are

6 combinations of partners.

Example 2: Mrs. Evans asked Steven, Jill,

and Lily to each explain a problem from their

assignment. How many different orders can

they explain their problem?

Use an organized list to find all permutations

of the order they will explain their problem.

Order does matter so we will keep the

repeating items.

From the list we can see that there are 6 orders

in which the students can give their answers.

Orders

S L

J

J L

S

L J

S

S

J

S

L

J

L

1st 2nd 3rd



1) Elise’s chores are to clean her bedroom, wash the dishes, vacuum the living room, and mow the

lawn. In how many different orders can she complete her chores?

2) Justin purchased three dress shirts. One was white, one was blue, and one was tan. He also

purchased three neckties. One was striped, One was checkered, and One was polka-dot.

List the ways Justin can match his dress shirts and neckties.

3) Pam wants to use two different fruits for her smoothie. She has strawberries, mangos, pineapples,

and bananas. How many different smoothies can she make?

4) Martin, Bintu, and Nate will play a game that requires them to form a line at the free-throw line of a

basketball court. Show the different ways in which they can form a line.

5) Larry has homework assignments for his math, science, and English classes. In how many different

orders can he complete the assignments?

6) For breakfast, a restaurant offers its customers small, medium, or large drinks. The customers

can choose coffee, tea, orange juice, or apple juice. List the different ways a drink can be ordered

at the restaurant.

7) Donna purchased three movies. One is a comedy, one is science-fiction, and one is a drama.

Show the different orders that she can watch the movies.

8) Pete’s Tacos sells soft and hard tacos with different choices for meat and salsa. The meat choices

are beef, chicken, and pork. The salsa choices are mild and hot. How many different ways can a taco

be ordered at Pete’s?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to apply positive and negative integers to real-world situations. Integers are positive

whole numbers, negative whole numbers, and zero. Integers cannot be fractions or decimals.

For example, temperatures can be 0, above zero or below zero. A temperature of 3 below zero is the

integer –3.

We also wrote opposite integers. Opposite integers are integers that are the same distance from 0 but on

the other side of the number line. So the opposite of –7 is 7 or

+7.

Directions for questions 1–6: Write an integer for the situation. Then plot it on the number line.

1) 11 feet below sea level:

2) An elevator went down 2 floors:

3) No withdrawals or savings activity in a bank account:


4) Stock prices dropped $2:

5) A gain of 19 yards in a football game:

6) A weight gain of 46 pounds:

Directions for questions 7–10: Write the opposite integer. Then plot it on the number line.

7) A car went in reverse for 25 feet:

8) Drove 5 miles per hour below the speed limit:

9) 17 meters above sea level:

10) –10°C:

Directions for questions 11 and 12: Write the integer that describes each.

11)


12)

Mixed Practice

13) Divide.

31.80 ÷ 1.06 =

14) On a trip, Tanner caught 24 fish and Nick caught 18 fish. They both caught the same number of fish

per hour. Find the GCF to determine the most fish Tanner and Nick could have caught each hour.

15) 4

1 ÷

6

2 =

16) 28

1 – 1.57 =

Word Problem

17) Ricardo is 1,000 feet above sea level.

Would Ricardo most likely be in an airplane

or in a submarine? Explain your thinking.

Plot Ricardo’s location on the number line.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned how to plot and label a given point, name the location of a plotted point, and determine

what quadrant a point belongs in by looking at the signs of the coordinates in an ordered pair.

To plot point C at (–7, 5):

1) Start at the origin. The x-coordinate is negative,

so we move 7 left along the x-axis.

2) The y-coordinate is positive, so we move 5 up.

3) Label the point as C.

To locate point B:

1) Draw a line or trace with your finger from the point to the

x-axis to find the x-coordinate. Point B crosses the x-axis at 6. 2) Draw a line or trace with your finger from the point to the

y-axis to find the y-coordinate. Point B crosses the y-axis at –6.

3) So point B is located at the ordered pair (6, –6)

Naming the quadrant:

Remember, there is a pattern to the quadrants on the coordinate

plane. The point (–8,

–3) is always located in Quadrant III because

it has both a negative x-coordinate and a negative y-coordinate.


Directions for questions 1–5: In which quadrant would you plot each of these points?

1) (–5, 3)

2) (7, –7)

3) (2, –8)

4) (–1,

–3)

5) (5, 6)

Directions for questions 6–10: Plot and label each point on the coordinate plane.

6) K (–5, 5) 7) B (8, 0) 8) A (

–6,

–4)

9) R (7, 9) 10) P (2, –3)


Directions for questions 11–15: Write the ordered pair for each point.

11) B

12) Q

13) C

14) E

15) W


Mixed Practice

16) Estimate.

34

1× 5

8

7


63

5

18) Write an integer for the situation. Then plot it on the number line.

Take 5 steps backwards.

19) Determine whether the triangle is scalene, isosceles or equilateral.

Word Problem

20) Tina is plotting point D on a grid. From the origin, she moves 5 to the left and 2 up. What is the

ordered pair for point D? In what quadrant will point D be? Explain your thinking.

10

10

6


Homework Problems

Name



Questions…

#’s

Quick Look

Today we applied our knowledge of plotting and locating points on a coordinate plane to identify and

create geometric shapes.

For example, we know these coordinates are three of the vertices of a square: E (4, 3) F (–4, 3)

G (–4,

–5).What is the missing coordinate for point H?

First, plot the known points on the coordinate plane. We know a square has four equal sides; therefore,

the missing point must align with point E and point G making the ordered pair for point H (4, –5).

To double check that we have created a square, we can count the units along each side to make

sure all sides are equal.


1) You have been asked to design a graphic for a t-shirt. The graphic must:

a) be a rhombus and

b) have a point located in each quadrant of the coordinate plane.

Step 1: Determine what shapes you could possibly use.

Step 2: Once you have determined which shape you would like to use, choose points, plot and

label them on the coordinate plane.

Step 3: List the ordered pair for each of the points.


Directions for questions 2–4: Plot each point on the coordinate plane and connect them in alphabetical

order. What type of polygon did the plotted coordinates make?

2) A (–5, 3) B (5, 2) C (

–5,

–5)

3) M (2, 5) N (4, 2)

O (2, –1) P (

–4,

–1)

Q (–6, 2) R (

–4, 5)


4) C (6, 6) D (2, –4)

E (–6,

–4) F (

–2, 6)

Explain your thinking for question 4:

5) You are designing a rectangular garden bed.

The following points have been plotted:

D (–6, 4) E (

–6,

–2) F (8,

–2).

Write the ordered pair for the final point;

use the grid to help you.


6) Mallory is creating a rectangular poster

for a bake sale. She has plotted the

following points:

N (–6, 2) O (4, 2) P (4, 0).



7) Suri is designing a rectangular quilt.

She has plotted the following points:

E (–10, 2) F (

–10,

–6) G (5,

–6).




Mixed Practice

8) A large pizza costs $13.95. What is the cost

of 6 large pizzas?

9) Put the fractions in order from least

to greatest.

5

1,7

1,

4

3,100

99,

6

5

10) Subtract.

4,008 – 3,959

11) Write all the factors of 20.

Word Problem

12) Jenny is designing her deck. She wants it

to be square in shape. She has started the

design for the posts that will hold the deck

to the ground:

P (–3, 6) Q (

–3,

–6) R (9,

–6).

What is the ordered pair for the missing

deck post, point S?

Explain how you found your answer:


Homework Problems

Name



Questions…

#’s

Quick Look

Today we compared and ordered integers. On a number line, the integer to the left is always less than the

integer to the right. Here’s an example!

Order –25, 63,

–9, and 0 from least to greatest.

The numbers from least to greatest are: –25,

–9, 0, 63.

1) Order the following numbers from least to greatest.

–85,

–109, 75, 0, 13

2) Is –15 greater or less than 0? Use the number line to explain your thinking.

3) Hank’s Drilling Company has two active drilling sites. One site has drilled 785 feet below the surface

(–785) and the second site has drilled 625 feet below the surface (

–625). Describe the relationship

between these two depths in words and as an inequality.


4) Order the following numbers from greatest to least.

5,285; –8,856; 10,015;

–4,455

5) Below are the balances of two bank accounts. Describe the relationship in words and as an

inequality. Explain your thinking.

6) Order the following number from least to greatest.

12,765; –15,980;

–10,834; 9,525

7) Two submarines descended. One submarine descended to 750 feet below sea level (–750) and

the other descended 606 feet below sea level (–606). Describe the relationship in words and as

an inequality.

8) Gene’s current credit card balance is –$7,099. Last month, it was

–$6,256. Compare these

two balances. Explain your thinking.

9) Is –346 greater or less than

–278?

10) Order the following numbers from greatest to least.

245, –105,

–254

11) Order the following scores from greatest to least.



–6,855;

5,345; 7,056;

–1,821

13) Compare the following temperatures.

23° F and –15° F

Mixed Practice

14) Keenan has recently purchased a new car for $14,897. He will need to make payments of $526.08

each month. For about how many months will Keenan make these payments?

15) Frank is building an addition on his back patio. He needs to purchase 75.6 feet of lumber. If each foot

costs $1.95 per foot, how much money will Frank need for lumber?


35

2, 3.6,

4

15, 3.25

17) When graphed, what quadrant does the following point (–5, 8) fall in?

Word Problem

18) Neil recorded the temperatures in Anchorage, Alaska over 4 days. Write the temperatures from

warmest to coldest.

–10 ° C, 0° C,

–4° C,

–6° C


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to find the absolute value of a number. The absolute value of a number is the number’s

distance from 0 on a number line. Here’s an example!

Is |–8| greater or less than |5|?

|–8| is greater than |5| because

–8 is 8 units away from 0 and 5 is only 5 units away from 0.

1) Which is greater, –6

4

1 or |6.28|? Explain your thinking.

2) Which amount is closer to 0: –$6.75 or $6.57?

3) Order the values from least to greatest.

|–89|, |95|, |

–93|


4) Which is less, |7.23| or –7

3

1 ?

5) Order the values from greatest to least.

|–9.32|, |

–8.75|, |9.015|, |

–9.25|

6) Which is less, |–3| or |2|?

7) Which is less, |–8.9| or |

–8.09|? Explain your thinking.

8) Order the values from greatest to least.

|0|, |–8.45|, |8.55|

9) Three checking accounts have the following balances: –$879.24, $0,

–$452.09. Which account has

the greatest debt? Explain your thinking.


Mixed Practice

10) What is the distance from point A to point B on the coordinate plane?

11) Order –9, 3,

–7, and 5

from least to greatest.

12) Find the LCM for 6 and 8.

13) Multiply.

5 × 73

1

Word Problem

14) Over three days, the value of Wayne Company stock changed each day by the following number of

points.

Day 1: –2.2 points

Day 2: 0.9 points

Day 3: –1.5 points

On which day did the value of Wayne Company stock change the least?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to problem solve using coordinates.

For this figure, the x-axis is the line of symmetry. Point E is opposite point A; they have the same

x-coordinates, but opposite y-coordinates. Similarly, point D is opposite point B. They are both at 2 on the

x-axis, but point B is at 3 and point D is at –3 on the y-axis.

We can find the length of side AE by finding the distance between point E and the x-axis, point A and the

x-axis, then adding to get the total distance. Remember, absolute value tells us the distance from 0.

|–2 | = 2 | 2 | = 2 2 + 2 = 4; side AE is 4 units long.


1) Aaron needs to finish the second part of his art project. He wants his figure to be symmetrical.

a) Use the x-axis as a line of symmetry to complete Aaron’s art project.

b) How tall is the polygon if each unit equals 1 inch?

2) Point A is located at (13, 20) and point B is located at (19, 20). If each unit equals 1 foot, what is the

distance from point A to point B?

3) Find the length of side AB.


4) Rachael wants to make her star exactly the same on the right side as it is on the left side.

a) Use the y-axis as a line of symmetry to complete Rachael’s star.

b) If each unit equals 1 yard, what is the width of the star?

5) Three corners of a new rectangular building are located at points R (5, –2), S (5, 7), and T (0, 7) on

the map.

a) Find the fourth corner of the building.

b) What is the length of RS?

6) The face of a building that Jim’s Construction needed to measure is in the shape of a rectangle.

They knew the coordinates of three of the vertices on the blueprint: point A (8, 20), point B (8, 0), and

point C (–8, 0).

a) Where is the fourth vertex located?

b) If each unit equals 10 feet, what is the length of side BC?


Mixed Practice

7) Find the value.

–

9

2

8) Order from least to greatest.

–6.786,

–

2

13, |

–7 |, –

3

22,

–5.9


10) Divide.

6,879 ÷ 5

Word Problem

11) Lisa started at point (–3, 1) and traveled horizontally for 5 units. To which two possible points did she

travel?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we created models to solve math problems. Here’s an example!

Four students did the standing board jump at their school’s field day. Jake jumped 5 feet farther

than Krystal. Pam jumped 5 feet farther than Li. Krystal jumped 2 feet less than Pam.

Who had the longest jump?

When we model the problem on the number line, it is easy to see that Jake had the longest jump.


1) Michele took 4 strokes less than Ana while playing golf. Henry took 3 more strokes than Tony, but

Tony took two more strokes than Michele. Order the golfers from the least number of strokes taken to

the greatest number of strokes taken.

2) A construction company is building a basketball arena. The company needs to determine the number

of seats that will be in the first row around the rectangular court. If the court measures 90 feet by 48

feet and for every 3 feet around the court there must be a seat, how many seats can fit in the first row

arrow the court?


3) In an egg toss competition, Joslyn completed a toss that was 7.6 yards longer than Kendra’s. Mark

completed a toss of 43 yards. Alonzo had a toss just 3.8 yards short of Mark’s toss. Kendra’s toss

was 5 yards short of Alonzo’s toss. How far of a toss did each person complete?

4) Every hour, a factory produces 135 baked goods. On average the factory has to discard 47 of the

baked goods each hour because of imperfections. About how many hours will it take for the factory

to produce 1,200 baked goods?

5) A family wants to know the area of a wall that is 14 feet tall and 8.5 feet wide. The wall has a door

that is 5

3 as tall as the wall and 4 feet wide. What is the area of the wall space?

6) On a game show, contestants lose 5 points for every wrong answer and earn 7 points for each

correct answer. If a contestant answers one question correct for every 2 questions she answers

wrong, what would her score be after 36 questions?

Mixed Practice

7) What is the distance between (16, –3) and

(16, 14) on the coordinate plane?

8) Complete the number sentence using <, >,

or =.

|–6.5 | ___ | 7 |

9) Divide.

25

14 ÷

5

7

10) Add.

4.09897 + 0.2932 + 2.21

Word Problem

11) Becky is putting a fence around her vegetable garden. The garden is a square-shaped with 6-foot

sides. She needs 1 fence post for each corner and 1 post for every 1 foot along the sides. How many

fence posts does she need?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to write ratios. A ratio is a comparison of 2 related quantities with the same or different

units of measure.

Let’s write a ratio for this problem:

There are 35 cars and 5 trucks in the parking lot.

Compare the number of cars to the number of trucks in the parking lot.

We can write the ratio three ways: 5

35 35:5, 35 to 5.

We can also write it in simplest form: 1

7, 7:1, 7 to 1.

So for every 7 cars in the parking lot, there is 1 truck.

This is a part-to-part comparison because it compares part of the vehicles, the cars, to another part of the

vehicles, the trucks.

Directions for questions 1–4: Write a ratio in simplest form three different ways.

1) Billy’s store sells ice cream. He sold 25 vanilla cones and 50 chocolate cones. Compare the number

of vanilla cones sold to the number of cones sold in all.

2) Crystal collects shells. She has 14 pink shells and 36 white shells. Compare the number of pink shells

to the number of white shells.

3) Mrs. Richardson gave a math test to her students. There were 12 addition problems and 9 subtraction

problems. Compare the number of subtraction problems to the total amount of problems.


4) There are 16 flowers in a vase. Some are red and 6 are white. Compare the number of red flowers to

the total flowers in the vase.

Directions for questions 5–8: Explain what the ratio means in words. Write if the ratio is a part-to-part,

part-to-whole, or whole-to-whole comparison.

5) Missy wrote the ratio 5 to 30 to compare the number of oranges to the total amount of fruit.

6) Rose wrote the ratio 2:3 to compare the number of boys to the number of girls in her homeroom.

7) John wrote the ratio 21

6 to compare the number of chapter books to the number of picture books on

his bookshelf.

8) Louise wrote the ratio 5:20 to compare the number of pigs on her farm to the number of pigs on her

neighbor’s farm.


Mixed Practice

9) What is an equivalent fraction for 10

2?

10) What is the GCF of 20 and 50?

11) 7

10 ÷

3

2 =

12) Use <, >, or = to compare.

|–14| 13

Word Problem

13) Sarah surveyed 100 students at her school. She found that 64 of them prefer the new chocolate

pudding in the cafeteria over the old. Write her findings as a ratio in simplest terms.

Describe your ratio in words.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to find equivalent ratios. Equivalent ratios are two or more ratios that describe the

same comparison. You can find equivalent ratios the same way you find equivalent fractions—

multiply or divide both parts of the ratio by the same number. One way to find equivalent ratios is to

use a ratio table.

Watermelons for Picnic

number of guests

number of watermelons

5 2

10 4

8

Ratio tables are also helpful to compare two ratios:

Watermelons for Picnic Watermelons for Brunch

number of guests

number of watermelons

number

of guests number of

watermelons

5 2 4 1

10 4 8 2

20 8 20 5

By looking at the table we can see that if there are 20 guests, you will need more watermelons for the

picnic than the brunch. You can also see that if there are 2 watermelons, you will feed more guests with it

at the brunch than at the picnic.

× 2 × 2

How many guests would

be at the picnic if there

are 8 watermelons?

When there are 4 × 2 = 8 watermelons, then there are 10 × 2 = 20 guests.


Directions for questions 1–4: Use the tables to answer each question.

1) Fill in the missing information from the table for Ms. Lin’s class.

Geoboards for Ms. Lin’s class

number of students

number of geoboards

4 3

8 6

16

18

2) If Ms. Lin has 12 students, how many geoboards does she need?

3) If both Ms. Lin and Mr. Mark have 48 students in their classes, which teacher needs

more geoboards?

4) If Ms. Lin and Mr. Mark have 12 geoboards each, how many students do they have in all?


Directions for questions 5–8: Use the tables to answer each question.

5) Fill in the missing information from the table showing Jerry’s punch recipe.

Geoboards for Mr. Mark’s class

number of students

number of geoboards

6 3

18 9

24 12

30 15

Jerry’s punch

raspberry juice

(ounces)

lemonade (ounces)

1 15

30

10

20

Della’s punch

raspberry juice

(ounces)

lemonade (ounces)

2 10

3 15

4 20

6 30


6) If Jerry uses 45 ounces of lemonade, how much raspberry juice will he use?

7) If both Jerry and Della use 2 ounces of raspberry juice, who will make more punch?

8) If both Jerry and Della use 90 ounces of lemonade, who will use more raspberry juice? Explain

your thinking.

Mixed Practice

9) Divide.

6.512 ÷ 1.44 =

10) Is79

13 closest to 0,

2

1, or 1?

11) Nicki wrote the ratio 12:42 to compare the number of minutes she ran to the number of minutes she

walked during her workout. Explain in your own words what the ratio means.

12) Order the numbers from least to greatest.

1.501, 1.055, 19

4

Word Problem

13) The ratio of girls to boys at Park Middle School is 8:9. How many boys are in the school if there are

340 students total?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to write rates and unit rates. Rates are a type of ratio that compares two different

units of measure. Unit rates are a type of rate that compares a quantity to 1 unit of another measure.

For example:

Leslie pays $2.68 for every 4 pounds of bananas.

The rate: pounds 4

$2.68 or $2.68 for every 4 pounds.

To find the unit rate, or the cost for 1 pound, we divide parts of the rate by 4:

pounds 4

$2.68

4

4

÷

÷

= pound

$0.67 or $0.67 per pound

1) Mr. Jay paid $99 for 10 hours of work.

a. At what rate did Mr. Jay pay for work? Write in words and as a ratio.

b. Write a unit rate to describe how much Mr. Jay paid for 1 hour of work.

2) It took Regina 4 minutes to complete 2 homework problems.

a. At what rate does Regina complete homework problems? Write in words and as a ratio.

b. Write a unit rate to describe how long it takes Regina to do 1 homework problem.


3) Simon ran 13 miles in 104 minutes.

a. At what rate did Simon run? Write in words and as a ratio.

b. Write the unit rate to describe how far Simon ran in 1 minute.

4) Mario paid $10 for 10 cookies.

a. At what rate did Mario pay for the cookies? Write in words and as a ratio.

b. Write a unit price to describe the cost of 1 cookie.

5) It took Adia 27 minutes to read 2 chapters. Explain what the rate means in words.

6) Antonio paid $3.18 for 1 gallon of milk. Explain what the rate means in words.

Mixed Practice

7) Write an integer to describe a withdrawal of

$50 from a bank account.

8) Multiply.

12

5 ×

10

6 =

9) Find the least common multiple of 8 and 14.

10) Use mental math to find the product.

940 × 8

Word Problem

11) It cost Abby $345 to stay in a hotel for 3 nights. Write a unit rate to describe how much it cost her per

night. Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned how to compare rates. For example:

It costs $5.49 for a 28 ounce container of peanut butter, but it costs Jen

$0.90 to make 4 ounces of peanut butter. Which peanut butter is cheaper?

To compare rates, find an equivalent rate so that one of the units in both of the rates has the same

quantity. You can use common factors and common multiples to compare. In this example, 4 is the GCF

of 4 and 28.

Store-bought Homemade

$0.80 4 ounces $0.60 4 ounces

$5.60 28 ounces

$0.80 for 4 ounces > $0.60 for 4 ounces. Jen can make her own peanut butter for less than she can buy

the store-bought kind.

You can always use unit rates to compare because one of the units will have a quantity of 1. Let’s find

how much 1 ounce of peanut butter costs for each type.

Store-bought

ounces 28

$5.60

÷

28

28 =

ounce

$0.20

Homemade

ounces 4

$0.60

÷

4

4 =

ounce

$0.15

$0.20 per ounce > $0.15 an ounce. We got the same answer either way.

÷ 7 ÷ 7


Directions for questions 1–6: Compare the two rates.

1) Ade and Rachel checked their heartbeats. Ade’s heart beat 37 times in 15 seconds and Rachel’s beat

124 times in 1 minute. Who had a faster heartbeat?

2) Team Cure ran 27 miles in 261 minutes. Team Speedster ran 13.5 miles in 117 minutes. Which team

ran at a faster speed?

3) Betty makes 80 donuts in one hour. Andre makes 64 donuts in 40 minutes. Who can make donuts at

a quicker rate? Explain your thinking.

4) A red game spinner makes 32 revolutions in 19 seconds. A blue game spinner makes 24 revolutions

in 13 seconds. Which color spinner is faster?

5) A 6-ounce steak costs $5.58 and a 10-ounce steak costs $8.90. Which steak is the better buy?


6) 3 slices of sausage pizza cost $3.90 and 4 slices of vegetable pizza cost $4.50. Which type of pizza

costs less per slice?


Mixed Practice

7) Subtract.

8.209 – 4.13 =

8) Convert to an improper fraction:

26

4 =

9) Divide.

24

5 ÷

15

8 =

10) Order these numbers from least to greatest:

215

6, 2.09, 2.538

Word Problem

11) Harper’s family eats 5 boxes of cereal in 3 days. Owen’s family eats 9 boxes of cereal in 5 days.

Which family will need to buy more cereal in one month? Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to use the Find a Pattern Strategy to solve a word problem. For example:

Ameen is trying to shorten the time it takes to do his chores. In week one, he finished them in

194 minutes. In week two, he finished them in 190 minutes. In week three, he finished them in

186 minutes. If he keeps going like this, by how many fewer minutes will it take him to do chores

in week seven than in week one?

Week one two three four five six seven

Minutes

to do

Chores

194 190 186 182 178 174 170

If the problem looks like it has a pattern, create a table for the given information. At least 3 pieces of

information are needed to determine a pattern. In this problem, the pattern is that Ameen shortens his

time each week by 4 minutes. Next, fill in the table to find how long it takes Ameen to do his chores in

week seven, 170 minutes. Finally, solve. It took him 194 minutes to do his chores on week one. The

difference in time between these two weeks is 194 – 170 = 24 minutes. So, Ameen takes 24 fewer

minutes to complete his chores in week seven than week one.


1) In Ramblebrook, it snowed 91.8 inches in December, 30.6 inches in January, and 10.2 inches in

February. If it continues snowing like this, how many inches total will the town get between the

months of December and March?

2) Rhonda does 5 sit-ups on day one, 10 sit-ups on day two, and 20 sit-ups on day three. If she keeps

doing sit-ups like this, how many will she do on day seven?


3) The height of Mrs. Robbin’s tree was 5.23 inches the first year. It was 8.36 inches tall the second

year, and 11.49 inches tall the third year. If it continues to grow like this, how much taller will it be in

the seventh year than in the first year?

4) A pancake house served 250 pancakes on Sunday, 235 pancakes on Monday, and 220 pancakes on

Tuesday. If they continue to serve pancakes like this, on what day will they serve 160 pancakes?

5) Leah’s garden grew 21 tomatoes the first summer, 42 tomatoes the second summer and 84 tomatoes

the third summer. If her garden continues to produce like this, how many tomatoes will grow the sixth

summer?

6) Will hiked 48 minutes on day one, 56 minutes on day two, and 1 hour and 4 minutes on day three. If

he continues like this, how many minutes in all will he hike for seven days?

Mixed Practice

7) Divide.

21 5,258 =

8) Multiply.

2.25 × 6.9 =

9) Write a ratio in three ways. Be sure to write the ratio in simplest form.

Alisha wrote the ratio 5 to 25 to compare the number of pennies in her pocket to the number of

pennies in her piggy bank.

10) Ferdinand ran 2 miles in 19.5 minutes. Felicia ran 3 miles in 27.25 minutes. Who ran at a faster rate?

Word Problem

11) Alex set up a phone tree to let people know when baseball games are rained out. During the first

round, 3 people are called, during the second round, 9 people are called, and during the third round,

27 people are called. How many people total are called after 5 rounds of the phone tree?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to convert units of different measure. Because conversions rate are a type of rate, find

an equivalent rate that has the value you are converting to.

Here are some examples!

1) There are 4 quarts in 1 gallon. How many quarts are in 6 gallons?

gallon 1

quarts 4×

6

6 =

gallons 6

quartsquartsquartsquarts 24242424

2) There are 24 quarts in 6 gallons. How many gallons are in 53 quarts?

Quart(s) Gallon(s)

24 6

1 0.25

53 13.25

First find the number of gallons in 1 quart, and then multiply by 53.

3) Sophie’s GPS measured the distance of her trip. On one setting it said 8.7 kilometers, and on

another setting it said 5.4 miles. If both measures represent the same distance, how many

miles are in 1 kilometer?

kilometers 8.7

miles 5.4 ÷

kilometers 8.7

kilometers 8.7 =

0.62 miles

1 kilometer

We found the unit rate or conversion rate.

We know there are about 0.62 miles in 1 kilometer.



1) There are 1.61 kilometers in 1 mile. How many kilometers are there in 12.5 miles?

2) There are 3 feet in 1 yard. How many yards are in 496 feet?

3) There are 39.37 inches in 1 meter. How many inches are in 2.5 meters?

4) 1 kilogram is the same as 1,000 grams. How many kilograms are equal to 2,036 grams?

5) Sandra measured the liquid in the tub and measured 122 pints. Juan measured the same liquid and

got 15.25 gallons. If both measures represent the same volume, how many pints are in a gallon?

6) There are 0.0005 tons in 1 pound. How many pounds are in 4.5 tons?

7) Aya measured the height of the plant as 100 centimeters. Andre measured the height as 3.28 feet.

If both measures represent the same length, how many centimeters are in 1 foot?

8) There are 48 teaspoons in 1 cup. How many teaspoons are in 25

2 cups?

9) One scale measures the weight of the flour at 40 ounces. Another scale measures 2.5 pounds.

If both measures represent the same weight, how many ounces are in a pound?


Homework Answers

1) There are 20.125 kilometers in 12.5 miles.

2) There are 1653

1 yards in 496 feet.

3) There are 98.43 inches in 2.5 meters.

4) There are 2.036 kilograms in 2,036 grams.

5) There are 8 pints in 1 gallon.

6) There are 9,000 pounds in 4.5 tons.

7) There are 30.49 centimeters in 1 foot.

8) There is 1155

1 teaspoons in 2

5

2 cups.

9) There are 16 ounces in 1 pound.

Mixed Practice

10) 1 to 4, 1:4, 4

1

11) $0.30 per ounce or ounce 1

$0.30

12) 36

5

13) Gillian’s restaurant used about 40 cups of kiwi juice to make the fruit punch.

Word Problem

14) There are 0.45 kilograms in 1 pound. Possible explanation: 14.8 kilograms per 31.6 pounds is a rate. To find the unit rate for 1 pound, I divided both 14.8 kilograms and 31.6 pounds by 31.6.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to solve real-world problems using the unit rate and equivalent rates. For example:

Nigel reads 20 pages in 29 minutes. We can find how long it will take him to finish a 337 page

book by finding an equivalent rate. Here are 3 different ways to solve the problem.

29 minutes = 488.65 minutes

20 pages 337 pages

It will take Nigel 488.65 minutes to read a 337 page book.

____________________________________________________________


1) 4 ounces of gold costs $79.65. At that price, how much will Quinn spend on 3.5 ounces of gold?

2) A remote-control car can go 13 miles per hour. How far will it travel in 4

1 of an hour?

Pages Minutes

20 29

1

337

Pages Minutes Pages Minutes

20 29 20 29

337 337

÷ 20 ÷ 20

× 337 × 337

×

20

337

×

20

337

× 16.85 × 16.85


3) Eddie drove 165 miles in 3 hours. At that rate, how long did it take him to travel 412.5 miles?

4) Marco runs 3.75 miles in 0.5 hour. At that rate, how far will he run in 5 hours?

5) Roast beef costs $5.95 per pound. At this price, how many pounds will $32.73 buy?

6) Ms. Biz can pack 125 lunches in 90 minutes. At this rate, how many lunches can she pack

in 42

1 hours?

7) Jimmy patches 5 bicycle tires at his shop in 10 minutes. At his rate how long will it take him to patch

42 tires?

8) Owen can sell 152 boxes of cookies in one week. At this rate, how many weeks will it take him to sell

418 boxes of cookies?

9) It costs $1.40 for 2 glasses of lemonade. At this price, how much will 51 glasses of lemonade cost?

10) Mrs. Louis popped 46 cups of popcorn for the school play in 1 hour. At this rate, how many cups of

popcorn can she pop in 34

3 hours?


Mixed Practice

11) In which quadrant would you plot the point

(¯4, ˉ7)?

12) Find the least common multiple of 5 and 7.

13) 8

4 ×

2

16

14) Divide.

7.78 ÷ 2.25 =

Word Problem

15) Maurice noticed that he installed 22

1

feet of fence in 25 minutes. If he continues to work at the same

pace, how long will it take him to install 30 more feet of fence? Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to graph rates and ratios. For example:

Jada uses 2 drops of blue dye for every 3 drops of yellow dye to make her green dye.

The chart shows a few equivalent ratios.

Jada’s dye

blue (drops)

yellow (drops)

2 3

4 6

8 12

We represented the equivalent ratios from the chart as points

on a graph to form a straight line. Any point along the line is

an equivalent ratio for 2 drops of blue to 3 drops of yellow.

We know that 6 drops of blue and 9 drops of yellow is an

equivalent ratio because the line passes through the point (6, 9).

We also know that 3 drops of blue and 4 drops of yellow is not

an equivalent ratio because the line does not pass through

the point (3, 4).


1) Draw a graph to show Carlo’s earnings per hour. Use the ratio table to create at least two more

points for your graph.

Directions for questions 2 and 3: Use the graph you created for question 1 to help you answer

each question.

2) How much money would Carlo make if he worked for 8 hours?

3) Does this graph show a ratio? Explain your thinking.

Carlo’s Hourly Rate

wage hours

$135 15


4) Draw a graph to show the rate of conversion for ounces and pounds. Use the ratio table to create at

least two more points for your graph.

Directions for questions 5 and 6: Use the graph you created for question 4 to help you answer

each question.

5) Jamie bought 5 pounds of cheese, and Joey bought 90 ounces. Who bought more cheese? Explain

your thinking.

6) How many ounces are in 4 pounds?

Conversion of Ounces to

Pounds

ounces pounds

96 6


Mixed Practice

7) What is the GCF of 45 and 60?

8) Convert 0.24 to a fraction in simplest terms.

9) Is 128

43closest to 0,

2

1, or 1?

10) What is the absolute value of 213– ?

Word Problem

11) Tom sold 37 smoothies in 1 day. He says that if he keeps selling smoothies at this rate, he will sell

409 smoothies in 12 days. Draw a graph to help you explain whether Tom is correct or not.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we used tape diagrams to help solve multi-step ratio problems. Here’s what they look like:

Jodi used a ratio of 2 cups of orange juice for every 5 cups of cranberry juice to make her fruit punch.

She decided to add 24 more cups of orange juice, and the amount of orange juice and cranberry juice

was equal. How much orange juice was in the mixture at first?

Jodi added 3 parts orange juice to make equal

parts. 3 parts = 24 cups.

That means 1 part = 24 ÷ 3 = 8 cups.

So the original 2 parts of orange juice is

8 × 2 = 16 cups.

The mixture had 16 cups of orange juice at first.

Directions for questions 1–6: Use the tape diagram to solve each problem.

1) Charlene and Alejandro were selling raffle tickets. At the end of the day, the ratio of Charlene’s tickets

to Alejandro’s was 7:3. Charlene gave 24 of her tickets to Alejandro so that they had equal amounts.

How many tickets do they have all together?

Charlene:

Alejandro:


2) Maurice and Jess have a sticker collection. The ratio of Maurice’s stickers to Jess’s stickers is 4:1.

After Jess acquired 39 new stickers, they had the same number of stickers. How many stickers does

Jess have in all now?

Maurice:

Jess:

3) Jamie had the same amount of bracelets and necklaces. When she made 24 more bracelets, the

ratio of bracelets to necklaces became 3:1. How many bracelets does Jamie have in all now?

bracelets:

necklaces:

4) Julie and Kara earned money from a yard sale. The ratio of Julie’s money to Kara’s was 3:5. After

Kara spent $28, she had the same amount of money that Julie had. How much money did Kara

originally have?

Julie:

Kara:

5) Rob and Erika picked up 21 passengers each during their taxi driving shifts. After Rob worked an

extra hour the ratio of Rob’s passengers to Erika’s passengers was 8:7. How many passengers did

Rob pick up during his extra hour of work?

Rob:

Erika:

6) Lashon and Adeline ran for an equal amount of time on Monday. On Tuesday, Lashon ran for 9 extra

minutes and Adeline ran the same amount of time as Monday. If the ratio of Lashon’s running time

on Tuesday to Adeline’s running time on Tuesday was 7:4, how long did each of them run

on Monday?

Lashon:

Adeline:


Mixed Practice

7) If Camren travels 30 miles in 45 minutes, how far will he travel in 120 minutes?

8) Gem purchased 12.5 square feet of concrete for $36.25. How much does it cost for 1 square foot

of concrete?

9) Subtract.

7

3 –

28

3=

10) Which is less |–8| or |7|?

Word Problem

11) Jen uses a ratio of 1 cup of oil to 1 cup of vinegar to make her salad dressing. She decided to add

6 more cups of oil, and she now has twice as much oil as vinegar. How much of each ingredient was

in the mixture first? How many cups of vinegar does she need to add to fix the recipe?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to problem solve with rates and ratios. For example:

Bri sells about 10 small juices an hour. For every small juice she sells, she sells 3 large juices.

We know how many small juices are sold in 1 hour and the ratio of small to large juices sold, so we can

predict how many small and large juices are sold in different amounts of time.

Juices Sold Large Juices Sold

small large large juice(s) hour(s)

1 3 30 1

10 30 60 2

20 60 150 5

We can graph ratios to visually show different information.


1) Solve.

Hardwood flooring is sold by the case at Lawry’s Hardwood Store. Mr. Lawry said it is cheaper to

complete a project with the butterscotch oak because $3.57 per square foot of butterscotch oak is

less than $3.91 per square foot of rustic oak.

butterscotch oak specifications

price per case $150 plank length varied square feet per case 42 plank width 3 inches commercial/residential residential plank thickness 0.375 inches

rustic oak specifications

price per case $90 plank length varied square feet per case 23 plank width 4 inches commercial/residential residential plank thickness 0.375 inches

Explain why Mr. Lawry’s reasoning is not always correct. Be sure to give an example to support

your explanation.

Mixed Practice

2) If there is 0.914 meter in a yard, how meters

are in 53

2yards?

3) What is 3

12× 5

4

1?

4) Solve.

4.36 + 0.0256 + 3,634


5) Plot and label point A at (–

6, –

2).

Word Problem

6) A customer has a project that requires 354 square feet of flooring. Which type of flooring is cheaper

for the project? Use the information in question 1 to solve.


Homework Problems

Name

Team Name Team Complete? Team Did Not Agree On

Questions…

#’s

Quick Look

Today we learned to write parts of a whole as percents, decimals, and fractions. We also learned to convert between fractions, percents, and decimals. A percent is a ratio of a number out of 100 with a percent sign (%). For example:

38 out of the 100 fish in an aquarium have stripes.

We also learned to convert fractions to percents.

12528 = 28 ÷ 125 = 0.224 = 22.4%

Directions for questions 1–3: Write each decimal as a percent.

1) 0.81

2) 0.4

3) 0.095

Directions for questions 4–6: Write each value as a percent and decimal.

4) 102

of the balloons popped.

5) 6817

of the balls were green.

6) 8025 books were fiction.

38 out of 100 fish

fraction decimal percent

10038 0.38 38%

5019


Directions for questions 7–9: Write each percent as a decimal and fraction in simplest form.

7) 11.2%

8 44%

9) 1%

Directions for questions 10 and 11: Show each value on the grid. Write as a fraction, decimal, and percent. Write the fraction as hundredths and in simplest form.

10) 50 out of 100 ice cream sundaes have caramel topping.

11) 71 out of 100 trees were oak.

Mixed Practice

12) Deann biked 25 miles in 13.2 minutes. Carlos biked 37 miles in 17.9 minutes. Who biked at the faster rate?

13) Which is greater |51| or |–12|?

14) Order the following from least to greatest.

0.84,7714 ,

2922

15) Multiply.

0.32 × 0.26

Word Problem

16) 78 out of 100 sixth graders voted to have lunch one hour earlier. Write a percent to describe the sixth graders who did not vote to have lunch one hour earlier.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we ordered and compared fractions, decimals, and percents. Here’s what that looks like!

Order11

5,

15

9, 0.536, 0.5, and 51% from least to greatest.

51% = 0.51

11

5<

2

1 because

11

5.5=

2

1

15

9= 0.6 because 9 ÷ 15 = 0.6

So the numbers from least to greatest are: 11

5, 0.5, 51%, 0.536,

15

9.

1) Write 34%, 0.76, 10

5, 18% from least to greatest.

2) Here is a record of a decrease in average rainfall for the month of August in three cities. Which city

has the greatest decrease in rainfall?

3) Write 20

15, 78%, 0.89, 45%, 100% from greatest to least.


4) Miranda and Thomas are competing for a faster time in a 1600 m run. After weeks of training,

Miranda improved her time by 13% and Thomas improved his time by 25

4. Who improved his or her

time by the lesser value?

5) Kendra, Juan, and Jake had their annual review last week. All three received raises. Who received

the least salary increase?

6) Write 0.315, 3

1, 31%, and 0.3 from least to greatest.

7) Wesley High School’s Science department wants to raise money for a new lab. They have decided to

sell raffle tickets in each of the science sections. If each class starts with the same number of raffle

tickets, which science class has been the most successful in selling tickets?

8) On Monday afternoon, Tim mowed 0.34 of his lawn. On Tuesday morning, he mowed 38% of his

lawn. Which day did Tim mow the lesser portion of his lawn?

9) Write 100%, 2

3, 61%, 0.625, 67% from greatest to least.

10) Which is greater, 3

2 or 70%?


Mixed Practice

11) Multiply.

3.45 × 8


13) Michelle and Haley are both selling girl group cookies. The ratio of cookies sold by Michelle to Haley

was 7:3. Haley was able to sell an additional 24 boxes so that they have each sold the same amount.

How many boxes did they each sell?

14) Estimate the value of 21

10.

Word Problem

15) Which flavor juice has the highest portion of fruit juice in their drink? Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to find the percent of a number. Here’s what that looks like!

15% of 30 is 4.5 because 0.15 × 30 = 4.5.

A percent is a ratio of a number out of 100, so 15% = 100

15=

30

5.4.

We also learned to find the whole when given a part and percent. We can use equivalent ratios to help

solve. Here’s an example!

Ms. Lin has collected 75% of the sixth’s graders permission slips. If she has 63 slips,

how many sixth graders are there?

If 63 represents 75% of the sixth graders, then 63 ÷ 3 = 21 makes 75% ÷ 3 = 25% of the sixth graders.

25% × 4 = 100%, so there are 21 × 4 = 84 sixth graders.

Or we can find an equivalent ratio:

1) About how much is 73% of 103?


2) Ryan had a large jug of water and he drank 6.5 fluid ounces of it, which was 9% of the total water in

the jug. About how much water was in his jug when it was full?

3) Monique’s yearly income from her job is $86,750. After creating a budget for her expenses, she found

that she could spend 12.4% of her income on items for herself. How much can Monique spend?


4) Emily held her breath under water for 23 seconds, which is only 56.5% as long as she is capable of

holding it. How long can Emily hold her breath?

5) Jamaal’s mother gave him $120.00 to go to the grocery store. If he only spent 88% of the money,

how much did Jamaal spend?

6) $54 is 75% of the money Bo has saved from babysitting. How much has he saved?

7) Joey lifted 67.6 pounds at the gym, which is only 70% of the total amount of weight he can lift.

How much can Joey lift? Explain your thinking.

8) Brent took an IQ test that was 240 questions. Of the total number of questions, he answered 95% of

them correctly! How many questions did he answer correctly?


Mixed Practice

9) Write the fraction as a percent.

8

5


0.77, 76%, 7

6, 82%

11) If there are 0.45 kilograms in a pound, about

how many kilograms are in 39.7 pounds?

12) Estimate.

0.4772 × 2.92

Word Problem

13) Liana is purchasing jeans that cost $32.99.

a. If sales tax is 6%, what is the sales tax on the jeans?

b. How much will Liana pay for the jeans including tax?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned to solve complex problems involving percents. For example:

Lou bought a hat that was 20% off and jeans that were 10% off. He saved 13% in all with the sale.

Item Original Price

hat $15

jeans $34

hat savings: 0.2 × $15 = $3.00

jeans savings: 0.1 × $34 = $3.40

savings before price total

savings total=

00.34$00.15$

40.3$00.3$

+

+=

00.49$

40.6$≈ 13% savings in all

_____________________________________________________________________

1) Ty is in a store that is having a sale. Everything is 25% off with an additional 20% off the sale price.

a) Ty said that if a shirt is on sale, then the shirt is 25% + 20% = 45% off the original price. What’s

wrong with his thinking?

b) Ty wants to buy a shirt that is originally marked as $38.00. How much will the shirt cost after the

discounts are applied?

c) If Ty buys the shirt, what percent of the original price did he save?


Mixed Practice

2) A canning company produced 30,260 cans of vegetables. If 132 cans fit in each shipping box, how

many shipping boxes does the company need to pack all of the cans of vegetables?

3) Write in order from greatest to least:

0.2, 7

2, 12

3

4) Convert 0.052 to a percent.

5) Multiply.

820

5×

5

24=

Word Problem

6) In part c of question 1 you calculated the percent Ty saved from the original price. With the same two

discounts, would he save the same percent you calculated for the shirt if he purchased a jacket that

costs a different amount of money? Why or why not?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned the Guess and Check strategy to solve problems. We made educated guesses to help

us prove the problem. An educated guess is a guess based on information you have. It is not a random

guess. Here’s an example!

Scarlett spent $62.06 on three different items at the home improvement store. What did she buy?

We know that she did not buy the towel bar because its price ends in 9 cents. There is not another item or

items that would add to give $0.06.

Now we make our best guesses and keep track of them until we find the correct combination:

light bulb + shower head + window screen = $63.90

doorbell + shower head + window screen = $62.06

So Scarlett bought a doorbell, showerhead, and window screen.


Directions for questions 1–6: Use the Guess and Check strategy to solve.

1) Rico spent $98.34 on three different items at a clothing store. What items did he buy?

2) Benny had 12 coins that add up to $2.04. What 12 coins does he have?

3) Mr. Donald spent $10.50 on three different flavors at a snowball stand. What three flavors did he buy?

4) Claire likes three kinds of fruit: apples, oranges, and strawberries. An apple weighs 5 ounces, an

orange weighs 7 ounces, and a strawberry weighs 0.8 ounces. If Claire buys different fruits that weigh

26.4 ounces in total, how many of each fruit did she buy?


5) Kim bought three different items at a pastry shop and spent $8.62. What three items did she buy?

6) Hank bought green, red, and blue string to make bracelets. The green string came in 12.5 feet per

package, the red string came in 13 feet per package, and the blue string came in 18.5 feet per

package. If the total length of string Hank bought was 57 feet, how many of each color did he buy?

Mixed Practice

7) Compare 9% and 0.055 using < , >, or =.

8) Write 0.7657 as a percent.

9) Greenville Movie Theatre sells two tickets

for $18.00. Springville Movie Stadium sells

four tickets for $34.00. Which is the better

deal?

10) 18 ÷ 114

6

Word Problem

11) Sylbia has 8 coins that add up to $0.47. What are the coins? Are there any other possibilities?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned about exponents. Exponents are a way to rewrite expressions that multiply the same

number or variable more than once. For example, we can rewrite 4 • 4 • 4 • 4 • 4 as 45 because we are

using 4 as a factor 5 times. We also see exponents in some formulas.

We find the area of a square by multiplying length times width.

On a square, the length and the width are the same size. So our formula is A = s • s. That’s

the same as A = s2. What is the area of this square?

A = s2

A = (5 in.)2 = 5 in. • 5 in. = 25 in.

2

____________________________________________________________________________________

Directions for questions 1 and 2: Rewrite using an exponent.

1) 12 • 12 • 12 • 12

2) 7 • 7 • 7 • 7 • 7 • 7 • 7 • 7

Directions for questions 3 and 4: Write the prime factorization using exponents.

3) 64

4) 600


Directions for questions 5–8: Show the math in the story using multiplication and an exponent.

5) The zoo has 4 lions. Each lion eats 4 meals a week. Each meal has 4 slabs of meat. How many slabs are eaten in all in one week?

6) There are 8 artists in the class.

Each artist drew 8 pictures.

There are 8 aliens in each picture.

Each alien has 8 arms.

Each arm has 8 fingers.

How many fingers in all?

7) There are 7 people playing a game.

Each person gets 7 clues.

Each clue has 7 facts.

Each fact is 7 words.

How many words in all?

8) 10 teams were competing in a contest.

Each team had 10 people on it.

Each person had to attempt 10 events.

Each event had 10 obstacles.

How many obstacles in all?

Directions for questions 9–12: Find the area of the square using the formula A = s2

9)

10)

11)

12)


Mixed Practice

13) Solve.

18 – 9 ÷ 3 • 2

14) There are 129 balloons at a party and 43

children in attendance. How many balloons

does each child receive if the balloons are

shared equally?

15) Charlene is paid $23.75 for every 3 hours

she babysits. How much would Charlene

earn if she babysat for 5.5 hours?

16) Write the integer to represent this phrase:

343 dollars in debt.

Word Problem

17) Giana’s garden is shaped like a square. Each side of the garden measures 12 feet. If Giana wants to

cover the garden with a layer of new potting soil, what is the area that she needs to cover?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we used the Order of Operations to find the value of expressions. The Order of Operations is a set

of rules that tells us which operations to do first, second, and so on.

Here’s an example; let’s use PEMDAS to help us find the value of this expression.

5 • (27 – 6) + 43 ÷ 2

Parentheses � 5 • 21 + 43 ÷ 2

Exponents � 5 • 21 + 64 ÷ 2

Multiplication & � 105 + 64 ÷ 2

Division 105 + 32

Addition & � 137

Subtraction

Directions for questions 1–8: Evaluate the expression.

1) 34 – 4 • (2 • 4 + 3)


3) 2 + 42

• 2

1 – 7

2) 17 – 82 • 0.25 + 2

5


4) 10 • (5 + 2 • 6 ÷ 4)

Remember, we do Multiplication and

Division in order from left to right.

Then we do Addition and

Subtraction in order from left to right.


5) 4

3 • 8 + 4 – 10 ÷ 2

6) (3 + 24) • 5 – 10 ÷

2

1

7) 6 • 8 – 12 • (72 – 15 ÷

3

1)

8) 100 • 0.2 ÷ 22 – 3

Mixed Practice

9) Rewrite using exponents.

7 • 4 • 4 • 3 • 7 • 4

10) Find the area using the formula A = s2.

11) Divide.

79

4 ÷ 3

12) Write the fraction as a percent.

8

3

Word Problem

13) Sara and Jarreth both evaluated the expression 54 + (2

2 • 8) – 4 ÷

5

2. Here is their work.

Sara Jarreth

54 + (2

2 • 8) – 4 ÷

5

2 5

4 + (2

2 • 8) – 4 ÷

5

2

625 + (4 • 8) – 4 ÷ 5

2 625 + (4 • 8) – 4 ÷

5

2

625 + 32 – 4 ÷ 5

2 625 + 32 – 4 ÷

5

2

625 + 32 – 10 657 – 4 ÷ 5

2

657 – 10 = 647 653 ÷ 5

2 = 1,632

2

1

Who got the correct value? Describe the mistakes the other made.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we used our knowledge of the Order of Operations and problem solving to answer real-world math

problems. First, we found the key words and numbers in the math stories and situations. Then, we turned

those words and numbers into numeric expressions. Finally, we used the Order of Operations to evaluate

the numeric expressions and answer the questions.

Here’s an example:

Gerald’s Toy Factory makes 3 colors of teddy bears: brown, tan, and yellow. Each type of teddy

bear uses 3 yards of fabric. The factory can create 50 teddy bears each hour. They make brown

teddy bears for 3 hours each day, tan teddy bears for 4 hours each day, and yellow teddy bears

for 2 hours each day. So how much fabric does Gerald’s Toy Factory use in a day to create

teddy bears?

The important information in the problem is highlighted in yellow. The question we have to answer is

highlighted in green. Let’s write a numeric expression to help us.

Teddy bears created each day: 50 hour

bearsteddy • (3 hours + 4 hours + 2 hours) • 3

bearteddy

fabric of yards

50 hour

bearsteddy • 9 hours • 3

bearteddy

fabric of yards

450 teddy bears • 3 bearteddy

fabric of yards = 1,350 yards of fabric each day.

No matter what color teddy bear is being made, Gerald’s Toy Factory makes 50 teddy bears each hour.

So we found the total hours that the factory makes teddy bears, multiplied that by the rate of teddy bears

created each hour. Then we multiplied that by the ratio of fabric needed to create each bear. We used the

Order of Operations to do the work in the parentheses first, then to multiply from left to right.


1) Chen is creating a pattern for the floor of his patio using wooden tiles in two types: pine wood and

cedar wood. Each tile is a square that is 6 inches on each side. Chen needs 44 pine wood squares

and 20 cedar wood squares to create the pattern for his patio.

Chen is purchasing the wood from the local hardware store as longer planks then cutting the planks

into the 6 inch squares.

Type of Wood Length of Plank Cost of Plank

Cedar 72 inches $21.34

Chestnut 60 inches $36.50

Pine 4.5 feet $15.11

Birch 7 feet $29.99

A) If the hardware store only allows customers to buy whole planks of wood, then how many planks of

each type of wood does Chen need to purchase?

B) If the tiles completely cover Chen’s patio, what is the total area of the patio?

C) What will Chen spend on wood to create the pattern for his patio?

Mixed Practice

2) Show the math in the story using

multiplication and using an exponent.

2 friends each have 2 cats.

Both cats have 2 types of collars.

Each color has 2 I.D. tags on it.

How many I.D. tags to the friends have

in all?

3) Evaluate the expression.

102 • (16 – 6 + 25) ÷ 5


4) What is the value of –213 ?

5) Ms. Connelly purchased 23 fluid ounces of

mercury for the chemistry lab for $28.98.

How much did she spend per ounce?

Word Problem

6) Jeremiah buys 3 cans of white paint and 4 cans of beige paint. Each can of paint costs $8.99.

Gheta buys 4 rolls of wall paper with flowers and 2 rolls of wall paper with stripes. Each roll of

wall paper costs $5. Write and evaluate a numeric expression to find how much more Jeremiah

spent on decorating supplies than Gheta.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we identified the unknown quantity in situations. Then, we assigned a variable to it.

Here’s an example!

It snowed 10.5 inches more this year than it did last year.

known quantity unknown quantity

If we know how many inches it snowed last year, we can determine how many inches it snowed this year.

Let s represent the amount of snow last year.

Directions for questions 1 and 2: Assign a variable to an unknown quantity in the situation.

1) Omar slept 30 minutes longer on Tuesday

night than on Monday night.

2) Trip and Anne-Marie both have coin

collections. Trip has twice as many

coins as Anne-Marie.

3) What is an unknown in this situation? What variable could you assign to that unknown value?


Directions for questions 4–8: Assign a variable to an unknown quantity in the situation.

4) Grant drove an average speed of 54 miles per hour on his trip to Nevada.

5) Sasha babysat for her neighbor last week. She earns $12 for each hour she babysits.


6) Logan and Trevor competed in an apple bobbing contest. Trevor picked up 3 more apples than Logan.

7) Dimitri finished his homework 7 minutes faster tonight than on Wednesday night. Explain your thinking.

8) Frank donated 0.25 of his lottery winnings to charity.

9) What is an unknown in this situation? What variable could you assign to that unknown value?


Directions for questions 10–12: Assign a variable to an unknown quantity in the situation.

10) Simon and Camilla both ride bicycles to stay in shape. On Monday, Camilla biked 1.2 miles farther

than Simon.

11) Nina was baking a cake and accidently put 4 times the amount of flour she was supposed to!

12) Kelvin and Rachel held the record at their school for the longest egg toss. This year, they completed

a toss 2 yards shorter than their previous record. Explain your thinking.

Mixed Practice


30 – 4 × 3 ÷ 6

14) Write the prime factorization of 100

using exponents.

15) Divide.

40.3 ÷ 0.25

16) Estimate the sum.

3558

9 + 5

35

2

Word Problem

17) Max compared sports drinks at two different grocery stores. The first grocery store sold the drinks for

2 cents an ounce less than the second grocery store. Assign a variable to an unknown quantity in the

situation. Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we identified terms associated with algebraic expressions:

Constant– A constant is a quantity that always stays the same.

Variable– A variable is an unknown value or a value that can change.

Coefficient– A coefficient is a number multiplied by a variable.

Term– A term is a single constant, variable, or variable with a coefficient.

Algebraic Expression– An algebraic expression is a collection of terms connected by

operations that includes one or more variables.

Here’s an example.

We can also represent the expression, x + 7,

with algebra tiles:

Directions for questions 1–6: Identify the variables, constants, number of terms, and coefficients.

1) 11w + 0.9 + 202

1

a. variable(s)

b. constant(s)

c. number of terms

d. coefficient(s)

2) 103y

a. variable(s)

b. constant(s)

c. number of terms

d. coefficient(s)


3) 3 + 3m + 4.5 + r

a. variable(s)

b. constant(s)

c. number of terms

d. coefficient(s)

4) 5p + 3p + 82

a. variable(s)

b. constant(s)

c. number of terms

d. coefficient(s)

5) x + 24

a. variable(s)

b. constant(s)

c. number of terms

d. coefficient(s)

6) 72 + 4k

a. variable(s)

b. constant(s)

c. number of terms

d. coefficient(s)

Directions for questions 7 and 8: Write an algebraic expression that represents the given algebra tiles.

7)

8)

Directions for questions 9 and 10: Sketch algebra tiles to represent the algebraic expression.

9) 4u + 2

10) b + 10


Mixed Practice

11) Assign a variable to an unknown quantity

in the situation.

Henry slept for 45 minutes longer

on Saturday night than he did on

Thursday night.

12) Convert 3.5% to a decimal.

13) What is 17% of 200?

14) Evaluate.

3 • (45 – 20 ÷ 4)

Word Problem

15) Sue added y and 3. How many terms are in her expression? What is the constant in her expression?

What is the coefficient in her expression?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we wrote algebraic expressions for math statements. Here’s what that looks like!

For the phrase, 6 more than k, if something is more than, it means it’s greater, so we need to add.

We can write that as 6 + k or k + 6.

We also wrote math statements for algebraic expressions.

For the expression, h ÷ 7, we can write that as:

h is divided into 7 equal parts or the quotient of h and 7

Directions for questions 1–5: Write an algebraic expression for the phrase.

1) twice x

2) 5 less than p

3) y more than 28.9

4) k squared

5) 10 parts out of b parts

Directions for questions 6–10: Write a math statement to describe the algebraic expression.

6) 50 + w

7) 16 – h

8) 3t

9) g3

10) 7

q


Mixed Practice

11) Estimate.

5 • 0.45

12) Find the greatest common factor.

50 and 25

13) Write a variable for the unknown quantity in

the situation.

Mrs. Jane’s college fund was split equally

between her 5 children.

14) Identify the variables, constants, number of

terms, and coefficient.

12 + 10y + 4 + n

a. variable(s)

b. constant(s)

c. number of terms

d. coefficient(s)

Word Problem

15) Amelia lengthened her jump rope of x inches by 5 more inches. Write an algebraic expression

describe the new length. Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we wrote algebraic expressions for multi-step math statements. Here’s what that looks like!

20 divided by the product of r and 30

20 is divided by a product, so it’s written as r30

20 or 20 ÷ (30r).

We also wrote math statements for multi-step algebraic expressions. For example:

(y + 3) – 20.5 can be represented in words: the sum of y and 32 minus 20.5.

Directions for questions 1–5: Write an algebraic expression for each phrase.

1) the difference between 4 times x and 18

2) 25 times the difference of 2

1 and f

3) the product of 10 and the sum of g and 2

4) the square of the quotient of 5 and y

5) t divided by the sum of 9.7 and 14


Directions for questions 6–10: Write a math statement to describe each algebraic expression.

6) 5b ÷ 3

7) 2

–5 x

8) 40 • (p – 0.4)

9) 9 – 18w

10) k • (6 + 3

2)

Mixed Practice

11) How many terms are in the following

expression?

y

2 + x


8

18, 2

4

3,5

9

13) How many liters are there in 84 ounces?

(33.8 ounces in 1 liter)

14) Is 306

158 closest to 0,

2

1, or 1?

Word Problem

15) Write the statement as an algebraic expression. Then explain your thinking.

Cindy divided the sum of 56 and w by 2.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we evaluated algebraic expressions for a given value of a variable. Here’s an example!

Evaluate 5 • (42 + h) when h = 25.

5 • (42 + 2.5) Substitute 2.5 for h.

5 • (16 + 2.5) By the Order of Operations, evaluate exponents first.

5 • 18.5 Add within parentheses.

92.5 Multiply.

Directions for questions 1–10: Evaluate the expression for the given variable.

1) 4

6c when c = 8.

2) 24g if g = 2.

3) (y

60 + 6.78) – (12 – 2.32) when y = 12.

4) 131.5 – 2p if p = 47.2.

5) 20 – 4v for v = 24

3.

6) 8w2 when w = 10.

7) v4 for v = 3

8) (3y + 14 ÷ 7) – 15 for y = 7.

9) 9n + (15.7 • 5) when n = 2.5.

10) h ÷ (3

2 •

10

21) • 2 if h = 14.


Mixed Practice

11) Find the area of the square.

12) Find the volume.

13) Patricia has x pairs of shoes. Kendra had 3 times the number of shoes that Patricia has, but lost

4 pairs. Write an expression to describe the number of pairs of shoes Kendra has.

14) The point (–8, 10) is in which quadrant of the coordinate plane?

Word Problem

15) Tina has 4x days of school left. If x = 14, how many days of school does Tina have left?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we wrote and evaluated expressions to describe perimeter and area. Here’s an example!

We can write an expression to describe the area of the rectangle: 7m.

Let’s find the area when m = 18

7m = 7 • 18 = 126, so the area is 126 units.

1)

a. Write an algebraic expression that

represents the perimeter of the figure.

b. Evaluate the algebric expression to find

the perimeter when p = 6, and then

when p = 2.

2)




the perimeter when y = 20.


3)

a. Write an algebraic expression that represents the area of the square.

b. Evaluate the algebric expression to find the area when k = 3, and then when k = 7

4.

4)


represents the area of the square.


the area when g = 2, and then when g = 8.

5) Which shape has a greater area? Explain your thinking.


6)

a. Write an algebraic expression that represents the area of the rectangle.

b. Evaluate the algebric expression to find the area when c = 10, and then when c = 6.

7)



b. Evaluate the algebraic expression to find the

perimeter when d = 54.

8) Charlie designed two diagrams for his school project. Which diagram has a greater perimeter?



Mixed Practice

9) Write an algebraic expression to represent the sum of 6.5 and the difference of x and 14.

10) What is the coefficient of m? What is the coefficient of 3m?

11) Simplify.

2 + (29 – 42)

12) Jane bought a pack of cards for $3.12. If 52 cards come in the deck, what is the unit price for

each card?

Word Problem

13) Write an expression for the area of a rectangle that has a length of t and height of 4. What will the

area be if the length of the rectangle is 21?


Homework Problems

Name



Questions…

#’s

Quick Look

Today you wrote an algebraic expression to describe a pattern. Here’s an example!

Complete the chart by writing an expression for the pattern.

The pattern is 3t.

3 • 14 = 32 3 • 21 = 63 3 • 37 = 111

We know 3t is the correct expression for the pattern because it applies to all the values in the table.

Directions for questions 1–5: Complete the chart by writing an expression for the pattern.

1)

2)

3)

4)

‘


5)

Directions for questions 6–10: Read and solve each problem.

6) Jafar was working on his golf game, hitting

more balls each day. On day y, how many

balls will he hit?

7) When Jake’s garden produces n tomatoes,

how many tomatoes will Amy’s garden

produce?

8) Joana has red and yellow marbles. If the

pattern continues, how many yellow marbles

will she have if she has b red marbles?

9) This chart shows how much Chris was paid

for the number of hours he worked. How

much will he be paid for working x hours?


10) Coach Franks was tracking how many basketball players they would have in all in the league if more

students signed up. How many players would there be in all if w more students join?

Mixed Practice

11) Write an expression to describe the

perimeter for a rectangle with a length

of p and a width of p + 12.

12) Evaluate 4 + (2p + 22) when p = 5.


68%,3

2, 65%, 0.67

14) Find the value.

| –4.5 |

Word Problem

15) If Wanda makes a $23.00 purchase, she gets $27.00 back in change. If she makes a $25.00

purchase, she gets $25.00 back in change. If she makes a $40.00 purchase, she gets $10.00

back in change. If she makes a purchase of h dollars, how much change will she get back?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we wrote an algebraic expression to describe a real-world situation. Then, we evaluated the

expression at a specific value. Here’s an example!

Sim made 78 scarves. He sold t scarves on Saturday and 30 scarves on Sunday.

Write an expression to describe how many scarves Sim has left.

78 – t – 30 or 78 – (t + 30)

Sim had 78 scarves. If he sold 20 on Saturday and t on Sunday, he sold 20 + t scarves in all. So to find

how many he had left, subtract the scarves he sold in all from the total amount of scarves he made.

Evaluate the expression when t = 45

If t = 45, that means he sold 45 scarves on Saturday. Replace t with 45 and evaluate using the

Order of Operations.

78 – (t + 30)

78 – (45 + 30)

78 – 75 = 3; Sim has 3 scarves left.

1) At an amusement park, x people are on a roller coaster. 40% of the people are kids under

the age of 13.

a. Write an algebraic expression to describe how many people on the roller coaster

are 13 and younger.

b. Evaluate the expression for x = 30.


2) The local car wash charges $8.00 to wash the outside of the car, and an additional $0.50 per minute

to clean the inside.

a. Write an algebraic expression to describe how much the car wash makes if a person gets both

the inside and outside of their car cleaned.

b. How much does it cost a customer that has the outside of his car washed and it takes 20 minutes

to clean the inside?

3) At a town hall meeting, w people came to vote on a new town ordinance. 3

2 of the people voted ‘yes’.

5 voters abstained from the vote.

a. Write an algebraic expression to describe the number of people who voted ‘no’.


b. Evaluate the expression if w = 45.

4) Janet donated pencils to four different disadvantaged schools and distributed them evenly.

a. Write an algebraic expression to describe how many pencils each school received.


b. How many pencils did each school get if Janet donated 8,000 pencils?

5) At the golf tournament, g golfers scored well enough to advance to the next round. 66 players

did not advance.

a. Write an algebraic expression to describe how many golfers there were in total.


b. Evaluate the expression for g = 34. Explain your thinking.

6) Ms. Sager donated 128 ounces of glue to the 6th grade art class. Mr. McEvoy donated 256 ounces of

glue. The 6th grade art class has z students.

a. Write an algebraic expression that describes the amount of glue each student could have if the

glue is divided equally.

b. Evaluate the expression for z = 15.

7) A restaurant paid their employees $150,000 from their total revenue.

a. Write an algebraic expression that describes how much money the restaurant has left after they

pay their employees.

b. How much money do they have left if their total revenue income was $400,000?

8) To dock a boat at Jerry’s Waterside Dock, it costs $250.00 in advance, and a $150 each month the

boat is docked in the spot.

a. Write an algebraic expression that describes how much it will cost to dock a boat.

b. How much will it cost if you want to dock a boat for 12 months? Explain your thinking.


Mixed Practice

9) Write an algebraic expression for the

math phrase.

2 less than the product of 4 and g

10) Write an expression to complete the pattern for

the table.

11) Add.

7

24 + 0.782 =

12) Write one unit rate to describe the

conversion between Teaspoons

and Tablespoons.

Word Problem

13) Each class has g reading groups. Each reading group has 5 students. Each student needs 5 binders.

Each binder has 5 tabs. Write an expression to describe the amount of tabs each class needs.

How many tabs does a class with 4 reading groups in it need? Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we used the Solve a Simpler Problem strategy to solve problems. Here’s an example!

Oli sold 124 cups of lemonade on a Sunday. Jake sold 1.5 times more cups of lemonade then Oli.

Rue sold 1.86 times fewer cups than Jake. How many cups did Rue sell?

Three people are selling lemonade. We need to determine how many cups Rue sold. Let’s use simpler

numbers to make this problem easier.

Oli sold 5 cups of lemonade on a Sunday. Jake sold 4 times more cups of lemonade than Oli.

Rue sold 2 times fewer cups than Jake. How many cups did Rue sell?

Here’s the solution with simpler numbers:

5 • 4 = 20 20 ÷ 2 = 10

Now, substitute the real numbers into the expressions you wrote:

124 • 1.5 = 186 86 ÷ 1.86 = 100

So Rue sold 100 cups of lemonade.


1) In 1991, the highest priced diamond was $6,050,000 more expensive than the most expensive

emerald. The most expensive emerald was 1.103 times more expensive than the most expensive

sapphire at the time, which was worth $2,791,723. Rounded to the nearest whole number, about how

much was the most expensive diamond worth?

2) Princeton University has 4,166 fewer students enrolled in total than the University of Notre Dame.

Notre Dame has 4.087 times fewer students than Michigan State University. If Michigan State has

47,954 students enrolled, then how many students are enrolled at Princeton?


3) Mount Everest is the highest mountain in the world at 29,029 feet. The fifth highest mountain, Makalu,

is 1.0427 times shorter than Everest. Makalu is 1,789 feet taller than the mountain Gyachung Kang.

How tall is Gyachung Kang?

4) The smallest animal in the world is the Dwarf Chameleon. It is 3.4 centimeters long. The smallest fish

in the world is Paedocypris progenetica which is 2.6 centimeters smaller than the Dwarf Chameleon.

The largest fish in the world is the Whale Shark which is 1,601 times biggest than the smallest fish in

the world. What is the length of the Whale Shark?

Mixed Practice

5) At a car race, x people are watching in the

stands. 0.6 people in the stands are wearing

a hat.

a. Write an algebraic expression to

describe how many people in the

stands are wearing a hat.

b. Evaluate the expression for x = 3,000.

6) Solve.

835.26 ÷ 0.86

7) Write an algebraic expression for

the phrase.

6 less than the product of 7.5 and p

8) Evaluate 8b ÷ 2 + 17 when b = 4

Word Problem

9) In 1998, the Houston Chronicle was the ninth most popular newspaper in the United States,

with about 550,000 papers in circulation. The Wall Street Journal was the most circulated daily

newspaper, with 3.166 times more newspapers in circulation than the Houston Chronicle.

The fifth most popular newspaper at the time was the Washington Post, which had 981,328 less

papers in circulation than the Wall Street Journal. How many newspapers did the Washington Post

have in circulation in 1998? Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we simplified algebraic expressions by combining common, or like, terms. Here’s an example!

The perimeter of the figure is 7k + 4k + 4 + 4.

7k and 4k are like terms, and 4 and 4 are like terms.

The simplified expression is 11k + 8.

Directions for questions 1–5: Combine like terms to simplify the expression.

1) 5x + 2x + 4y +

11

10

2) 2

1x +

2

1x + 3

3) g + 10g + 2g + 4h

4) 23y + 19y + 8y

5) c2 + 6c

2 + 11c


Directions for questions 6–8: Write an expression to describe the perimeter of the figure; be sure to

combine like terms.

6)

7)

8)

Directions for questions 9 and 10: Write an expression to describe the area of the figure; be sure to

combine like terms.

9)

10)


Mixed Practice

11) Angelica had a collection of marbles. 15 of the marbles were pink, 12 were brown, and 8 were blue.

What is the ratio of pink marbles to the total number of marbles in all?

12) Find the expression for the pattern and complete the chart.

1 2 3 n

4 8 12

13) 15

14 ÷

45

2

14) Find the absolute value.

| –83 |

Word Problem

15) The lengths of the sides of the playground are 43 feet, 43 feet, 7h feet, and 7h feet. Write an

expression that describes the perimeter of the playground. Be sure to combine like terms.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we used the Properties of Addition to make numeric expressions easier to evaluate and to simplify

algebraic expressions. Here are some examples!

By changing the order and grouping the numbers with fractions, it is easier to evaluate this expression.

42 + 2 + 78

3 + 55.12 + 7

8

1

= 42 + 2 + 78

3 + 7

8

1 + 55.12 Commutative Property

= 42 + 2 + (78

3 + 7

8

1) + 55.12 Associative Property

= 113.62

Changing the order and the grouping to make sure like terms are together makes simplifying easier.

20y2 + (1 + 2x) + y

2 + 30

= 20y2 + 1 + 2x + y

2 + 30 Associative Property

= 20y2 + y

2 + 2x + 1 + 30 Commutative Property

= 21y2 + 2x + 31

Directions for questions 1–5: Use the Properties of Addition to simplify the expression. Be sure to

combine like terms.

1) (4q + 9) + (23 + 8q) + d

2) 40h3 + (5h + 7h

3 + k)

3) 209s + 34 + (111s + 4.5)

4) (2x + y2 + 7y

2) + 5x

5) (3x + 14y + x2) + (6y + 9x)


Directions for questions 6–8: Answer questions a and b.

6) 79 + (m + 0.15) + 65 = 79 + (0.15 + 0.99) + 65

a. What is the value of variable m?

b. What property did you use to find

the value?

7) 1,500 + h + 2,700 = 2,700 + 1,500

a. What is the value of variable h?


the value?

8) (7 + 6.5) + y = 18 + (6.5 + 7)

a. What is the value of variable y?

b. What property did you use to find the value?

Directions for questions 9 and 10: Write the numeric expression a different way using the Properties of

Addition. Simplify both expressions to show they have identical results.

9) (34.54 + 1.27) + 5.46 + 8.73

10) 39

5 + (7.45 + 12

9

4) + 13.55

Mixed Practice

11) Rewrite the expression using exponents.

7 • 7 • 7 • 5 • 5 • 8

12) Amy has 10 boxes of candy canes, but doesn’t know how many are in each box. Also, at home she

has 4 more of the same boxes of candy canes. Write an expression to describe how many candy

canes she has in all.

13) Evaluate the expression if x = 4.

(3x + 20x) + 2x

14) What is 55% of 1,645?


Word Problem

15) Karina said that you can put “+ 0” next to any number of this expression to make an equivalent

expression. Is Karina correct? Explain your thinking.

21 + 7 + 14 – 3


Homework Problems

Name



Questions…

#’s

Quick Look

Today we evaluated and re-wrote expressions to determine whether two expressions are equivalent.

Here’s an example.

Is (5x + x) + 5x2 + 3x + 12 equivalent to 9x + 5x

2 + 12?

Yes, because when x = 2, both expressions name the same number.

(5 • 2 + 2) + 5 • 22 + 3 • 2 + 12 = 50 9 • 2 + 5 • 2

2 + 12 = 50

Also because when you use the Properties of Addition to combine like terms,

(5x + x) + 5x2 + 3x + 12 simplifies to 9x + 5x

2 + 12.

1) Is 12w + 9w2 +

(7w + w

2) equivalent to 10w

2 + 19w?

2) Austin bought q amount of balloons for Meredith’s birthday party. Jennifer bought 3.5q balloons for

the party, and Meredith had 20 balloons at her house already. Two parents created expressions to

describe the total number of balloons. Which parent is correct? Explain your thinking.

Parent 1: q + 3.5q + 20

Parent 2: 24.5q

3) Is 7u + (7

6x

2 + 2u + 5y) + 11y equivalent to

7

6x

2 + 9u + 16y?


4) Is 120x + 6y + 22 equivalent to 6 + (55x + y) + (65x + 5y + 15) + 2?

5) Mr. Darnell, the basketball coach, has his players run 5x laps the first week of practice. The second

week he has them run 8 laps more than the previous week. The third week they run 20 more laps

than they ran the first week. Both Mr. Darnell and the team came up with expressions to describe how

many laps they run in 3 weeks. Who is correct?

Mr. Darnell: 15x + 28

Team: 5x + (5x + 8) + (5x + 20)

6) Is 5t + 1 equivalent to (t + 1) + 4t2? Explain your thinking.

7) Is 4

3b + 10.5 +

4

1r + 1.5 equivalent to b + 12?

8) Georgia hiked a mountain one week. The first day, she traveled h feet. The second day she climbed

3h feet. The third day Georgia covered 50 feet more than she did on the second day. Georgia and her

hiking instructor both wrote expressions to describe how high she climbed over the three days. Who

is correct?

Georgia: h + (h + 3) + (h + 3 + h + 50)

Her instructor: 7h + 50

9) Is (3v2 + 14) + 2 equivalent to 5v

2 + 16?

10) Is (0.35p + 0.9p2) + 2.55 + 0.1p

2 + 0.65p equivalent to p

2 + p + 2.55? Explain your thinking.


Mixed Practice

11) Simplify.

3b + k2 + 12b + 4k

2

12) What is the value of g?

45 + (2 + 9) = (9 + 2) + g

13) What’s the GCF of 36 and 108?

14) 57

6 ×

82

42

Word Problem

15) Maddie and Jon were asked to write an expression for this word problem:

On Monday, Dr. Grimmel traveled for m minutes. On Tuesday, she traveled for 10 minutes longer

than Monday. One Wednesday, she traveled 3 times the amount of time she traveled on Monday.

Write an expression to represent how long Dr. Grimmel has traveled in all.

Maddie wrote the expressions for time traveled each day. Jon wrote one expression for all three days.

Are Maddie and Jon both correct? How do you know?

Maddie’s work Jon’s Work

Monday’s time: m 5m + 10

Tuesday’s time: m + 10

Wednesday’s time: 3m


Homework Problems

Name



Questions…

#’s

Quick Look

Today we identified four Properties of Multiplication: Commutative, Associative, Identity, and Zero. Here are some examples of how we used them: By changing the order and grouping of the numbers and variables, it is easier to simplify this expression. 30 • (y • 5) • y = 30 • y • 5 • y Associative Property = 30 • 5 • y • y Commutative Property = 150y

2

y • y = y2 just like 5 • 5 = 5

2 and 2 cm • 2 cm = 4 cm

2

We can use the properties to identify the value of variables j and k in the expressions below.

65j = 65 We know j = 1 because of the Identity Property of Multiplication—any number times 1 is that

same number.

4 + 5 • k = 4 We know k = 0 because of the Zero Property of Multiplication—any number times 0 equals 0.

Directions for questions 1–7: Use the Properties of Multiplication to solve.

1) Use the Properties of Multiplication to

simplify the expression. Show your work.

8 • (x • 0.5)

2) k • 252

1 + 6 = 6

a. What is the value of the variable k?


the value?


3) Use the Properties of Multiplication to simplify the expression. Show your work.

8y • 0 • y2

4) Monica used the Properties of Multiplication to simplify the expression. Why did she solve the

problem that way? Is her work correct? Be sure to indicate which Property of Multiplication she used.

7

6 +

28

1 = Monica’s work:

4

4 •

7

6 +

28

1=

28

24 +

28

1 =

28

25

5) 4 • s • 3 = 7 • 3 • 4

a. What is the value of the variable s?


the value?



2 • a • 7 • a

7) Jake used the Properties of Multiplication to evaluate the expression. Why did he solve the problem

this way? Is his work correct? Be sure to indicate which Property of Multiplication he used.

5p • (3 • 8p) Jake’s work: 5p • (3 • 8p)

5p • 3 • 8p

5p • 8p • 3

40p • 3 = 120p

Mixed Practice

8) What is the greatest common factor of 28

and 32?

9) Simplify the expression.

a + 7a + 24


10) 8 + w + 2 = 3 + 8 + 2

a. What is the value of w?


the value?

11) What is the least common multiple of

12 and 30?

Word Problem

12) Josie said you can multiply any number or variable in this expression by 1 to make an equivalent

expression. Is Josie correct? Explain your thinking.

56 • m • 4


Homework Problems

Name



Questions…

#’s

Quick Look

Today we identified factors in expressions. For example, what are the factors in 6 • (h + 3)?

Factors are numbers, variables, terms, or expressions that are multiplied. In this expression, 6 and a sum are being multiplied. That means that there are two factors in this expression, 6 and (h + 3). Each factor can divide evenly into the expression. We also found the greatest common factor (GCF) of two expressions. What is the GCF of these expressions? 30m

2k 36m

2k

2

To find the GCF, write the prime factorization of both expressions to determine the most they have in common.

Both expressions have 3 • 2 • m • m • k in common, so multiply the common factors to find the GCF, which is 6m

2k.


1) What is the GCF of the two expressions?

10k3p 35k

2p

2

2) What are the factors in the expression?

40 • (6 + 2)


12ty4 16t

3y

2


2(w2 – 14)


5) Draw a factor tree and write the prime

factorization for the expression.

8p3


20a3

2b2d

7) Draw a factor tree and write the prime

factorization for the expression.

17a2b

2


12p2 36p

2


(c – 1.6) • (11 + h)

Mixed Practice



8 • (3y • 0.5)


(4x + 19) + (8 + 22x)

12) Evaluate 2 • (g + 5)2

when g = 4.

13) Multiply 27

2 and

4

3.

Word Problem

14) Write an expression for the statement. Then identify the factors of the expression.

The product of the sum of w and 3 and the sum of w and 5.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we re-wrote expressions using the Distributive Property. Here are some examples!

3(y + x)

Distribute the 3 to both terms in the parentheses to write a new expression.

= 3y + 3x

We can also pull out the greatest common factor (GCF) of an expression to re-write it another way.

Here the GCF is 12g, so we ask ourselves what can we multiply 12g by to get 24g2 and 36g?

24g2 + 36g = 12g ( ___ + ___) = 12g(2g + 3)

Directions for questions 1–6: Use the Distributive Property to write the expression a different way.

1) 12kn + 8k

2) 19c(2 + 3d)

3) 6x(2x + 1)

4) 9x + 3

5) 7(8 + 11p2)

6) 20y2 + 5


Directions for questions 7 and 8: Write two expressions for the math story using the Distributive Property.

7) Cameron bought 9 pounds of steak for $10 per pound, and Amelia bought 9 pounds of vegetables for

u dollars per pound. Write two expressions to describe how much money Cameron and Amelia spent

in all.

8) Pam bought 20 balloons for the party and Shawn bought 45. They both went back when they realized

they needed more and bought the same amount a second time. Write two expressions to describe

how many balloons Pam and Shawn bought altogether.

Mixed Practice

9) Is 10y + (5 + y) equivalent to 5 + 11y?

10) Is –5 or

–7 closer to 0?

11) Carlos read 2 books over the summer.

He read 501 pages in all. Which 2 books

did Carlos read?


210 – 4 • 52 + 10

Word Problem

15) Molly bought 6 bags of oranges that cost 4 dollars each and 6 bags of apples that cost 3 dollars each.

Write two expressions using the Distributive Property to describe how much they spent in all. Explain

how you know that the expressions are equivalent.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we evaluated and re-wrote expressions to determine whether two expressions are equivalent.


Is 5x + 6x2 equivalent to x(5 + 6x)?

Yes, because when x = 2, both expressions have a value of 34.

5 • 2 + 6 • 22 = 34 2(5 + 6 • 2) = 34

Also, we can use the Properties of Multiplication to rewrite or simplify one expression to see if it can be

rewritten as the second. Here we used the Distributive Property to rewrite the second expression to look

like the first expression. This tells us that the two expressions are equivalent.

1) Tony and Willis wrote an expression for the area of the figure.

Tony’s expression: 6(9 • p)

Willis’ expression: 9 • p + 6

Do both expressions represent the same area

of the figure?

2) Is 15x + 21 equivalent to (2.5x • 2 + 7) • 3? Explain your thinking.


3) The package courier delivered packages to 12 businesses on his route. Each delivery had m fragile

packages and p regular boxes. Two of the courier’s coworkers wrote expressions to describe the total

number of packages he delivered.

Employee 1: 12m + p Employee 2: 12(m + p)

Do both expressions describe the total number of packages delivered on this route?

4) Is 5t + 10t2 equivalent to 5(t + 2t

2)?

5) At the grocery store, Mr. Rogers purchased g packs of gum and each pack had 4 pieces. His friend

Mrs. Daniels purchased w packages of water with 4 bottles per pack. They both wrote expressions to

determine how many pieces of gum and bottles of water they bought all together.

Mr. Rogers: 4(g + w) Mrs. Daniels: 4g + 4w

Do both expressions correctly describe the total number of items?

6) Is 28g equivalent to 4g(3g + 4g)? Explain your thinking.

7) Jillian and Meredith wrote an expression for the area of the figure.

Jillian’s expression: 12(6q + 15) Meredith’s expression: 12 • 15 + 12 • 6q

Do both expressions represent the same area of the figure?

8) Is 6b + 6c equivalent to 6(b + c)?


Mixed Practice

9) What is the value of |–8|?

10) If Jess runs 3 miles in 25 minutes, how long

will it take her to run 2 miles?


67

1,

7

45, 6

14

3,

7

40

12) Estimate.

334.53 ÷ 3.1447

Word Problem

13) At the grocery store, one box of raisins cost x dollars and one box of cranberries cost 2x dollars.

Jessie wrote two expressions to describe how many boxes of cranberries and raisins he purchased.

Use his equivalent expressions to determine how many boxes of cranberries and raisins he bought.


4(x + 2x) = 4x + 8x


Homework Problems

Name



Questions…

#’s

Quick Look

Today we used the Work Backwards strategy to solve word problems. Here’s an example.

Larry has a cup of paper clips. He took out 10 and gave them to his friend. Then he put half of what was

left in his desk. After that, 7 were left in the cup. How many paper clips were in the cup when he started?

First, organize the data:

Then work backwards:

So there were 24 paper clips to begin with.

Don’t forget to check your work! Just use your answer and work forward through the steps of the problem:


Directions for questions 1–5: Solve each problem.

1) Diane won a lottery game. She spent $120 of the winnings on clothes. She spent twice that amount

on groceries. Then, outside the grocery store, she found $20! With that $20 plus her remaining

winnings, Diane had $1,200 left. How much did Diane win?

2) Jimmy is a huge sports fan! He has 5 more football jerseys than baseball jerseys. He has twice as

many soccer jerseys as baseball jerseys. He has 3 more basketball jerseys than soccer jerseys.

Jimmy has 5 basketball jerseys. How many jerseys does Jimmy have in all?

3) At the start of a concert, the venue was not filled up. Five minutes later, 350 more people showed up.

Half the people at the end stayed around to get an autograph. If 2,000 people stayed around trying to

get an autograph, then how many people were there at the start of the concert?

4) Nicole has a jar of rubber bands. She used half of the rubber bands to make a necklace. Then she

took the rest and divided them into 4 equal groups. Each pile had 20 rubber bands. How many rubber

bands were in the jar when Nicole started?

5) Lindsay walked from her house to Rico’s house in a half of an hour. They played whiffle ball for 2

hours and then had dinner. Dinner took twice as long as the walk to Rico’s. Dinner was over at 8:00

p.m. What time did Lindsay leave for Rico’s house?

Mixed Practice

6) Is 7a • 5 • a equivalent to 40a?

7) Use the Distributive Property to write the

expression a different way.

48x + 36

8) Use the Properties of Addition to simplify the

expression. Be sure to combine like terms.

(5k + 20) + 14k + 0.4


9) It took Angie 24 minutes to read 2 chapters.

a. What is Angie’s reading rate? Write her rate in words and as a ratio.

b. Write a unit rate to describe how much Angie reads in 1 hour.

Word Problem

10) Bill put his pennies in two piles. The first pile had 150 pennies, and he put that pile in his coin bank.

He put the pennies from the second pile into paper rolls. It took 5 rolls to hold all those pennies.

Each roll holds 50 pennies. How many pennies did Bill have in all? Explain your thinking,


Homework Problems

Name



Questions…

#’s

Quick Look

Today we recognized that the two sides of an equation are equal and balanced. We used scales to

represent equations; they are only balanced when each side has an equal value.

To balance this scale, remove 3 unit tiles from the right side of the scale.

The equation, 4 = 7 – 3, show how we balanced the scale. The balanced scale is an equation.

This scale is already balanced but we don’t know the value of the variable, s.

To find the value of s, remove 5 unit tiles from both sides of the scale.

This isolates the variable on the right while keeping the scale balanced.


Directions for questions 1–7: Use the images to solve.

1)

a. Explain how you can balance both sides by

only making changes to one of the sides.

b. Write an equation that describes how you

balanced the scale.

2)

a. Write an equation that describes the scale.

b. Use the scale to find the value of p.

3)



b. Write an equation that describe how you

balanced the scale.


4) What is the weight of the stack of paper? Explain your thinking.

5)


b. Use the scale to find the value of m.


6)




balanced the scale.


7)


b. Use the sclae to find the value of x.

Mixed Practice

8) Is 3v • v • 7 equivalent to 21v3?

9) What is the GCF of 18a2b and 27ab?

10) 5p + p + 42

a. variable(s)

b. constant(s)

c. number of terms

d. coefficient(s)

11) Write the opposite integer:

20 feet below sea level

Word Problem

12) Alvin estimated that his pet iguana weighed six pounds, so he placed six one-pound blocks on the left

side of the scale. He then placed his pet iguana on the other side of the scale, but the scale still

leaned to the left. To balance the scale, he added two more one-pound blocks to the right side.

What is the weight of Alvin’s iguana?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we substituted a given value for the variable in an equation to determine if it is the solution.

Here are some examples:

Is x = 3 a solution for 7 = x

6 + 5? Let’s substitute 3 for x and find out.

7 = x

6 + 5

7 = 3

6 + 5

7 = 2 + 5

7 = 7

x = 3 is the solution for 7 = x

6 + 5 because it kept both sides of the expression balanced.

Is x = 3 a solution for 8x = 27.75 – 2.25?

8x = 27.75 – 2.25

8(3) = 27.75 – 2.25

24 ≠ 25.5

x = 3 is not a solution for 8x = 27.75 – 2.25 because it does not keep both sides of the expression balanced.

1) Is t = 11 a solution for each equation?

a. 55 = 4t + 11

b. (t – 3)2 = 64

2) Is d = 5

2 a solution for each equation?

a. 5d – 2 = 1

b. 4 = (d ÷ 10

1)


3) Is q = 7 a solution for each equation?

a. 100 – 51 = q2

b. 3q = 80 ÷ 4

4) Is s = 15 a solution for each equation?

a. 35 = 5(2s)

b. (s + 1) ÷ 2 = 16

5) Is f = 3.5 a solution for each equation?

a. f + 2.5 – 1 = 5

b. 4f = 2 • 7 + 1

6) Is y = 6 is a solution for each equation?

a. 7y = 42 + 3

b. y2 + 4 = 42

Mixed Practice

7)



b. Write an equation that describe how you

balanced the scale.

8) Write an algebraic expression to complete

the chart.

9) What is 75

34 as a percent?


10) Plot an account balance of –$34 on a number line.

Word Problem

11) Is s = 48 a solution for the sum of 30 and 25 is equal to s?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we used mental math and guess and check strategies to solve equations. Here are some examples!

4k = 60

This equation says that 4 times something equals 60. I know that 4 • 5 = 20 and 20 • 3 = 60,

so 4 • 15 must equal 60.

I better check my work. So if k = 15,

4 • 15 = 60

60 = 60

The solution to 4k = 60 is k = 15 because it keeps both sides of the equation balanced.

Directions for questions 1–8: Solve using mental math or guess and check strategies.

1) 130 – f = 70

2) v

68 = 4

3) 25 = 10 + k

4) 95 = 5p

5) 2.5 + m = 8.5

6) 5600 = 7b

7) 152

1 = c – 8

8) 18 ÷ g = 2


Mixed Practice

9) Is h = 16 a solution for the equation?

55 + h = 90 – 25

10) Estimate:

516

1 + 23

6

5

11) Write an expression to describe

the perimeter of the figure; be

sure to combine like terms.

12) Estimate. Show your work

5,742 • 83

Word Problem

13) 56 is equal to the product of 7 and z. What is the value of z? Use mental math and guess and check

strategies to help you.


Homework Problems

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Questions…

#’s

Quick Look

Today we used images to help us solve equations related to area and perimeter. Here’s an example!

Ms. Sue knows that the perimeter of the triangle is 38 feet. Here is her work:

P = f + g + h

38 = 11 + g + 9

How can the image help Ms. Sue find the value of g?

Perimeter is the distance around the triangle, so we add all the side’s lengths of the triangle. We can see

in the image that g must equal 8, it is the missing side length from the equation to find perimeter.

Both sides describe the perimeter—they are just expressed in two different ways.

After determining the value of g, be sure to check to make sure both sides of the equation are still balanced:

8 + 11 + 9 = 28

28 = 28 g = 11 is the solution.

1) Jamal is finding the perimeter of this parallelogram. He used the diagram to find the length of one of the

sides. Here is his work:

P = 2l + 2w

20 cm = 2(6 cm) + 2 • w

What should Jamal use as the value

of w in his equation?


2) Benny is finding the area of a rectangle. He used the diagram to find the width of the rectangle.

Here is his work:

A = l • w

525 m2 = l • 21 m

What should Benny use as the value

of l in his equation?

3) Sarah is finding the perimeter of an isosceles triangle. She used the diagram to find the length of two

sides of the triangle. Here is her work:

P = s + s + t

50 in. = 14 in. + s + 22 in.

What should Sarah use as the value

of s in her equation?

4) Darius is finding the area of a square. He used the diagram to find the width of the square.

Here is his work:

A = l • w

56.25 ft2 = l • 7.5 ft

What should Darius use as the value of l in

his equation?

5) Kim is finding the perimeter of a rectangle. She used the diagram to find the length of the sides.

Here is her work:

P = l + l + w + w

810 mm = 324 mm + 324 mm + w + w

What should Kim use as the value

of w in her equation?


6) Gino is finding the area of a rectangle. He used the diagram to find the width of one of the sides.

Here is his work:

A = l • w

603

2 in.

2 = l • 10

What should Gino use as the value

of l in his equation?

7) Janie is finding the perimeter of a regular pentagon. (Remember, regular means the shape has equal

sides.) He used the diagram to find the length of one of the sides. Here is his work:

P = 5s

15 yd = 5 • s

What should Janie use as the value

of s in her equation?

8) Miguel is finding the perimeter a rhombus. He used the diagram to find the length of one of the sides.

Here is his work:

P = 2s + 2s

64 cm = 2(16 cm) + 2s

What should Miguel use as the value

of s in his equation?

Mixed Practice

9) Is k = 4 a solution to the equation?

48 = 9k + 10

10) Solve using mental math or guess and

check strategies.

8

t = 40


11) Jeremy has 5 more red shirts than he has yellow shirts. He has three times as many yellow shirts

compared to blue shirts. Jeremy has 2 blue shirts. How many red shirts does Jeremy have?

12) If $42.50 is 40% of Mr. Simm’s grocery bill, what is the total bill?

Word Problem

13) Javier found the perimeter of his rectangular garden. His garden measures 11 feet on one side and

9 feet on the other. What should Javier use as the value of w in his equation?

P = 2(l) + 2(w)

40 = 2(9) + 2w


Homework Problems

Name



Questions…

#’s

Quick Look

Today we discussed inverse operations and we used them to solve equations equal to 1 or 0.

For example, addition and subtraction are inverse operations:

u + 25 = 0 r – 18 = 0

– 25 – 25 + 18 + 18

u = –25 r = 18

Also, multiplication and division are inverse operations:

3v = 1 13

q = 1

3v ÷ 3 = 1 ÷ 3 13 • 13

q = 1 • 13

v = 3

1 q = 13

Using the inverse operation to solve these simple equations helped us isolate the variable on one side of

the equation. This is similar to moving the unit blocks from each side of a scale to get the variable tile by

itself. Just like with the scale, when whatever we do to one side of the equation, we must do the same to

the other side to keep the equation balanced.

Directions for questions 1–5: Solve each equation.

1) 42 + t = 0

2) 1 = a • 2

3) e ÷ 18 = 1

4) y – 5.9 = 0

5) 0 = 39 + x


Directions for questions 6–10: Use the equation to answer each question.

6) 12 • 3 = 36

a. What is the operation in this equation?

b. What is the inverse operation?

c. How could you rewrite the equation

using the inverse operation?

7) 4.09 = 5 – 0.91





8) 500 ÷ 25 = 20





9) 18 = 14 + 4





10) 17 • 11 = 187






Mixed Practice

11) Write a ratio to represent the situation.

In 2 hours, Danielle read 60 pages of

her book.

12) Complete the chart by writing an expression

for the pattern.

13) 7

4 ÷

14

3

14) What is the value of | –3 |?

Word Problem

15) Petra divided her pictures into 35 groups. After she divided, she had 1 photo on each page of her

photo album. How many photos does Petra have?

p ÷ 35 = 1


Homework Problems

Name



Questions…

#’s

Quick Look

Today we solved addition and subtraction equations using inverse operations. In these equations, we

used the inverse operation to find the solution for each variable. We made sure that whatever we added

to or subtracted from one side of the equation that we did the same to the other side. This keeps the

equation balanced, like a scale.

For example, let’s solve the equation: y + 1,382 = 2,400

We can estimate first to see about what our solution will be.

y + 1,400 = 2,400

1,000 + 1,400 = 2,400, so y is about equal to 1,000.

When we solve the equation we use the inverse operation to help us:

y + 1,382 = 2,400

– 1,382 – 1,382

y = 1,018

We should check to see if our solution is correct by substituting it into the original equation.

y + 1,382 = 2,400

1,018 + 1,382 = 2,400

2,400 = 2,400

We know our solution is correct because the equation remains balanced!

Directions for questions 1–8: Solve the equation. Show your work.

1) 3,660 = b – 320

2) p – (8.5 – 6.5) = 19

3) h + 500 = 500

4) 2,610 = m + (800 – 5)


5) z + 10.6 = 14 Explain your thinking.

6) 33

1 = k – 3

7) j – (15 + 3) = 52

8) x – 4 = 24 Explain your thinking.

Mixed Practice

9) Evaluate.

8 + 6 • 9 – 33

10) Solve the equation.

45k = 1

11) Write a mathematical statement to describe

the expression.

(9 + 20) ÷ 5

12) Is y = 20 a solution for this equation?

(y – 15)2 = 25

Word Problem

13) A panda bear has gained 18 pounds this month and now weighs 116 pounds. Solve the equation

p + 18 = 116 to find how much the panda weighed on month ago. Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we solved multiplication and division equations using inverse operations.

For example, let’s solve the equation: y • 25 = 450.

We can estimate first to see what a reasonable solution will be.

y • 25 = 50 I know that 2 • 25 = 50, so 20 • 25 = 500. That means y is about equal to 25.

Next we solve the actual problem.

y • 25 = 450

25 25

y = 18

Our solution is close to our estimate! But let’s check for sure by substituting our solution into the original equation.

18 • 25 = 450

450 = 450

Directions for questions 1–8: Solve each equation. Show your work.

1) 12p = 600

2) 6.5 = 4

m

3) 4

3 • d = 15

4) 800 = w ÷ 0.5

5) t ÷ 8 = 96

6) 48,384 = 14b


7) 81 = 18 • k Explain your thinking.

8) n ÷ 28 = 2 Explain your thinking.

Mixed Practice

9) Clay got paid $120 for 6 hours of work

building a deck.

Write a unit rate to describe how much

Clay was paid for 1 hour of work.

10) Evaluate the expression if x = 7

6x + 5 • 2

11) Solve the equation. Show your work.

46.7 + r = 50


13 = g – 2

Word Problem

13) An egg carton holds 18 eggs. One day a farmer gathers 7,614 eggs. Solve the equation 18e = 7,614

to find how many cartons are needed for the eggs. Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we answered real-world problems by solving addition, subtraction, multiplication, and division

equations. We identified the variable in each equation as representing the question we have to answer.

So solving the equation for the variable also answered the question!

For example:

Sara is filling containers with water from the cooler. Each container holds 2

1 a gallon of water.

If the cooler holds 25 ½ gallons, then how many containers can Sara fill?

Let’s use this equation to answer the question in the math story! 2

1c = 25

2

1

Each container holds 2

1 gallon of water, that’s multiplication! The variable, c, represents the number of

containers. If we solve the equation for c, then we can see how many containers Sara can fill!

Estimate:

1 gallon equals 2 half gallons.

So 25 gallons would be 50

half gallons.

c ≈ 50

Solve: 2

1c = 25

2

1

2

1

2

1

c = 51

Check: 2

1c = 25

2

1

2

1(51) = 25

2

1

252

1 = 25

2

1

It will take 51 half–gallon

containers to fill the cooler.

Directions for questions 1–8: Use the equation to answer each question.

1) Jay and Scotty competed against each other in a high school basketball game. Scotty scored 3 times

as many points as Jay. If Scotty scored 30 points, how many points did Jay score?

3j = 30


2) There were 203 passengers taking a flight to Jacksonville, Florida. 92 of the passengers were male.

How many passengers were female? Explain your thinking.

203 = 92 + f

3) In 2009, there were 151 million main line telephones being used. This number is 128 million less than

the number of cellular phones in use. How many cell phones were being used in 2009?

151 million = c – 128 million

4) Penelope bought a bag of oranges at the grocery store. She separated the oranges into 5 equal

groups. She was left with 8 oranges in each group. How many oranges did she buy originally?

b ÷ 5 = 8

5) Brittany bought some pecans and 22

1 pounds of cashews. She bought 6

4

3 pounds of nuts in all.

How many pounds of pecans did she purchase?

p + 22

1 = 6

4

3

6) Eric did 5 sets of pushups throughout the day. He did the same number of pushups for each set.

At the end of the day, he had completed 240 pushups. How many pushups did Eric do in each set?


240 = h • 5

7) Joshua and Cam raced each other. Cam’s time was 2.9 seconds faster than Joshua’s. If Cam

finished the race in 43.6 seconds, then what was Joshua’s time?

m – 2.9 = 43.6


8) The history museum acquired new artifacts to exhibit this year. They divided the artifacts equally

among the 11 different exhibits at the museum. If each exhibit got 9 artifacts, then how many artifacts

did the museum acquire in all?

11

r = 9

Mixed Practice

9) Write the fraction in simplest terms.

112

14

10) Evaluate the expression when t = 1.6.

40t – 55


(10.5 – 8.5)2 •

4

1

12) Write the fraction as a decimal and

a percent.

25

13

Word Problem

13) It took Jonah 7 days to bike from Patapsco Valley State Park to the Apalachicola National Forest.

He biked the same distance each day, and traveled a total distance of 966 miles. How many miles

did he bike each day? Use the equation to answer the question. Explain your thinking.

966 = r • 7


Homework Problems

Name



Questions…

#’s

Quick Look

Today we identified addition and multiplication equations that represented math stories. We used our

knowledge of keywords and phrases to match the math story with the correct equation. We also identified

the missing information to help us know what the variable in the equation stood for.

For example, which equation best represents this story?

Erik scored several points in today’s game. Yesterday, he scored 25 points in the game.

He made a total of 44 points in the two games. How many points did Erik score today?

a. m • 25 = 44

The words ‘and’ and ‘total’ tell me the problem is about multiplication, Choice a is addition,

so choice a is not correct.

b. 25 + m = 44

Choice b shows adding 25 to today’s score and equaling 44. It is correct!

c. m = 44 + 25

Erik made a total of 44 points, so 44 should be alone on one side of the equation.

Choice c is not correct.

Directions for questions 1–8: Choose the equation that best represents each math story.

1) Baron drank some water at halftime of his soccer game. At the end of the game, he drank 23 more

fluid ounces of water. Baron drank 44.5 fluid ounces of water in all. How much water did he drink at

halftime of the game? Explain your thinking.

a. 23w = 44.5 b. w + 23 = 44.5 c. 23 = 44.5 + w


2) Sharon went to the store and bought packages of hot dogs. Each package contains 5 hot dogs.

Altogether, she bought 45 hot dogs. How many packages did she buy?

a. h • 5 = 45 b. 5 + h = 45 c. 45 • 5 = h

3) Keenan ran for 42

1 miles. After taking a short break, he ran farther. At the end of his run, Keenan had

run 11 miles. How many miles did he run after the short break?

a. k – 42

1 = 11 b. 4

2

1 + 11 = k c. k + 4

2

1= 11

4) John downloaded some songs from one artist. Then, he downloaded 14 songs by another artist.

In all, John downloaded 32 songs. How many songs did he download from the first artist?

a.14 • s = 32 b. s = 14 + 32 c. s + 14 = 32

5) Sasha donated some money to a charity this month. Her father promised whatever she donated, he

would donate 4 times as much. If Sasha’s father donated $2,000, then how much did Sasha donate?

a. 4m = 2,000 b. m ÷ 4 = 2,000 c. m • 2,000 = 4

6) Pam went fishing this weekend. She caught some fish on Saturday, and then caught 2 more fish on

Sunday. In all she caught 12 fish! How many fish did she catch on Saturday?

a. 12 + 2 = p b. p + 2 = 12 c. 12 ÷ 2 = p

7) Jack was in charge of 6 groups of kids at the camp. Each group of campers has the same number of

kids. If Joe was responsible for 36 campers in total, then how many campers were in each group?


a. 6 • c = 36 b. 36 – 6 = c c. 36(6) = c

8) Mr. Joseph bought 29 packages of plastic cups for his retirement party. Each package contains the

same number of cups. That was a total of 435 cups. How many cups were in each package?

a. 435j = 29 b. 435 = 29j c. 29 + j = 435


Mixed Practice


0.345, 0.339, 0.453, 0.35

10) Is x = 5 a solution for this expression?

4x + (8 – 3) = 25

11) Ken is finding the perimeter of a rectangle. He used the diagram to find the length of the sides.

Here is his work:

P = l + w + l + w

6.6 ft = 2.5 ft + 0.8 ft + 2.5 ft + w

What should Ken use as the value

of w in his equation?

12) Multiply.

7

2 • 5

4

1

Word Problem

13) William has filled his car’s gas tank several times this month. He needs 16 gallons of gas each time to

fill his tank. If he purchased a total of 128 gallons of gas this month, then how many times has he

filled his tank? Explain your thinking.

a. g + 16 = 128 b. g • 16 = 128 c. g = 16 • 128


Homework Problems

Name



Questions…

#’s

Quick Look

Today we identified subtraction and division equations that represented math stories. We used our

knowledge of keywords and phrases to match the math story with the correct equation. We also identified

the missing information to help us know what the variable in the equation stood for. This is a lot like

matching math stories to addition and multiplication equations, which we did in the last lesson.

For example, which equation best represents this story?

Michael withdrew $45.67 from his rainy day account. He had $78.91 left in his account.

How much money did he have before he made the withdrawal?

a. 78.91 + 45.67 = m b. m – 78.91 = 45.67 c. m – 45.67 = 78.91

Directions for questions 1–8: Choose the equation that best represents each math story.

1) Tyler collected 120 canned goods for the charity drive. He separated the cans equally into bags to

deliver. There were 6 canned goods in each bag. How many bags did Tyler deliver?

a. g ÷ 6 = 120 b. g

120 = 6 c. 120g = 6

2) Keisha wrote a long report for her history project. On the way to school she lost 4 pages of the report.

She only had 7 pages left to turn in. How many pages was Keisha’s report originally?

a. p – 4 = 7 b. p + 4 = 7 c. 7 – 4 = p


3) Skip ran the mile in the fastest time in his grade. Angie finished 2 minutes behind him. It took her

72

1 minutes to run the mile. How long did it take Skip?

a. 2 + 72

1 = t b. t – 2 = 7

2

1 c. 7

2

1 – t = 2

4) Mr. Boland prepared meat at his deli. He had 150 pounds of fresh meat to sell today. He split it

equally among the packages of meat to sell. If each package had 1.5 pounds of meat, then how many

packages did Mr. Boland prepare? Explain your thinking.

a. g

150 = 1.5 b. 150 + 1.5 = g c. 150 = g ÷ 1.5

5) Rod picked some flowers for his mother. By accident, he dropped 4 of them. He gave his mother the

8 flowers he had left. How many flowers did Rod pick? Explain your thinking.

a. 8 – f = 4 b. f = 8 – 4 c. f – 4 = 8

6) Boomer made 4.8 gallons of juice from fresh apples. He gave equal amounts of juice to his friends. If

each friend got 1.2 gallons of juice, then to how many friends did Boomer give juice?

a. 1.2 • 4.8 = c b. 4.8 ÷ c = 1.2 c. 4.8 = 1.2 ÷ c

7) Lee started with 14 dollars in allowance money. She spent some money on lunch with her friends.

After lunch, she only had 3 dollars left. How much did Lee’s lunch cost?

a. 14 ÷ 3 = m b. 3 = 14 – m c. m – 3 = 14

8) After winning the grand prize in the school academic contest, 4 friends split the winnings evenly. Each

person got $165.00. How much did the friends win in all?

a. w = 165 – 4 b. 165 ÷ 4 = w c. w ÷ 4 = 165


Mixed Practice

9) Complete the chart by writing an expression

for the pattern.

10) Write an expression for the phrase.

5 less than the product of 3 and z



4xy + 2y


12

r = 4

Word Problem

13) Kendrick cut a wooden plank into 4 equal pieces to make a picture frame. If each cut piece was

32

1 feet, how long was the original piece of wood? Explain your thinking.

a. m ÷ 4 = 32

1 b. 4 ÷ m = 3

2

1 c. m – 4 = 3

2

1


Homework Problems

Name



Questions…

#’s

Quick Look

Today we wrote equations to represent real-world math stories. Then we solved the equations to answer

questions. We looked for keywords and phrases to help us write the equations. We also identified the

known information and the unknown information and assigned a variable to the unknown. Finally, we

solved the equations for the variable to answer the question.

For example:

Mr. Bortz purchased tickets for the aquarium for his students. Each ticket cost the same amount, and he

has 14 students. If Mr. Bortz spent $343 in all, how much did he spend on each ticket?

b • 14 = $343

b = $24.50

The words ‘each’ and ‘in all’ mean to multiply. We multiplied 14 tickets by the cost of each ticket, b,

which equals the total cost, $343. Then we solved for b to answer the question by dividing both sides

of the equation by 14!

Directions for questions 1–8: Write an equation for each math story. Then solve the equation to answer

the question.

1) David baked a cake for his class. He divided the cake into even slices and each of the 16 students

got 2.5 square inches of cake. How many square inches of cake did the cake start as?

2) Andre started his newspaper route with a full load of newspapers. He delivered 67 newspapers during

the day, and had 22 left over at the end of the day. How many newspapers did Andre start with?

3) At summer camp, there are different groups of campers. Each group has 18 campers. If there are

90 campers in all, then how many groups of campers are there?


4) Samantha is carrying a bag that weighs 17.3 pounds. After her brother adds a textbook, the bag

weighs 19.7 pounds. How much does the textbook weigh? Explain your thinking.

5) Clarke separated jelly beans into 10 equal groups. He ended up with 61 jelly beans in each group.

How many jelly beans did Clarke start with?

6) Esmeralda packed a number of outfits for her vacation. 4 of her outfits included a skirt, the rest

included shorts. If Esmeralda packed 14 outfits in all, then how many of her outfits include shorts?

7) Mackey did 5 sets of sit-ups throughout the day. He did an equal number of sit-ups in each set.

By the end of the day, he had done 175 sit-ups in total. How many sit-ups did Mackey do per set?


8) Liam took the money he saved to buy new clothes at the mall. He spent $40.90 and left the mall with

$7.25. How much money did Liam bring with him to the mall?

Mixed Practice

9) Combine like terms to simplify the expression.

4 + 9p2 + 18 + 2p

2

10) 11,000 + x + 230 = 230 + 11,000

a. What is the value of variable x?

b. What property did you use to find the value?


11) Find the length of AB.


Demarcus lost $8.00 at the post office.

Word Problem

13) Eve decided to order Chinese food. She bought Hot and Sour Soup and one other item on the menu.

Eve spent $6.70 in all on Chinese food.

Write an equation to find how much Eve spent on the second item she ordered. Then use the menu

to identify which item she bought.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned about the difference between equations and inequalities and identified and wrote

inequalities. Here’s an example!

The books weigh more than 4 pounds.

This scale shows that the weight of the books

is greater than 4 pounds, we can write it as

an inequality.

If b = weight of the books, then:

b > 4 (b is greater than 4)

4 < b (4 is less than b)

Both inequalities are correct; the weight of the

books is greater than 4 pounds or 4 pounds is

less than the weight of the books.

Directions for questions 1–8: Does the situation represent an equation or an inequality? Write the

equation or inequality for each situation.

1) Nick caught more than 7 fish.

2) Mr. Davis taught 80 students in all.

3)

4)


5)

6)

7) Kevin jumped 4.5 feet.

8) The animal shelter can take care of fewer

than 55 animals.

Mixed Practice


y – 27 = 41


w ÷ 627 = 1

11) Write as a fraction in simplest terms.

32%

12) Find the length of side AB.


Word Problem

13) Write an inequality or an equation to describe that Susan ate less than 2,000 calories.



Homework Problems

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Questions…

#’s

Quick Look

Today we graphed inequalities on number lines. For example, let’s represent g < 5 + 2 on a number line.

First, simplify the right side of the inequality:

5 + 2 = 7, so g < 7.

Second, graph the inequality:

Use an open circle to indicate that g is not equal to 7.

Going left on the number line shows less than.

g is less than 7, so we shade everything to the left of 7.

We shade the arrow to show that numbers beyond –10 are also less than 7.

Finally, what are some solutions to the inequality?

g = –3 is a solution to the inequality.

It is in the shaded region of the number line and it keeps the inequality true.

g < 7

–3 < 7 True

But g = 8 is not a solution to the inequality.

It is not in the shaded region of the number line and it does not keep the inequality true.

g < 7

8 < 7 Not True

1) 20 – 7 < x

a. Graph the inequality on the number line.

b. Is 12 a solution to the inequality?


2)

a. Write an inequality to describe the number line.

b. Is 2 a solution to the inequality? Explain your thinking.

3) m < 2(9)


b. Is –5 a solution to the inequality?

4) 5 > g


b. Is 10 a solution to the inequality?

5)




6)


b. Is 0.5 a solution to the inequality?

7) k > –1


b. Is 0 a solution to the inequality? Explain your thinking.

8)


b. Is 8.8 a solution to the inequality?


Mixed Practice

9) Does the situation represent an inequality or

an equation? Write the inequality or

equation that represents the situation.


terms, and coefficients.

h + 20

a. variable(s)

b. constant(s)

c. number of terms

d. coefficient(s)


15y = 600

12) 55

3 •

4

1

Word Problem

13) Graph the inequality: 16 divided by 2 is less than k. Is k = 8.1 a solution to the inequality?


Homework Problems

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Questions…

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Quick Look

Today we found solutions to inequalities. Let’s find three solutions to this inequality.

63 – k < 40

The difference between 63 and k is less than 40. That means we need to subtract a number from

63 that will give us a difference that is less than 40.

Let’s try when k = 30

63 – k < 40

63 – 30 < 40

33 < 40 True

k = 30 is a solution because it keeps the inequality true. That means if we subtract a number

larger than 30 from 63, it will also keep the inequality true. What if k = 40 or k = 63?

63 – k < 40 63 – k < 40

63 – 40 < 40 63 – 43 < 40

23 < 40 20 < 40

True True

So three solutions to the inequality are 30, 40, and 43.

Directions for questions 1–3: Use mental math or guess and check strategies to find three solutions to

the inequality.

1) 3 > b + 2

2) 10d < 200

3) 4

c > 4


Directions for questions 4–6: Which values in the set make the inequality true?

4) 24.5 – f < 10, for f = {10, 14, 14.5, 15}

5) 5 < r ÷ 3, for r = {3, 6, 10, 15}

6) 54 + x > 80, for t = {23, 26, 30, 40}

Mixed Practice

7) 17 + 8 > p


b. Is p = 17 a solution to the inequality?

8) Amanda found some sea shells on the beach. The next day, she found 29 sea shells. Altogether,

Amanda found 44 sea shells. How many did she find the first day? Choose the equation that best

represents the math story.

a. 29q = 44 b. q + 29 = 44 c. 44 + q = 29


v ÷ 14 = 6

10) Order the following credit card balances from

least to greatest:

74.35, 0, 2.64, –403.23

Word Problem

11) Find three solutions for this inequality: 36 is greater than 2 times v.


Homework Problems

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Questions…

#’s

Quick Look

Today we wrote inequalities to represent real-life situations. We also found solutions to the inequalities to

answer questions about the real-life situation. Here’s an example!

Leo’s goal is to lose more than 10 pounds.

If p = the number of pounds Leo wants to lose, then p > 10.

If Leo lost 7 pounds the first month and 5 pounds the second month,

would he meet his goal?

If p = 7 + 5,

7 + 5 > 10

12 > 10

If Leo lost 7 + 5 = 12 pounds, he would meet his goal

because 12 pounds is greater than 10 pounds.

1) The coldest recorded temperature in the United States is –62.1°C in Prospect Creek, Alaska.

a. Write an inequality to describe a temperature that is colder than the record.

b. Which temperatures in the set would break the record? {–50.5°C,

–48°C,

–60°C,

–63°C}

2) Mr. Whitehurst had a goal to sell more than 50 t-shirts from his company in two weeks.

a. Write an inequality to describe how many shirts Mr. Whitehurst needs to sell to meet his goal.

b. If he sells 32 shirts the first week and 19 shirts the second week, has he met his goal?


3) The record for the most spoons balanced on a person’s face is 17 spoons.

a. Write an inequality to describe how many spoons someone needs to balance on his or her face to

beat the record.

b. Leo balanced 12 spoons on his face and then added 3 more. Did Leo beat the record?

4) Antonio finished the 100-meter dash in 17.5 seconds last week. His goal is to run the race 1 second

faster this week.

a. Write an inequality to describe the number of seconds Antonio could run to meet his goal.

b. Which values from 15.1–16.9 seconds will meet his goal?

Mixed Practice

5) Graph n < –12 on the number line.


x ÷ 8 = 100

7) One scale measures the weight of the flour

at 30 ounces. Another scale measures

1.875 pounds. If both measures represent

the same weight, how many ounces are in

1 pound?

8) Explain what the ratio means in words. Write if the ratio is a part-to-part, part-to-whole, or whole-to-

whole comparison.

Jay wrote the ratio 15:7 to describe the number of lasagna trays made to the number of lasagna

trays sold at the school fundraiser.

Word Problem

9) Jakob’s boat can carry less than 500 pounds. Jakob and his equipment weigh 320 pounds.

Write an inequality to describe how many pounds of fish can be loaded onto the boat.


Homework Problems

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Questions…

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Quick Look

Today we identified the independent and dependent variables in math tables and real-world math

situations. We also explained the relationship between the variables; did they both increase? Both

decrease? Did one increase while the other decreased?


In this situation, the room temperature increases as the number of people in the room increases. You

could also say that the room temperature decreases as the number of people in the room decreases. The

room temperature depends on the number of people in the room, so the room temperature is the

dependent variable. The number of people in the room affects the room temperature, so it is the

independent variable.

Directions for questions 1–8: Name the independent and dependent variables in the situation.

Then, describe the relationship in terms of the variables.

1) The less you exercise the dog, the more the dog gains weight.


2)

3) The more raffle tickets Kim sells, the more money she raises for the charity.

4)

5) When Miranda studies more, her test score is higher.

6)


7) The more Jack runs each week, the less time it takes him to run a mile.

8) The less time Anquan sleeps, the more time he spends napping the next day.

Mixed Practice

9) Use mental math or guess and check strategies to find three solutions to the inequality: 4x < 100.

10) Does the situation represent an inequality or an equation? Write the inequality or equation.

11) Write an equation for the math story. Then solve the equation to answer the question.

Aaron brought money for his dinner. He spent $24.50 on dinner and desert. When he left the

restaurant, he had $35. How much money did Aaron bring?

12) Complete the chart by writing an expression for the pattern.

Word Problem

13) Describe a cause and effect situation. Determine what the impendent and dependent variables are in

your situation.


Homework Problems

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Questions…

#’s

Quick Look

Today we identified independent and dependent variables. Here’s an example!

Dan is determining the distance he travels when he walks 2 miles per hour.

d = 2t d is the distance and t is the time he has walked in hours.

The value of d depends on what you multiply 2 by. That means the dependent variable is d, and the

independent variable is t. The distance depends of the amount of time Dan has walked.

We also completed charts to show how the dependent variable is affected by the independent variable.

This chart shows different values for time and distance. To complete a chart, select a value for the

independent variable and solve.

For example, when t = 3, d = 6. Here are some other values for d and t.

Directions for questions 1–8: Complete each table. Name the independent and dependent variables.

1) n = 18 + z

2) 36.2 – u = y


3) Ms. Pamela wants to know how many

students will be in each group if she

wants 4 students per team.

r = number of students in the class

p = how many groups

r ÷ 4 = p

4) Mr. Willis is finding the total number of

students on the field trip. The 9 buses each

have the same number of students.

s = the number of students on each bus

m = the total number of students going on

the field trip

m = s • 9

5) c = 8

h

6) 10v = w

7) Kwame is determining how much he has left of

the $25.50 he brought to the game.

x = the amount he spent at the game

y = what he has left

25.5 – x = y


8) There were 7 people waiting to board the

train, and then more people joined them.

How many people are waiting now?

t = total people waiting now

b = people who came after the original 7

t = b + 7

Mixed Practice

9) Use mental math or guess and check strategies

to find three solutions to the inequality:

5n > 90

10) What is the area of a square that has a side

length of 45 meters?


Manny received a tax return check and decided to donate some of it. He donated $800, and still

had $1,785 left from the check. How much was the tax return check for?

12) 58

1 +

4

6

Word Problem

13) Complete the table for the equation: b equals a divided into 6 equal parts. Name the independent and

dependent variables.


Homework Problems

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Questions…

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Quick Look

Today we wrote equations for real-world situations involving area, perimeter, and volume. For example:

Nevaeh is choosing between three different side lengths for a square table.

How do the different lengths change the total area?

To find the area of a square, multiply length

by width. That’s A = s2. Let’s use a chart to

track how changing the side length of the

table changes the total area.

The independent variable is the side length, and the dependent variable is the area.

Nevaeh will choose a side length for her table that gives the area she wants.

Here are some geometry formulas that may help you write equations for these problems.

Area: A = l • w A = s2

Volume: V = B • h V = l • w • h

Perimeter (square): P = s + s + s + s P = 4s

Perimeter (rectangle): P = l + l + w + w P = 2l + 2w

Directions for questions 1–3: Use the information in the problem to answer questions a, b, and c.

1) A construction crew is creating a rectangular patch of pavement for a statue in the park.

The width of the pavement will be 4 feet, but they want to how different lengths would affect

the total area of the rectangle.

a. Write an equation to describe the situation.


b. Complete the chart.

c. Name the independent and dependent variables.

2) Mavis is selecting pre-cut wood to use to make a square picture frame. She is looking to see how the

side length she selects will change the perimeter of the frame.




3) The Libby is building a pool behind her house. She wants the pool to be 12 feet wide and 24 feet long,

but she wants to know how different depths (heights) would affect the total volume of the pool.





Mixed Practice

4) Complete the table. Name the independent and dependent variables.

h = 7g

5)




p – 12 = 19

7) Which is less?

| –20 | or | 3 |

Word Problem

8) In the formula A = l • w, there are three variables: A, l, and w. Classify each variable as independent

or dependent and explain your thinking.


Homework Problems

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Questions…

#’s

Quick Look

Today we wrote equations and graphed data to describe the relationship between independent and

dependent variables. Here’s an example!

The table shows us original and sale prices. As the original cost decreases, the sale price also

decreases. The sale price depends on the original price, so the sale price is the dependent variable and

the original price is the independent variable.

On the graph:

x is always the independent variable, and

y is always the dependent variable.

All points on the line represent what the sale

price would be for any original price.

We can use the data from the table or graph

to create an equation.

The pattern is: subtract $2 from the original price

to get the sale price.

That’s y = x – 2.


1) A birdwatcher recorded the time and distance of a goose’s flight.

a. Use the table to make a graph.

b. Write an equation to describe the graph.

c. Describe the relationship in terms of the variables.

d. If the goose flew for 9 hours, how many miles did it travel? Explain your thinking.

e. If the goose traveled 40 miles, for how long did it fly?


Mixed Practice

2) Multiply.

0.43 • 86.5


d – 15 = 3

4) Graph –3 > t.

5) If 3 feet are in a yard, how many yards are in 45 feet?

Word Problem

6) Another bird watcher said he saw a Teal bird that traveled 110 miles in 2 hours. Did the Teal travel at

the same speed as the goose? Use question 1 to help you, and explain your thinking.


Homework Problems

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Questions…

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Quick Look

Today we converted between customary measurements and between metric measurements to answer

real-world questions. We used multiplication, division, fractions, decimals, and ratios to help us!

For example:

Willie drove 5,284 meters. How long was his trip in kilometers?

We can use conversion factors to convert from meters to kilometers.

km 5.284hm 10

km 1•

dam 10

hm 1•

m 10

dam 1•m 5,284 =

We can also use the metric chart to convert from meters to kilometers.

We are changing from a smaller unit, meters, to a large unit, kilometers, so the number will be smaller.

Kilometers are three steps to the left of meters; that means we move our decimal three places to the left.

Directions for questions 1–8: Convert to the given unit. Show your work.

1) The tallest man in the world was recorded at 2.72 meters. How many kilometers tall was he?

2) Deanna ran 25 miles one day in preparation for an upcoming marathon. How many feet did she run?


3) Spike drank 2 gallons of water during the day. How many pints of water did he drink?

4) The heaviest man was recorded at about 635,000 grams in 1978. How many kilograms did he weigh?

5) The gym teacher measured Blaine’s vertical jump at 35 inches. How many yards can Blaine jump?

6) The longest snake in captivity is 7.3 meters long. What is the length of the snake in millimeters?

7) Don put 3 tablespoons of water in a recipe. How many gallons of water is that?

8) The longest jump recorded on a unicycle is 0.295 dekameter. How many decimeters did he jump?

Mixed Practice

9) Find the value of 13y + 4 when y = 1.42.

10) How much is 72% of 200?

11) Graph x < 12 on the number line.

12) Find the greatest common factor of 75 and 90.

Word Problem

13) An American football field is 160 feet wide. What is the width in yards?


Homework Problems

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Questions…

#’s

Quick Look

Today we learned that converting between measurements is one type of linear relationship. We used the unit rate to write a linear equation for the relationship and to create a chart that showed different measurements in the relationship. We also graphed the relationship using information from our chart. Whenever we converted between two measurements, like inches and centimeters, we saw that as one measure got larger, so did the second. When we graphed it, we saw the linear relationship.

For example:

Did you know that male lions patrol a vast territory to protect their pride, or family? Normally, this distance covers 100 square miles, or 259 square kilometers.

We can write a unit rate to describe the relationship between the two units of measure:

259 sq km = 2.59 sq km 100 sq mi 1 sq mi

So 1 square mile equals 2.59 square kilometers.

Knowing the unit rate can help us write an equation to represent the relationship. To get from square miles to square kilometers, multiply by 2.59. So if k stands for square kilometers and m stands for square miles, then k = 2.59m.

Now that we know the equation, we can easily find missing information. If a park rests on 500 square kilometers, how many square miles is that? Use the equation to find out! Substitute 500 for k and solve for m.

k = 2.59m 500 = 2.59m 193.05 = m

The park is 193.05 square miles!


1) Chef Bodele wrote the equation m = 29.57f to represent the relationship between milliliters and fluid ounces. In the equation, m represents milliliters and f represents fluid ounces.

a. Complete the chart.

b. Graph the relationship between fluid ounces and milliliters on graph paper.

c. If Chef Bodele measured 295.74 milliliters, what is the capacity in fluid ounces?

2) Nichola ran 3.84 miles around a track but recorded it as 6.179 kilometers.

a. Write a unit rate to describe the relationship between miles and kilometers.

b. Write an equation to describe the relationship between miles and kilometers.

c. Nichola ran 1.2 miles the next day, how many kilometers did she run? Explain your thinking.

Fluid Ounces Milliliters

1 29.57

5

207.02

9


3) This graph represents rope measurements taken in meters and feet.

a. Write a unit rate to describe the relationship between meters and feet.

b. Write an equation for the relationship between meters and feet.

c. If a rope measures 30 feet, what is the measurement in meters? Explain your thinking.

4) The hospital weighed a newborn baby. He weighed 9 pounds on one scale and 4.08 kilograms on another.

a. Write an equation to describe the relationship between pounds and kilograms.

b. What is a 7 pound newborn’s weight in kilograms?


Mixed Practice


4.8 + 3 • (32 • 4) – 1

6) Janelle spent $31.60 on dinner and gave the

waiter a tip that was 20% of the cost of her

dinner. What is the total amount of money

that Janelle spent on the tip?


1,591.8 = t – 12.5

8) Write an inequality for the situation.

Jaina wove more than 12 baskets each day

this week.

Word Problem

9) At the 2008 summer Olympics, Michael Phelps swam the 400 meter individual medley in 4 minutes and 3.84 seconds. 400 meters is equal to 1,312 feet.

a. Write an equation to describe the relationship between feet and meters.


Meters Feet

400 1,312

100

820


Homework Problems

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Questions…

#’s

Quick Look

Today we solved multiple-step problems about real-world math situations. We used our knowledge of converting measures, finding unit rates, comparing rates, and even geometric formulas to answer real-world questions. In these questions we converted and combined measures of length, weight, and capacity. We worked with both customary and metric units of measurement.

For example:

Aiden bought chips and salsa to serve at his party. He bought 10 bags of chips that each contained 1 pound of chips. He also bought a 1 gallon jar of salsa. Does Aiden have enough salsa to serve 6 fluid ounces to each of his 20 party guests?

He bought salsa in a gallon jar but wants to share it in servings of 6 fluid ounces. Let’s compare the fluid ounces he bought to the fluid ounces he needs for the party:

Salsa bought: 1 gal • gal 1

oz fl 128 = 128 fl oz

Salsa needed: 20 guests • 6 fl oz per guest = 120 fl oz

Aiden needs 120 fluid ounces of salsa to serve each of his guests. He bought 128 fluid ounces of salsa, so he will have enough for the party!


1) Judah bought a new model airplane. The box states the landing distance for the plane is 60 meters or

65.6 yards and another 55 meters or 60.1 yards is necessary for safety. Terrence also bought a new

model airplane. His box noted the landing distance was 70 yards with an additional 45 yards

recommended for safety. The model airplane field is 486 feet long.

a. Each boy wants to allow enough distance for a safe landing. Does the field allow enough room for

each airplane to safely land? Explain your thinking.

b. Who needs a longer distance to land? How much longer?

c. Terrence found that when landing his plane, it consistently landed an additional 265 inches

beyond the calculated 345 feet. What is his plane’s actual landing distance?

2) Emily and her grandmother are planning a family breakfast. Emily goes to the store to buy orange

juice. 6 family members each want 12 fluid ounces of orange juice. The grocery store is having a

special on cans of frozen orange juice concentrate. Each can makes 2 quarts of juice.

a. How many cans of concentrate should Emily buy to have enough?

b. Emily's grandmother would like to use the remaining orange juice for a recipe. The recipe calls for

3 cups of orange juice. She wants to make 2 batches of the recipe. Will there be enough juice?

c. Emily spills some juice on the floor. She pours the rest in a measuring cup to see how much is

left. If Emily measures 7.5 pints, will there be enough juice for the family and the recipe?

3) The tallest living person is 8 feet 3 inches tall. The shortest living person is 21.5 inches tall.

a. How many times shorter is the shortest living person than the tallest living person?

b. If the shortest person grew 3.25 inches, then how many feet tall would that person be?

c. Anders says that if both the tallest and shortest living people grew 10 inches, then the answer to question a would remain the same. Is he correct? Why or why not?


Mixed Practice


5) 28.1 + s = 84.9

6) If both Leila and Don use 16 cups of powder, who will make more cement in all?

7) 17.5 – 12.5 > y


b. Is y = 0 a solution to the inequality?

Word Problem

8) A city block is one-twentieth of a mile. Holly runs 14 blocks every day.

a. How far does she run in yards?

b. How far does she run in feet?

c. How many days will it take Holly to meet her goal to run 100 miles?


Homework Problems

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Questions…

#’s

Quick Look

Today we examined the properties of polygons. We explored different ways polygons could be identified and categorized. We identified polygons based on sight and description. We also described polygons in very specific detail. Given coordinates, we even drew polygons and identified them as well.

We used some of the following vocabulary when describing polygons:

Polygon – a two-dimensional, closed figure made up of 3 or more line segments

Equilateral – all sides are the same length (congruent)

Parallel – line segments that do not intersect because they are always the same distance apart

Perpendicular – two lines that intersect at right angles

Scalene – a triangle with no congruent sides

Isosceles – a polygon with two congruent sides, usually a triangle or trapezoid

Acute – an angle whose measure is greater than 0 and less than 90 degrees

Obtuse – an angle whose measure is greater than 90 and less than 180 degrees

Right – an angle whose measure is exactly 90 degrees

For example, we could describe this polygon:

This polygon has four sides and four angles, meaning it is a quadrilateral. This quadrilateral has exactly one set of parallel sides, making it a trapezoid. Furthermore, the two sides that are not parallel are congruent. So this is an isosceles trapezoid.


Directions for questions 1–3: Describe the polygon. Be sure to talk about the sides and angles.

1)

2)

3)


Directions for questions 4–6: Identify and draw the polygon that is described.

4) This shape has four sides and four angles. It has opposite sides that are the same length and are

parallel. It also has four right angles.

5) This shape has three sides and three angles. All sides are different lengths. One angle measures

90 degrees. The remaining angles are less than 90 degrees.

6) This shape has four equal sides, four angles, and two sets of parallel sides. The shape does not have any right angles.

Mixed Practice


8) 83 • 2

32

9) 265 +

31 +

43

10) 4 ÷ 2 + (3 • 5) – 32

Word Problem

11) Ming’s boss told her to make kites that are shaped like quadrilaterals. He wants the kite to have exactly one pair of parallel sides and two right angles. Draw the design for the kite that Ming will create. What polygon did you draw?


Homework Problems

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Questions…

#’s

Quick Look

Today we learned how to find the area of rectangles and triangles. The area is the space inside a closed

figure. To find the area of a rectangle, we multiply the length by the width: A = l • w. We learned that a

rectangle can be divided in half to create two triangles. That means we find the area of a triangle by

dividing the area of a rectangle in half: A = 2

1 b • h.

A = 2

1 b • h

A = 2

1 • 13 in. • 6 in.

A = 39 in.2

Remember, area is in two dimensions, length and width, so our units are always square units.

Directions for questions 1–6: Find the area.

1)

2)


3)

4)

5)

6)

Mixed Practice

7) Convert 123

2 to an improper fraction.


14 + x = 53


|–4.5|, 5,

–4, |6|


10) Find the distance of line XY.

Word Problem

11) Kenyatta is designing a poster. She is making triangles using red construction paper that have a base

of 14.5 centimeters and a height of 19.75 centimeters.

a. What is the area of one triangle that Kenyatta creates?

b. If Kenyatta needs 8 triangles to make her poster, what is the total area of red construction

paper that she will use?


Homework Problems

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Questions…

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Quick Look

Today we learned how to find the area of special quadrilaterals. We broke apart and rearranged

parallelograms, trapezoids, and rhombi to create rectangles and triangles. We used the formulas for area

of a rectangle and a triangle to help us find the total area of the special quadrilaterals. We also used the

formula for area of a rectangle to help us find the formula for area of a parallelogram.

Here’s what we did!

We broke apart a triangle from the parallelogram and rearranged it to create a rectangle. It’s easy to find

the area of a rectangle.

Area = l • w

A = 12 km • 3.5 km = 42 km²

The area of the parallelogram is 42 km².

Directions for questions 1–6: Find the area.

1)

2)


3)

4)

5)

6)

Mixed Practice

7) Name the independent and dependent variable in the situation:

The colder the temperature is, the more layers of clothing people wear.


12.4 • (g • 40)

9) Emily scored a goal in soccer from 53 feet away. If there are 3 feet in each yard and 1,760 yards in a

mile, then from how many miles away did she score?


10) Which values in the set make the inequality true?

14 < k • 4, for r = {2, 3, 3.5, 4}

Word Problem

11) Teodoro is painting a tile for the mosaic his art class is creating. His tile is shaped like a trapezoid.

What is the area of Teodoro’s tile?


Homework Problems

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Questions…

#’s

Quick Look

Today we broke complex shapes into rectangles and triangles so we could easily find the area of the

shape. Sometimes, there are multiple ways to divide a shape up to make easier shapes, but the total area

is always the same. Here’s an example!

We can divide this polygon into one rectangle and two triangles. Then we can find the area of

each shape.

Area of the rectangle: A = l • w

A = 7 units • 6 units = 42 units²

Area of the top triangle: A = 2

1b • h

A = 2

1• 2 units • 5 units = 5 units²

Area of the bottom triangle: A =2

1b • h

A = 2

1• 2 units • 5 units = 5 units²

Now add to find the total area:

42 units² + 5 units² + 5 units² = 52 units² So the area of the polygon is 52 units².

Directions for questions 1–5: Find the area. Show your work

1)


2)

3)


4)

5)

Mixed Practice


Annabel collected 52 books at the book drive before lunch. She collected more books throughout the

day. At the end of the day, she had 101 books. How many books were donated after lunch?



6 – (32 ÷ 9) + 0.5

8) Nikki delivered 46 papers in 3 hours and Miles delivered 75 papers in 5 hours. Who was delivering

papers at a faster rate?

9) Find the quotient.

8

5 ÷

6

35

Word Problem

10) Alejandro drew a picture of his house. The wall of the house he drew was 5 inches tall, and the house

was 9.3 inches in height from the tip of the roof to the ground. If Alejandro’s drawing is also 5 inches

wide, then what is the area of the drawing?


Homework Problems

Name

Team Name Team Complete? Team Did Not Agree On

Questions…

#’s

Quick Look

Today we solved multiple-step problems about real-world situations involving area. We investigated math stories for necessary information and eliminated extraneous information. We used the formulas for area of a rectangle and a triangle to help us find the total area. For some problems, it was helpful to sketch a model of the situation in the word problem. Here is an example!

A store sells two types of wrapping paper. Type A i s a solid color. It has 4 rolls per package and each roll is 29 inches by 59 inches. Type B is very glossy and has lots of graphics.

It has a single roll and is 35 inches by 197 inches . Which type gives you more wrapping paper?

First, find the area of Type A by multiplying the length and width of a single roll. A = l • w A = 29 in. • 59 in. A = 1,711 in²

Then, multiply the area of the single roll of Type A by 4, because there are 4 rolls in a package. A = 1,711 in.² • 4 = 6,844 in.²

Next, find the area of Type B. A = l • w A = 35 in. • 197 in. A = 6,895 in.²

6,844 in. 2 < 6,895 in. 2, so Type B gives you more wrapping paper!


1) Tyron cuts grass for his parents and gets paid $0.10 per square meter. This is a drawing of Tyron’s family house and yard from above.

a. If he cuts the lawn 4 times this month, then how much land did he mow?

b. If Tyron wants to save $1,000, then how many times will he need to mow his family’s lawn?

2) Lin is painting the back of his daughter’s dollhouse. The house is three stories tall and has a roof. Each story and the roof are the same height. Each story is 33 inches long. The height of the entire house is 50.5 inches.

a. What is the total area that Lin is painting?

b. What is the percentage of the area of the back of the dollhouse is the area of the roof?

c. If he painted the front of the dollhouse in the same way, what will the total painted area be then?


3) The city approved a grant for a neighborhood association to create a community garden. The neighborhood association wants to include each of the following in the space for the garden:

a) a plot of land for carrots that is 25 feet long and 15 feet wide, b) a plot for turnips that is 25 feet long and 15 feet wide, c) a plot for cabbage that is 35 feet long and 15 feet wide, d) and a plot for corn that is 20 feet long and 10 feet wide.

There are three potential lots in the neighborhood where the community garden could be built.

Lot A

Lot B

Lot C

a. Which garden should the neighborhood association choose? Why do you think so?

b. Draw and design the vegetable garden. Be sure to label each vegetable space. What is the total area of the garden you drew?


Mixed Practice

4) Write an algebraic expression that represents the perimeter of the shape.

5) Solve. Round your answer to the nearest hundredth.

0.321 ÷ 0.123


x + (531

+ 351

) = 101511


withdrawal of $35 from a bank account

Word Problem

8) The star is made of right and acute triangles. The base of every right triangle Is 4 centimeters and the height is 3 centimeters. Each acute triangle is half the area of a right triangle.

a. What is the area of one acute triangle?

b. What is the total area of the star?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we found the volume of unit fraction cubes. We used unit cubes whose edge lengths were 1 unit to

determine how many unit fraction cubes fit into the larger cube. Here’s an example!

It takes 64 cubes that measure 4

1foot on each edge to fill a cube that measures 1 foot on each edge.

That means the volume of the unit fraction cube is 64

1of the volume of the unit cube: 1 ft

3 ÷ 64 =

64

1ft

3.

We can also use the formula for finding volume of a rectangular prism:

V = l • w • h

V =4

1ft •

4

1ft •

4

1 ft

V =64

1 ft

3



1)

a. What is the volume of cube F?

b. How many of cube G are needed to fill cube F?

c. What is the volume of cube G?

2)

a. The cubes that make up the larger cube

have equal edge lengths. What is the edge

length of one of the smaller cubes?

b. How many smaller cubes make up the

larger cube?

c. What is the volume of the smaller cube?


3)

a. What is the volume of cube W?

b. How many of cube U are needed to fill cube W?

c. What is the volume of cube U?

4)

a. The cubes that make up the larger cube



b. How many smaller cubes make up the

larger cube?

c. What is the volume of the smaller cube?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we found the volume of rectangular prisms with fractional edges by packing them with unit fraction

cubes. Here’s an example!

About what is the volume of the rectangular prism?

Estimate: 1 cm • 2 cm • 2 cm = 4 cm3

How many unit fractions cubes make up the rectangular prism?

3 rows of 7 cubes are used to make the bottom layer. That’s 3 • 7 = 21 cubes.

8 layers of 21 cubes are needed to fill the prism. That’s 8 • 21 = 168 cubes in all.

What is the actual volume of the cube?

Each unit fraction cube has a volume of 64

1cm

3. So

64

1cm

3 • 168 cubes = 2

8

5cm

3.

Does our answer make sense?

28

5cm

3 is close to our estimate of 4 cm

3.


1)

a. Estimate the volume of the rectangular prism.

b. How many unit fraction cubes are needed to pack the rectangular prism?

c. What is the volume of the rectangular prism?

2)

a. If all of the cubes have the same

measurements, what is the length of

each edge of each unit fraction cube?

b. What is the volume of the

rectangular prism?


3)

a. Estimate the volume of the rectangular prism.

b. How many unit fraction cubes are needed to pack the rectangular prism?

c. What is the volume of the rectangular prism?

4)

a. If all of the cubes have the same

measurements, what is the length of

each edge of each unit fraction cube?

b. What is the volume of the

rectangular prism?


Mixed Practice

5)




balanced the scale.

6) Complete each table. Name the independent and dependent variables.

b = a ÷ 3



5u(7u + 2)


536 ÷ 0.52

Word Problem

9) What is the volume of a package that has a height of 1 yard, width of3

2yard and length of 1

3

1yards?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we used the formulas V = B • h (Volume = area of the base • height) and V = l • w • h (Volume =

length • width • height) to find the volume of rectangular prisms with fractional edge lengths.


Use the formula V = l • w • h to find the volume.

V = 54

3in. • 12

2

1in. • 7 in.

V = 5038

1in.

3

Or, use the formula V = B • h.

V = 7 in. • 718

7in.

2

V = 5038

1in.

3

The volume is 5038

1 cubic inches. Both formulas give us the same result!

Directions for questions 1–8: Find the volume.

1) A pool has a height of 42

1 feet, and the area

of the base is 308 square feet.

What is the volume of the pool?

2) Joe’s crate is 1 meter high, 1.2 meters wide,

and 1.4 meters long. What is the volume of

the crate?

The base is the area of

the bottom of the figure.

54

3in. • 12

2

1in = 71

8

7in.

2


3)

4)

5)

6) A student desk’s has a storage area for

books that is 202

1inches long, 15 inches

wide, and 54

1inches high. What is the

volume of the book storage area?

Mixed Practice

7) Subtract.

25,369 – 336.05


12 + n = 31

9) Find the area.

10) Madeline is using 17.25 square feet of red

fabric and 23.5 square feet of blue fabric to

create a quilt. How many square feet of

fabric is Madeline using in all for her quilt?

Word Problem

11) Ambre’s Art studio has a floor space with an area of 1,035 square feet. If the ceiling is 10.5 feet high,

what is the volume of the art studio?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we found the volumes of three-dimensional figures. We divided these complex figures into

rectangular prisms and added or subtracted the volumes of the parts to find the total volume of the figure.


First, we divide the figure into two rectangular prisms. You can draw a dotted line to help you see the

two sections.

Now, we use the formula V = l • w • h to find the volume of each rectangular prism.

V = 172

1 cm • 82

1 cm • 2 cm

V = 2972

1

cm

3

V = 84

1 cm • 19 cm • 2 cm

V = 3132

1

cm

3

Finally, we add the volume of the rectangular prisms to find the volume of the entire figure.

2972

1

cm

3 + 313

2

1

cm

3 = 611 cm

3

The total volume of the figure is 611 cm3.


Directions for questions 1–4: Find the volume.

1) A truck driver needs to unload his cargo in the company garage. How much volume of the garage will

be left over after the cargo is put inside it? Show your work.

2) What is the volume of the figure? Show your work.

3) This is all that is left of the cake Maria baked. What is the volume of the remaining cake? Show your work.


4) What is the volume of the figure? Show your work.

Mixed Practice


17.7 ÷ 6.3

6) Divide.

20

7 ÷

8

3


32.5%, 50

32, 0.3,

3

1

8) What is the volume of a cube that measures 4

1 in. on each side?

Word Problem

9) Darla has a package that is 1 foot wide, 22

1 feet long, and 4

4

1 feet wide. She placed

8

7cubic feet of

packing peanuts inside the package. What is the volume of the package that is not filled up yet?

Show your work.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we solved real world problems involving volume of rectangular prisms. Here’s an example!

Aaron wanted to fill the container 4

3of the way.

How many gallons of water does he need if there are 231 cubic inches in 1 gallon?

If Aaron fills the container 4

3of the way, then the water will have a height of 8 in. •

4

3 = 6 in.

So the volume of the water will be 6 in. • 16 in. • 42

1in. = 432 in.

3.

To determine the number of gallons of water Aaron needs, convert the cubic inches to gallons.

That means Aaron needs 1.87 gallons of water.

1) Sal is creating a wall for a garden.


a. What is the volume of the wall?

b. Sal is considering making the wall from concrete. One bag of concrete makes 2

1 cubic foot

concrete. How many bags of concrete does he need to fill his wall?

c. Sal is also considering making the wall from granite cubes that measure 2

1 foot on each edge.

He said that he will need the same number of cubes to fill the wall as bags of concrete.

Explain what’s wrong with his thinking.

d. How many granite cubes that measure 2

1 foot on each edge does he actually need?

Mixed Practice

2) Write 35.4% as a decimal and fraction.

3) If there are 2 pints in a quart and 4 quarts in

a gallon, how many pints are in 3 gallons?

4) Complete the table. Name the independent

and dependent variables.

g + 25 = h

g h



16a2 + 40

Word Problem

6) Sal is doubling the length of the wall. Before, it was 8 feet, and now it will be 16 feet. How many more

granite cubes that measure 2

1 foot on each edge does Sal need to double the length of the wall?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we drew nets to represent solid figures. Here’s an example!

This net represents the rectangular pyramid because if you fold the net, you will get the rectangular

pyramid. Notice that the net and solid figure both have one face that is a rectangle and four faces that

are triangles.

Directions for questions 1–3: Name the solid figure that the net represents.

1)


2)

3)

Directions for questions 4–6: Draw a net to represent the figure.

4)


5)

6)

7) Which net(s) can be folded to form a triangular pyramid?


Mixed Practice

8) What’s the area of the rectangle?

9) What is the area of the figure?

10) Dara’s car drove 220 miles on 18 gallons of gas. Write a unit rate to describe how far Dara’s car can

go on 1 gallon of gas.

11) Cindy is purchasing a shirt for $24.99. If the sales tax is 6%, how much will she pay in sales tax?

Word Problem

12) Bakari is making a cardboard container out of four triangles. What solid shape will he be creating?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we found the surface area of triangular and rectangular prisms. Here’s an example!

Use a net to find the area of each face. In this rectangular prism, there are three different rectangles.

Then, add the areas together to find the surface area:

18 cm2 + 12 cm

2 + 18 cm

2 + 12 cm

2 + 6 cm

2 + 6 cm

2 = 72 cm

2

We can also write a numeric expression to help solve. There are three pairs of congruent rectangles, so

we can multiply each different sized rectangle by two.

2(6 cm • 2 cm) + 2(3 cm • 2 cm) + 2(6 cm • 3 cm) = 72 cm2


1)

a. Write a numeric expression to show the surface area of the figure.

b. What is the surface area of the figure?

2)

a. Is the triangle that forms the base of the prism equilateral, isosceles, or scalene?

b. Write a numeric expression to show the surface area of the figure.

c. What is the surface area of the figure?

d. How did the number of congruent faces on the figure help you write your numeric expression?


3)



4)





5)




6)



c. How did the number of congruent faces on the figure help you write the numeric expression?


Mixed Practice

7) Find the volume.

8) Does the scale represent an equation or

an inequality? Write the equation or

inequality show on the scale.

9) Evaluate the number sentence.

42 + 3(10 – 2)

10) Add.

3

14 + 2

5

1

Word Problem

11) Carl is constructing a cardboard box. How many square feet of cardboard will he use to construct

this box:


Homework Problems

Name



Questions…

#’s

Quick Look

Today we found the surface area of pyramids. Here’s an example!

Use a net to find the area of each face. In this square pyramid,

there is one square face and four congruent triangular faces.

Then, add the areas together to find the surface area:

225 m2 + 67.5 m

2 + 67.5 m

2 + 67.5 m

2 + 67.5 m

2 = 495 m

2

We also used numeric expressions to help us find surface area:

(15 m • 15 m) + 4(2

1• 15 m • 9 m) = 495 m

2


1)

a. Write a numeric expression for the surface

area of the pyramid.

b. What is the surface area of the pyramid?

c. Explain how you used the shape of the base to find the surface area.

2)




3)




The base

is a square.

All faces are congruent

equilateral triangles.

The base

is a rectangle.


4)




Mixed Practice

5) Use mental math or guess and check

strategies to find three solutions for

the inequality.

9n < 97


simplify the expression.

5(a • 3a)

7) Write an algebraic expression that

represents the given algebra tiles.

8) Write the prime factorization of 300

using exponents.

Word Problem

9) Ameen is painting all faces of this square pyramid. What is the surface area he is painting?

The base is an

equilateral triangle.

Its height is 3.9 cm.


Homework Problems

Name



Questions…

#’s

Quick Look

Today your student solved complex problems involving surface area. Here’s an example!

Frank is using brown paint to paint the bottom face and bottom 4

1of each side of this toy box. How much

area is Frank painting brown?

What’s going on?

Frank is painting part of the rectangular prism. He needs to find the surface area that he will be

painting brown.

What’s the plan?

Find the area of the bottom face. Then, find the area of 4

1 of each side.

area of bottom face:

7 in. • 10 in. = 70 in.2

area of 4

1 of each side:

2(7 in. • 8 in.) + 2(10 in. • 8 in.) = 272 in.2

272 in.2 •

4

1 = 68 in.

2

surface area in all to be painted brown:

68 in.2 + 70 in.

2 = 138 in.

2


1) A baker is making a three-layer cake, and each layer will have a square base. Each layer is 3 inches

high. The cake will be frosted after the cake is assembled. Only the parts of the cake that can be

seen will be frosted.

a. What is the surface area of the cake that is

being frosted?

b. Each layer will be white except the top layer

which will be yellow. What percentage of the

surface area of the cake will be yellow?

c. The baker used exactly two batches of frosting to cover the

top and all four sides of a one-layer cake. Based on this cake,

how many whole batches of icing should be made to frost

the three-layer cake above?

Mixed Practice

2) Subtract.

0.2359 – 0.00325

3) Estimate the product.

57

1 • 25

4) Solve.

200 = b ÷ 5


terms, and coefficients.

24c + 2

a. variable(s) _______________________

b. constant(s) ______________________

c. number of terms __________________

d. coefficient(s) _____________________


Homework Problems

Name



Questions…

#’s

Quick Look

Today we identified statistical questions, numerical data, and categorical data. Here’s an example!

Mitch wanted to know more about the marching band at school. He made a list of survey questions to ask:

a. How many hours do you practice your instrument at home?

b. What instrument do you play?

c. How many hours did the band practice at school this week?

d. What percentage of middle schools in the U.S. have marching bands?

Questions A and B are statistical questions because the responses will tell Mitch more about the

marching band. They will also have variability, or a range of different answers, because students practice

different number of hours at home and play different instruments.

Question A will give categorical data because people will respond with different instruments.

They may respond with piccolo, clarinet, tuba, or cymbals!

Question B will give numerical data because people will responds with different numbers of

hours. They may respond with 0, 3.5, or 10 hours!

Question C is not a statistical question. All the responses will be the same number of hours, so there will

be no variability in the data.

Question D is not a statistical question about the marching band at school. The responses will all be the

same and will not give more information about the school marching band.

1) Reem is interested in what afterschool activities her classmates enjoy the most. Which statistical

question would give Reem the BEST data?

a. How many times a week do you go to the movies?

b. Do you like afterschool activities?

c. How many times a week do you play sports?

d. What is your favorite afterschool activity?


2) Will the data collected be categorical or numerical?

What is your favorite movie?

3) Mia wants to know more about the daily servings of vegetables eaten by students in her class. Which

statistical question would give Mia the BEST data?

a. What is your favorite vegetable?

b. How many servings of vegetables did you eat yesterday?

c. How many servings of vegetables should you eat?

d. Do you like eating vegetables?

4) Is the data displayed categorical or numerical?

5) Mr. Holmes wants to know more about his neighborhood and the people who live there. Which is

NOT a statistical question he could ask?

a. What year did you move into the neighborhood?

b. How many years have you lived here?

c. Is this the only place you’ve ever lived?

d. How many children live in your household?


6) Will the data collected by categorical or numerical?

How many times a day do you wash your hands?

7) Liam wants to know how athletic his classmates are. Which is NOT a statistical question he

could ask?

a. Have you ever played sports before?

b. How long does it take you to run one mile?

c. How many pull-ups can you do?

d. How many times a week do you play a sport?

8) Is the data displayed categorical or numerical?

Mixed Practice

9) Find the surface area.


10) What is the volume of a cube that measures 32

1 feet on each edge?

11) If there are 3 teaspoons in 1 tablespoon, how many teaspoons are in 22

1 tablespoons?

12) Is 6b + 5 + b2 equivalent to 6b

3 + 5?

Word Problem

13) Kame asked 6th graders: “How many siblings do you have?” Will the data Kame collects be

categorical or numerical? Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we evaluated and wrote statistical questions. Here’s an example!

Noreen wanted to find out what time 6th graders woke up on school mornings. Her question is:

Do you wake up before 7 a.m.?

This is not a good statistical question. Noreen will only get yes and no responses. That will not help her

find out what time 6th graders wake up.

A better question is: What time do you wake up on school mornings?

The new question will get different times as responses. It will help her find out what time 6th graders

wake up on school mornings. Her responses will also have variability—some students may respond with

6:45 a.m. and others may respond with 7:30 a.m.

1) Write a statistical question that could have been asked to collect this data.


2) The swim team will be holding a bake sale at the next parent-teacher conference. They are

determining what bake goods to prepare for the sale.

a. Write one statistical question that will help determine the baked goods to prepare for the sale.

b. Will this question give categorical or numerical data?

3) Jess wants to find out more about the type of pets 6th graders have. Her survey question is:

How many pets do you have?

Did Jess ask a good statistical question? Why do you think so? If not, what statistical question

would you ask?

4) Write a statistical question that could have been asked to collect this data.

5) Malik needs to know how much food to get for his party.

a. Write one statistical question that will help him determine how much pizza he should get.

b. Will this question give categorical or numerical data?


6) Uma wants to know how much time students in her class watch TV. Her survey question is:

How many hours did you spend watching TV last week?

Did Uma ask a good statistical question? Why do you think so? If not, what statistical question

would you ask?

Mixed Practice

7) Is the ratio a part-to-part, part-to-whole, or whole-to-whole comparison? Explain what the ratio means

in words.

Jamal wrote the ratio 3:10 to compare the number of homework problems he completed

to the number of homework problems in all.

8) Sasha is shipping an object with a length of 1.5 feet, a width of 3 feet, and a height of 1 foot.

What volume of the shipping box will remain after the object has been placed inside it?


18y = 144

10) What is the LCM of 8 and 80?

Word Problem

11) What are some things to consider when writing a statistical question?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we solved problems involving variability. Here’s an example!

Anastasia is taking her car for an emissions test. Carbon dioxide levels in her car emissions can be

between 13% and 16% and oxygen levels can be between 0.3% and 1.5%.

Will the data for the cars that pass the test have more variability in the carbon dioxide levels or in

the oxygen levels? How do we know?

There will be greater variability in the carbon dioxide levels because they can be between 13% and 16%,

or vary by 3 percentage points. The oxygen levels can only be between 0.3% and 1.5%, so they only vary

by 1.2 percentage points.

1) Dara asked the 6th graders in her class: What is your favorite animal? She got too many different

responses. Explain how you would help Dara decrease her variability.


2) A restaurant asked its customers to rate two new dishes on a scale from 1–10 with 10 being the best

dish and 0 being the worst dish. So far, they received the following results. Which of the two new

dishes should they add to their menu? Explain your thinking. Be sure to discuss the variability of each

dish’s ratings in your explanation.

3) Joe is selecting a new printer. Printer A has an ink cartridge with enough ink to print 200–1,000 4 × 6

photos and printer B has an ink cartridge with enough ink to print 800–900 4 × 6 photos. Which printer

should Joe pick? Explain your thinking.

Mixed Practice

4) Kamryn wants to know more about her community’s swimming pool. Which is NOT a good statistical

question she could ask?

a. How many days do you visit the pool during the summer?

b. About how many hours do you usually stay at the pool during each visit?

c. How many miles do you live from the pool?

d. How many days is the pool open during the summer?


5) Graph x < –0.5 on the number line.

6) If 3 feet are in 1 yard, how many feet are in

173

2yards?

7) Multiply.

0.153 • 64

Word Problem

8) The teacher of a cooking class asked her students to measure the volume of one batch of their

favorite cupcake batter. Will there be more variability in the volumes reported by the class if the

teacher asks them to find the volume in tablespoons or cups? Explain your thinking.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we analyzed data on bar graphs and circle graphs. Here’s an example!

We can use circle graphs and bar graphs to display categorical data. The graphs below display Meg’s

daily activities during the week.

In both graphs it is easy to see that Meg spends the most time at school. In the circle graph, we can tell

that Meg spends about 50% of her time each weekday at school. In the bar graph, we see the actual

amount of time Meg spends at school; it’s about 8 hours.


1) Paul took a survey to see which kind of dog his classmates liked the best out of the four options he

gave. From which graph would it be easiest to see which type of dog is the most popular choice?



2) Maslin made a circle graph to display the type of music on his playlist. He listens to World Party, Pop,

Rock, Jazz, and R&B, and has 210 songs on the playlist.

a. Complete the graph by labeling the missing categories.

• 3

2 of the playlist is R&B

• There is an equal number of Pop and Rock on his playlist.

b. How many R&B songs are on the playlist?

c. Is a circle graph an appropriate way to display the data? Explain your thinking.

3) Chef Damon wants to remove one item from his current menu. He collected data by surveying his

customers; he asked which of his dishes is their favorite, and then planned to remove the least

popular dish. Which graph best represents the data Damon is looking for? Explain your thinking.


4) Mrs. Cooley keeps track of each team of four in her art class. Each member of the team has to

complete 10 projects by the end of the year for the team to pass the class. This is the data she

collected for one team:

a. Which student is halfway completed with their project goal for the year?

b. How many more projects does the team still need to complete in all?

c. Is a bar graph an appropriate way to display this data? Explain your thinking.


Mixed Practice

5) Which is closer to 0?

–0.35 or 0.4

6) Is 5n + n + 20 equivalent to 6n + 20?

7) Draw a net to represent this figure. The base of the shape is an equilateral triangle.

8) Write the ordered pair for point A.

Word Problem

9) Janice is collecting data on how she spends her money each month. Her categories will include

housing, utilities, health care, food, transportation, clothing, recreation, and other. Will a circle graph

or bar graph help her best show the percent of money she spends in each category?



Homework Problems

Name



Questions…

#’s

Quick Look

Today we analyzed numerical data in stem and leaf plots, histograms, and dot plots. Here’s an example:

Mr. Zimmerman collected data on the number of minutes his students read last night.

10

28

20

22

35

22

26

12

15

14

17

18

15

20

25

25

20

Stem and leaf plots are helpful for organizing data.

Dot or line plots display each piece of data as a dot or ‘X’ on the number line.


Histograms show the frequency of data.

We use different types of graphs to highlight different information. In the stem and leaf plot and the dot

plot, we can see every data point. On the dot plot it is easy to see outliers (like 35 minutes), the least time

spent reading (10 minutes), and the most time spent reading (35 minutes). In the histogram, we can

quickly see the number of students who read in each time interval

1) Are there any outliers? Explain which graph you used to find the answer.


2)

a. Jen said that temperatures in June ranged from 80°F to 104°F. What’s wrong with her thinking?

b. In which range do temperatures most frequently fall?

c. In which range do temperatures least frequently fall?

3)


a. What is the most common number of math problems answered correctly?

b. How many answered less than 10 problems correctly?

Mixed Practice

4) What is the length of side AD?

5) Which values in the set make the inequality true?

x – 67.5 < 10, for f = {68, 77.5, 80, 100}


5

4, 85%, 0.78, 75%

7) Find the area.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we created dot plots. Here’s an example!

Alicia recorded the weights (in ounces) of the newborn kittens born on her farm this year.

3.4 4.0 3.2 3.6

3.1 3.4 3.5 3.5

4.1 3.3 3.7 3.5

We can draw a dot plot to display this information. Dot plots help us organize data so we can draw more

conclusions from it.

We can draw different conclusions from the dot plot such as: the most frequent weight for a newborn

kitten on Alicia’s farm is 3.5 ounces. This graph does not tell us everything we may want to know about

the situation. For example, we do not know how many litters of kittens were born this year.

The title tells us what the

data is about and

includes the units of

measurement (ounces).

Be sure to set a

scale that is

appropriate for the

data. The data

here is from 3.1 to

4.1 ounces, so the

scale has a tick

mark for every

0.1 ounce.


1) A jewelry store recorded the weight, in carats, of diamonds they sold during their weekend sale.

Weight

(carats) 4

1

2

1

4

3 1 1

4

1 1

2

1 2

Number of

Diamonds 8 5 4 7 3 2 1

a. Draw a dot plot on grid paper for the data.

b. Draw one conclusion from the dot plot.

c. Write one question that cannot be answered by looking at the dot plot.

2) A principal recorded the ride length, in minutes, for each of the morning buses.

a. Draw a line plot on grid paper for the data.

b. Draw one conclusion from the dot plot.


3) A burger restaurant recorded the prices, in dollars, for each burger on their menu.

$3.00 $3.50 $3.50 $3.75 $4.00 $3.75

$6.00 $3.25 $4.00 $4.00 $3.75 $3.75

$3.75 $4.50 $4.50 $4.25 $3.50 $3.25

a. Draw a dot plot on grid paper for the data.

b. Does this data have any outliers? If so, what are they?



Mixed Practice

4) Rose is asking students how many minutes

they exercise each week. Will the data

collected be categorical or numerical?

5) Use the Properties of Addition to simplify the

expression. Be sure to combine like terms.

(3t + 5) + (9 + t) + 1

6) Find the surface area of the rectangular prism.


20 meters below sea level

Word Problem

8) How many more students ate 2 slices of pizza than 3 slices of pizza?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we created histograms. Here’s an example!

Zoe recorded the number of online videos her classmates watch in one week.

14 6 5 8 4 12

15 11 3 0 13 18

25 21 15 18 6 11

Most students watch fewer than 20 videos each week.

The graph does not tell us how many students watched exactly 10 videos. It also does not tell us how

many minutes students spend watching videos.

Each bar

represents a

range of

numbers.

The y-axis

goes from 0 to

6 because the

greatest

frequency is 5

responses.


1)

a. Draw one conclusion from the histogram.

b. Write one question that cannot be answered by looking at the histogram.

2) A printing company tracks how many days one black ink cartridge lasts in home printers.

123 536 836 259 152

91 60 73 31 185

682 289 135 452 620

285 185 481 301 528

a. Create a histogram on graph paper to display the data.

b. Draw one conclusion from the histogram.

c. Write one question that cannot be answered by looking at the histogram.

3) A new cartoon on television recorded the ages of its viewers.

Age 3 4 5 6 7

Number of Viewers 23 74 83 43 19

a. Create a histogram on graph paper to display the data.

b. Write one conclusion from the histogram.

c. Write one question that cannot be answered by looking at the histogram.


Mixed Practice

4) What is the value?

|352|

5) Evaluate.

7.3(17 – 13)2

6) Mark spent $37.98 for 80 fluid ounces of a

blue liquid for a chemistry experiment. How

much did he spend per ounce?

7) What is the surface area?

Word Problem

8) On a histogram, sometimes each bar represents a single number, and other times each bar

represents a range of numbers. Pretend you’ve been asked to show a given set of data on a

histogram. Explain how you would determine if the bars on your histogram should represent one

number or a range of numbers.

All faces are congruent

equilateral triangles.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we created line graphs. Here’s an example!

Denisha’s Heart Rate (in beats per minute) on Swings

resting 2 minutes 4 minutes 6 minutes 1 minute after stop

77 82 100 112 90

This is a line graph because it shows Denisha’s heart rate over time. At any point during this activity,

Denisha has a heart rate.

Each dot represents one piece of data and line segments connect the dots. We can guess that Denisha’s

heart rate was about 80 beats per minute at 1 minute.

Denisha’s heart rate changed the most between 6 minutes after starting the exercise and 1 minute after

stopping.

The trend is that Denisha’s heart rate increases when she started swinging and then decreases after she

stops swinging at 6 minutes.


1) Use the data below to answer the following questions.

Temperature on December 3 in Dominic’s Town

Time Temperature

12 a.m. –3°F

3 a.m. –3°F

6 a.m. –4°F

9 a.m. –5°F

12 p.m. –1°F

3 p.m. 3°F

6 p.m. 2°F

9 p.m. –1°F

a. Draw a line graph to show the data.

b. During which period of time did the temperature increase the most?

c. What is the trend shown on the graph?

2) Use the line graph to answer the following questions.


a. Can you determine the highest water level of Deb’s tub from this graph? Explain your thinking.

b. What is the trend show on the graph?

3) Is a line graph appropriate for this data? Explain your thinking.

Mixed Practice

4) Mr. Born surveyed 90 of his English students to find out what their favorite types of books are.

How many students responded with graphic novel?


5) John wants to figure out what types of activities to plan for the student field day. His survey question

is: Did you participate in field day last year?

Did John ask a good statistical question? Why do you think so? If not, what statistical question would

you ask?

6) Add.

4

14+ 5

6

1

7) Solve using mental math.

432 = 10n

Word Problem

8) What it the trend shown in the graph?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we drew graphs to display different sets of data. Here’s an example!

We can display this information on a

bar graph. It would not be appropriate

to display all of the data using a

histogram because the subjects are

not broken into equal size intervals.

The graph shows that more people

are enrolled in college than in high

school. This could be because people

in high school are about ages 14 to

18, and people in college could be

ages 17 to 100 or more!

The U.S. Census Bureau collects data to determine

the number of people enrolled in school.

http://factfinder2.census.gov/faces/tableservices/jsf/

pages/productview.xhtml?pid=ACS_11_1YR_S140

1&prodType=table

We can enter the data into a

spreadsheet to create a graph. The

independent variable goes in the

first column.


1) The World Bank collects data on the number of internet users, per 100 people, in

different countries.

a. Visit http://data.worldbank.org/indicator/IT.NET.USER.P2 and record the percentages of internet

users for eight different countries. If you do not have access to the internet, you can use the

data below.

Percentage of Internet Users

Country Name 2011

U.S. 78.2%

Ethiopia 0.8%

Argentina 47.7%

Costa Rica 42.2%

France 76.8%

Iceland 96.6%

Singapore 75.1%

Egypt 35.6%

b. Create an appropriate data display (on graph paper or spreadsheet software) for the data.

c. Draw one conclusion from the display.

d. Write one question that cannot be answered by looking at the display.

2) The Bureau of Labor Statistics collects data on how American spend their time.

a. Visit http://www.bls.gov/tus/charts/chart8.txt and record the average hours per day employed or

not employed students spend doing various activities. If you do not have access to the

internet, you can use the data below.

b. Create an appropriate data display (on graph paper or spreadsheet software) for the data.


c. Draw one conclusion from the display.

d. Write one question that cannot be answered by looking at the display.

Mixed Practice

3) Dan collected data on how many miles 300 people in his community drove each month. The

responses ranged from 0 miles to 1,150 miles. Would you show this data in a histogram, dot plot, or

stem and leaf plot? Explain your thinking,

4) Emiko is thinking of two whole numbers, and Betty has to guess what they are. Emiko gives Betty the

following clues: The two numbers multiplied together equal 36. When added together, the numbers

equal 15. What are the two whole numbers?

5) The cubes that make up the larger cube



6) Name the solid figure the net represents.

Word Problem

7) What graph did you draw to display the data in question 1? Explain why you chose this graph.


Homework Problems

Name



Questions…

#’s

Quick Look

Today we described the shape of data distributions, that is, what the whole set of data looks like when

graphed. We looked at data displayed in histograms and dot plots. We described the shape as

symmetric, skewed left or right and as having clusters, peaks, or gaps. We also answered questions

directly based on the shape of the data.

We used the following vocabulary about the distribution of data displayed in dot plots and histograms:

Skew – A graph is skewed if it is more developed on one side or in one direction than another. Skewed

graphs are not symmetrical and are skewed left or right depending on the direction of the “tail”.

The “tail” of a graph represents the outlier data.

Symmetric – A distribution of data is symmetric if there is a center of the data and the shape of the data

to the left and right of that center mirror each other.

Gap – Gaps are large spaces in the data or intervals where there is no data.

Peaks – Peaks in the data look like the top of a hill that slopes on either side. Peaks are values with a

higher frequency than their neighbors.

Cluster – Clusters are “clumps” of data separated by gaps.

For example,

We can describe the distribution of data on this graph by saying it is approximately symmetrical.

The data starts low on the left, rises in the center, and descends on the right. The peak at 70-74 is

not in the center, which prevents this from being truly symmetrical. Also, this data has no gaps or clusters.


1)

a. Use words to describe the shape of the distribution in the graph.

b. What do the gaps in the distribution tell you about the number of hours the students slept?


2)


b. Are there any peaks in the data? If so, what does that tell you about the vacation days left?


3)


b. Does the data distribution indicate that more families have 2 to 5 members or 6 to 9 members?

Mixed Practice

4) Find the surface area.

5) Name the independent and dependent variables in the situation.

As the temperature gets colder, the money spent on heating a house increases.

The base

is a square.


6) Find the area.

7) Kara wants to know how many days of school her classmates have missed. Her survey question is:

How many days have you been sick this year?

Did Kara ask a good statistical question? Why do you think so? If not, what statistical question

would you ask?

Word Problem

8) Shantel is trying a new tutoring method for her students. She quizzed her students on April 1 and

then began the new tutoring method after the quiz. What does the shape of the graphs indicate about

her new method?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we made box-and-whisker plots. These plots show the data distribution divided into quartiles, or

quarters, of the full set of data. We also identified the extremes, quartiles, range, interquartile range, and

median. We used the following vocabulary when we constructed the box-and-whisker plots:

Extreme – The greatest and least numbers in a set of data are the upper and lower extremes.

Range – The range is the difference between the greatest and least values in a set of data. The range

can also be given as an interval.

Median – The median is a number arrived at by counting to the middle of an ordered array of numerical data.

Quartile – The upper and lower quartiles are the medians of the upper and lower halves of the ordered

data values.

Interquartile range – The distance between the first and third quartiles is the interquartile range. This

number serves as a very useful measure of variability.

To make a box-and-whisker plot:

1) Write all the data values in ascending order.

2) Identify the upper and lower extremes.

3) Find the median of the data set.

4) Find the upper and lower quartiles.

5) Plot these numbers above a number line; box in the quartiles and draw whiskers from the

quartiles to the extremes.

For example, given the set of data: 64, 81, 169, 25, 1, 225, 49, 144, 16, 196, 9, 36, 4, 100, 121

1) Rewrite it in order: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

2) The lower extreme is 1 and the upper extreme is 225.

3) The median is 64.

4) The lower quartile is 16 and the upper quartile is 144.

5) The box plot appears like this:


1) Use the data below to construct a box plot.

2) Use the data to answer questions a–c:

Julius’ recorded how many steps he took each day for two weeks: 6,200; 6,250; 6,220; 6,210; 6,240;

6,255; 6,270; 6,205; 6,225; 6,230; 6,280; 6,270; 6,205; 6,265.

a. What is the lower quartile?

b. What is the interquartile range?

c. What is the upper extreme?




Ashlee is getting ready for volleyball try-outs. She keeps track of how many times she can bump the

ball in the air to herself before it drops. Here are her bumps today: 12, 28, 22, 18, 30, 15, 30, 16, 27,

21, 24, 23, and 31.

a. What is the range?

b. What is the median?

c. What is the upper quartile?



Alysa’s homework points (out of 20): 18, 16, 15, 17, 20, 16, 20, 0, 14, 19, 20, 15

a. What is the upper quartile?

b. What is the range?

c. Where is 16.5 is relation to the shape of the data?


Mixed Practice

7) Find the area of the quadrilateral.

8)



b. What is the surface area of the

rectangular pyramid?

9) Find the volume.

10) Donna puts 8 tablespoons of milk in the cake she’s baking. How many gallons of milk did Donna use?

Word Problem

11) Tydia surveyed her classmates about how many text messages they sent yesterday. 50% of the data

is between 51 and 80. The least number of texts was 25 with a range of 60. What will Tydia’s graph

look like?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we compared box plots. Box plots are an excellent way to compare data sets because the middle

of the data and the quartiles are clearly marked and easy to interpret. Today we described the shape of

the distribution and discussed what that meant in terms of the other box plots. We looked for key

differences between the box plots and answered questions based on the data.

For example, if we examine these box plots, there are several things we can deduce based on the shape.

The Regular Season box plot is approximately symmetrical but the Playoffs box plot is skewed

right. During the regular season, the all-time leaders scored about 22 points per game whereas

all-time leaders in the playoffs scored about 25 points per game. We can also see that about 50%

of the points per game scored during the playoffs was greater than 75% of the points per game

scored during the regular season.

The plots show there is a very clear difference in the number of points per game scored during different

times in the basketball season.


Directions for questions 1–4: Use the box plots to answer the questions.

1)

a. Describe the key differences between the sales for January and February.

b. In which month were there more sales?

2)

a. Describe the key differences between the time spent exercising on the three days.

b. Does the data indicate that these adults generally exercised more on Sunday than Saturday?


3)

a. Describe the key differences between the price of domestic crude oil.

b. Does the data indicate that the price of crude oil has gradually increased over the years?

4)

a. Describe the key differences between the number of wins of the two teams.

b. Can you tell which team has won more games?


Mixed Practice

5) Find the area.

6) Find the median, lower quartile, and upper quartile for the following data:

Vashti’s minutes spent practicing piano this week: 0, 12, 33, 19, 40, 0, 26


Quinn made lasagna for a party and cut it into equal-sized servings. His party guests ate

39 servings of lasagna. If there were 9 servings left at the end of the party, then how many

servings of lasagna did Quinn make for the party?

8) How much is 68% of 202?

Word Problem

9) Julio is doing a science experiment on the effects of growing bean sprouts in soil versus water.

He recorded the growth of his bean sprouts over 9 weeks as follows (in centimeters):

Bean sprouts in soil: 2, 2, 3, 3, 3, 4, 4, 5, 5

Bean sprouts in water: 2, 3, 3, 4, 5, 5, 6, 7, 7

If Julio makes a box plot for each set of data, what will be the shape of the distributions?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we found the mean, median, and mode of a data set. We worked with whole numbers, fractions,

and decimals. We already know how to find the median from our work with box plots. Today we learned

how to calculate the mean of a data set.

Mean = sum of data ÷ number of data items

We also found the mode, the number that occurs most, in a data set. When all numbers in a data set are

different, there is no mode. If there is more than one mode, all the most frequently occurring numbers

must be recorded. For example, in this data set; 15, 34, 49, 55, 37, 44, 48, 49, 30, 3, 55; the mean is

39.2, the median is 40.5, and the modes are 49 and 55.

1) Darius is keeping track of how long his classmates study during the week, in hours. Here are this

week’s results:

42

1, 6

4

1, 8

5

1, 5

2

1, 9

4

1, 7

5

2, 10

4

1, 9

5

1, 5

2

1, 4

2

1, 6

5

1, 4

2

1, 8

4

1, 7

5

2, 4

2

1, 5

5

1, and 4

2

1.

a. Find the mean, median, and mode of his classmates’ study times.

b. In this situation, describe what the mean represents in your own words.

2) In various cities in 2012, one gallon of gas costs: $3.29, $4.09, $3.49, $2.99, $2.89, $2.59, $3.59,

$4.19, and $3.89.

a. Find the mean, median, and mode of the prices.


b. If another data value, $2.29, is included, what would that do to the mean, median, and mode?

3) Hipolito measured the heights of students in his class in centimeters. Find the mean, median, and

mode of his results.

134 179 139 178 172

141 144 169 152 165

172 149 154 144 164

a. Find the mean, median, and mode of the students’ heights.


4) The monthly precipitation amounts (in inches) for the year were: 3.97, 1.97, 4.00, 1.53, 1.49, 4.20,

8.53, 6.88, 6.19, 5.89, 1.51, and 2.24.

a. Find the mean, median, and mode of the monthly precipitations.


5) The first line of the sheet music had notes with the following lengths:

4

1,

2

1,

4

1,

8

1,

4

1,

4

1,

4

1,

2

1,

8

1,

4

1, and

8

1.


b. If 4

1 were added to the data, what would that do to the mean, median, and mode?


6) Amy saw jeans advertised for the following prices at the mall: $46, $48, $39, $76, $58, $63, $57, $75,

$46, $56, $46, and $62.


b. If $145 were added to the data, how would that affect the mean, median, and mode?

Mixed Practice

7) 5.1284 + 54.5797

8) 18

7 ÷

9

5

9) How much is 25% of $120?

10) Brianna wants to know more about the games that students in her class play. She asked: What is

your favorite game? Every student responded with a different game. Explain how you could help

Brianna decrease her variability.

Word Problem

11) In 1990, the budget for the end-of-the-year play was $575. Each year, the budget has increased by

$5. How much was the budget in 2005? Find the mean, median, and mode of budget from 1990 to

2005.


Homework Problems

Name



Questions…

#’s

Quick Look

Today, we examined data sets to decide whether the mean or the median is the better measure of center

in the context of the questions posed. We learned that sometimes the mean is not the best measure of

center. When outliers skew the data, the mean has a tendency to be pulled toward the extreme value,

usually much more than the median.

For example,

Last week’s high temperatures were 78, 82, 85, 84, 81, 78, and 79. The mean is the best measure of

center for this situation. The data is not affected by any outliers that could skew the mean towards an

extreme value.

1) Lenny’s scores during the gymnastics tryouts were: 7.8, 8.1, 8.3, 7.8, 8.5, 8.4, 7.7, 7.9, 8.2, and 8.0.

Which measure of center, the mean or median, is best to use when describing this data?

2) A small village has a population of 100 people. One resident is a millionaire. The rest of the villagers’

incomes range from $50,000 to $75,000. Which measure of center, the mean or median, is best to

use when describing this data?

3) The areas, in square miles, of ten countries in Europe are shown in the table. Which measure of

center, the mean or median, is best to use when describing this data? Explain your thinking.

Country Area, in square miles

Germany 137,846

Greece 50,942

Italy 116,305

Norway 125,182


Poland 120,728

Russia 6,592,771

Spain 194,897

Sweden 173,732

Ukraine 233,090

United Kingdom 94,525

4) The table represents one stock’s increases over a two-week period. Which measure of center, the

mean or median, is best to use when describing this data? Explain your thinking.

98

5 7

8

1 7

8

4 8

8

3 6

8

2

58

6 4

8

3 6

8

2 5

8

7 5

8

5

5) Ted weighed some pumpkins in pounds. Which measure of center, the mean or median, is best to

use when describing this data?

53

1 6

4

3 6

8

5 5

16

13

64

1 5

8

7 6

16

3 5

16

11

516

13 6

2

1 5

16

15 6

8

7


6) Rae’s phone bill lists the number of texts transmitted. Which measure of center, the mean or median,

is best to use when describing this data?

Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Number

of Texts 125 45 70 65 9 81 165

Mixed Practice


x + (6,225 + 3,881) = 12,345

8) Use mental math or guess and check strategies to find three solutions to the inequality.

50 > 3c

9) Name the independent and dependent variable in the situation: The more Reyes studies, the better

his grades.

10) One very hot day Shauna drank 3 gallons of water. How many cups is that?

Word Problem

11) Chet went online to check out restaurant ratings. The scores were based on taste, service, and wait

times. Restaurants scores ranged from 0 (lowest) to 10 (highest). Why do you think Chet decided to

go to Restaurant B? Explain your reasoning.

Restaurant A: 7, 7, 3, 2, 4, 7, 8, 7, 8, 5, 6, 4, 8, 5, 7

Restaurant B: 7, 7, 6, 7, 8, 7, 6, 7, 7, 8, 7, 6, 7, 8, 7


Homework Problems

Name



Questions…

#’s

Quick Look

Today we learned about the spread in a data set. First we chose the measure of center that represented

the data set. We learned that when the mean is the best measure of center, we find the mean absolute

deviation (MAD) for the measure of spread. We also learned that when the median is the best measure of

center, we find the interquartile range (IQR) for the measure of spread. Then we discussed what the

measure of variation tells us about the data.

To find the mean absolute deviation (MAD):

Step 1: Find the absolute value of the distance between each data value and the mean.

Step 2: Find the mean of the distances.

To find the interquartile range (IQR):

Step 1: Identify the lower and upper quartile values of the data set.

Step 2: Subtract the lower quartile from the upper quartile.

For example, this chart lists the high temperatures in a city over a two week period.

81 80 82 82 83 85 86

88 102 105 88 86 84 83

When we find the mean of the data (86.78) and the median (84.5), we see that the mean is affected by

the higher temperatures, whereas the median is less affected. Since the median is the best measure of

center, we find the interquartile range by subtracting the lower quartile from the upper quartile. So the

measure of spread is 6, which is close to zero. This tells me that the middle half of the data is consistent,

or the high temperatures are very close together.


1) Nelle used an online retailer to compare prices for keyboards. One retailer’s mean is $288 and has a

MAD of $202.80.

a. Which histogram could show that online retailer’s data?

Graph 1

Graph 2

Graph 3

b. What do these measures tell you about the data?


2) The boys in Donte’s class had a contest to see who could do the most push-ups in one minute. The

results were 34, 39, 30, 34, 36, 32, 29, 36, and 31.

a. Which measure of center, the mean or median, is best for this data?

b. What does the measure of variation tell you about the data?

3) Guy graphed the running times of the Best Picture winners from 1950 to 1970.

a. Looking at the graph, what measure of center, the mean or the median, is best for this data?

b. The graph’s measure of variation is 57. What does this indicate about the spread of the data?

4) Horatio made a wish list of presents he wants for his birthday. The prices were: $20, $25, $35, $15,

$40, $30, $18, $22, $28, and $120.


b. What does the measure of variation tell you about the data?

5) Donna is researching the ages of governors in 2012, specifically in the western section of the United

States. Here are her results:

State AK AZ CA CO HI ID MT NV NM OR UT WA WY

Governor’s

Age in

2012

46 64 72 58 72 64 49 47 51 63 62 57 48



b. Find the corresponding measure of center.

c. What do these measures tell you about the data set?

Mixed Practice

6) Use words to describe the shape of the distribution in the graph.

7) Jazmin is researching average life spans of captive animals (in years). On graph paper, create a

histogram to display the data.

18 26 17 36 24 11 21

21 17 10 7 9 20 29

14 50 7 25 27 5 8

8) As class president, Leonard needs to represent student concerns to the teachers and administrators

of his school. He wants input from all the students at the school. Write one statistical question that will

help the class president find out what issues or problems are most important to students.


9) Find the mean, median, and mode of the data set. The heights of the first 20 US Presidents (in

inches): 74, 67, 742

1, 64, 72, 67

2

1, 73, 66, 68, 72, 68, 68, 69, 70, 72, 76, 70, 68, 68

2

1, and 72.

Word Problem

10) Reynaldo recorded the retail prices for different cars he saw on the street, in thousands of dollars. His

data are: 12, 56, 22, 45, 33, 40, 26, 15, and 36. Without calculating, what does the data tell you about

the variation of the prices Reynaldo recorded?


Homework Problems

Name



Questions…

#’s

Quick Look

Today we solved multiple-step problems about real-world situations involving data. We investigated math

stories for necessary information. We analyzed and determined the best measure of center for each data

set. We also analyzed what the measure of spread told us about the data set. Then we answered

questions related to the problem.

For example:

If you were shopping through an online retailer, you would examine the ratings of different companies.

You would also see what their performance has been over a period of time and how it has or has not

improved. You would also compare one retailer against another to see who has the best results. All of

these things involve looking at and analyzing data.

1) A local art collector purchased 5 small paintings from an online auction. She paid: $250, $180, $350,

$295, and $325.

a. There is a processing fee that is 5% of the total purchase. What is the fee the art collector paid?

b. If she can prove the paintings are originals by a noted artist, she can sell each piece for twice the

purchase price. What would be the mean price if she could prove this?

c. If she does not prove validity, the actual value will be half of what she paid. What will be the

value of each painting if she does not get proof?

d. Find what percent of the total value the processing fee is if she proves they are original paintings.

Also find the percent if they are not original.


e. Use box plots to graph: (1) the purchase price of the paintings, not including the fee, (2) the

values if they are original, and (3) the values if they are not original. Then compare

the distributions.

Mixed Practice

2) Which treats have 50 or more responses?

3) Which of the following questions are statistical questions you could ask about the pottery?

a. How many pots are in this collection?

b. What countries are the pots from?

c. What is the average amount of money

Americans spend on pottery in one year?

d. What is the volume of the pots?


4) What is the surface area?

5) Graph the inequality (3 > y) on the number line.

Word Problem

6) What conclusions could you draw based on the following graph?

The base

is a square.


Homework Problems

Name



Questions…

#’s

Quick Look

Today you learned about market research and target audiences. Businesses use market research to

help them make decisions about what items and services to offer their customers. The data they compile

from their research helps them to make better products and offer better services that will appeal to the

most people. This is important for businesses to make enough money to be profitable and to keep doing

more business.

When a business does market research they have to make sure to work with members in their target

audience to get the most helpful data to make business decisions. For example, if a company creates

office supplies, their target audience would be people who worked in and managed offices. They probably

would not want to survey children in elementary school or retired couples.

Finally, today you created a survey of questions for your new travel agency to help you do market

research about the vacation destinations and the activities that would most appeal to families to buy your

three-day Family Weekend Vacation Getaway. This week you will use the data from your survey to create

data displays and to make decisions for your travel agency business.

For your travel agency you also want to know the best way to reach new potential customers. What kind

of advertising should you do? Tonight, you will create a short survey for your customers to help you

determine what sort of advertising might be most effective.

1) Brainstorm the different ways that businesses do advertising. (Hint: Businesses use many methods to

get in touch with potential customers. Think about T.V., mail, email, and internet advertising to get

started with your list.)


2) Use your brainstorm from question 1 to create a good survey question to ask potential customers to

help you know the best possible method to advertise and reach your customers.

3) Describe the target audience for your survey question from question 2. Think about who sees

advertisements and makes decisions about purchasing vacation packages from a travel planner.

4) What kind of data will you get when you ask your survey question from question 2, categorical or

numerical? What type of data display might you use for that data? (Hint: line/dot plot, bar graph,

histogram, line graph, circle graph, or box plot)

5) You also want to know how much small businesses, like yours, typically spend on advertising each

month. Who would be the target audience for a survey question about advertising costs?

6) Write a good survey question that will help you gather data about the monthly advertising costs for a

small and new business.

7) What kind of data will you get when you ask your survey question from question 6, categorical or

numerical? What type of data display might you use for that data? (Hint: line/dot plot, bar graph,

histogram, line graph, circle graph, or box plot)


Mixed Practice

8) Janet is analyzing her current test scores in math. So far this semester, she has the following scores:

88, 97, 94, 83, 99, and 79. What is her mean, or average, test score?

9) What is Janet’s median test score?

10) Which measure of center (mean or median) do you think better describes the center of Janet’s test

scores? Why do you think so?

11) What is 129% of 45?

Word Problem

12) Why do you think it is important for a business to identify their target audience, conduct market

research, and analyze the data they get from their research?


Homework Problems

Name



Questions…

#’s

Quick Look

Today you continued your research as an up and coming travel planner! You used the data gathered from

the survey you created yesterday to create various data displays. You thought about the types, amount,

and variety of data you gathered to make the best decisions about which data displays you would use.

For categorical data, you had to choose between a dot plot, a circle graph, and a bar graph to best

represent your data. For numerical data, you had to choose between a line plot, a stem-and-leaf plot, a

box plot, a histogram, and a line graph to best represent your data.

For homework, you will use data concerning advertising for your travel business to make new data

displays. In the next lesson, you will use the data displays you have created to analyze your data, design

a family vacation package, and to make decisions for your new business!

Directions for questions 1–3: Use the given data to help you answer each question.

When 50 randomly chosen people in families in your community were chosen for your survey, they

were asked, “Which method of advertising do you encounter more each day: television commercials,

radio ads, magazine ads, advertisements on web pages, or billboards?” You received the following

data to the question.

Television commercials: | | | | | | | | | | | | |

Radio ads: | | | | |

Magazine ads: | | | |

Advertisements on web pages: | | | | | | | | | | | | | | |

Billboards: | | | | |


1) Describe the data that was gathered with this survey question. Is it numerical or categorical? How

many pieces of data are there? How many DIFFERENT responses are there (for example, ‘red’ and

‘blue’ are different responses, ‘red’ and ‘red’ are not different responses)?

2) What are the possible ways that you could display the data from this survey question?

(Hint: line/dot plot, bar graph, histogram, line graph, circle graph, or box plot)

3) Which data display will you choose for the data about types of advertising? Create that display using

the data collected from this survey.

Directions for questions 4 and 5: Use the given data to help you answer each question.

Another small travel planning business in your area answered a survey to share data on how much it

spends on average for advertising costs each month for the past year. Here the data:

January: $15,000 February: $12,000 March: $10,000 April: $20,000

May: $25,000 June: $25,000 July: $20,000 August: $18,000

September: $12,000 October: $10,000 November: $10,000 December: $12,000

4) Describe the data you gathered from this survey question. What are the possible ways that you could

display the data? (Hint: line/dot plot, bar graph, histogram, line graph, circle graph, or box plot)


5) Which data display will you choose for the data about this business’s monthly spending on

advertising? Create that display using the data collected from the survey.

Mixed Practice

6) About what is the change in enrollment at Issac’s school between 1990 and 2005?

7) Based on the trend in the graph of the enrollment data from Issac’s school, what do you predict the

enrollment will be in 2015?

8) Order the following from least to greatest.

0.382 38% 0.0999 51

19

9) Rewrite the expression using an exponent.

4 • 4 • 4 • 4 • 4


Word Problem

10) Explain why one data display might be preferred over another for a particular data set. For example,

why might you choose to use a histogram to display your data instead of a stem-and-leaf plot?


Homework Problems

Name



Questions…

#’s

Quick Look

Today you completed the analysis of the data you collected and graphed about a family weekend

vacation. You used the graphs and plots you made to show the data you collected, then you analyzed

them to decide the location of the vacation, the number of family activities it would include, and what

those activities would be.

You also created the first draft of your email blast that you will send out to potential new customers. This

email included your contact information as well as the details about your first travel package, the Family

Weekend Vacation Getaway!

Tonight, you will continue to work on analyzing marketing data for your travel planning business. You will

use graphs to make decisions about the type of advertising that you will do for your business and about

how much money you would spend on a monthly basis for that advertising.

Directions for questions 1–4: Use the graph to answer each question.


1) Based on the bar graph, which type of advertising is encountered the most by people in families on a

daily basis? What is the type of advertising encountered the least? Why do you think the data looks

like this?

2) Which type of advertising do you think would be the most effective for your travel planning business?

3) Do you think that most businesses only use one type of advertising to reach potential customers?

Why or why not?

4) If you had to choose multiple forms of advertising to reach your customers, which would you choose

and why? Use the data in the graph to help you.

Mixed Practice

5) List the following from greatest to least.

–4.3 4.2 4.09

–5

6) Write an algebraic expression to describe the situation. Define any variable(s) that you use.

Andrew is 3.5 times older than Marnie.


9 + p = 44


8) What is the area of a right triangle that has a height of 6.7 inches and a base length of 5.3 inches?

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