Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department Dear Incoming Grade 8 Students,

To better prepare for Grade 8 mathematics entry process, summer work is assigned to ensure an easier transition into your next math course. The expectation is that all students bring the completed assignment to their first math class in the Fall 2013. If you need help completing the problems, you have a couple of options:

Visit links to examples, explanations, and instructional videos provided in the packet Use the copy of the textbooks available at the Duxbury Free

Library.

A TI-83(plus)/84(plus) graphing calculator will be necessary to complete the calculator section. All Grade 8 mathematics courses will use of this type of calculator.

Therefore, it is essential that every student obtain

one.

Grade 7 Topics Mastered Prior to Grade 8:

Ratios and Proportional Relationships• Analyze proportional relationships and use them to solve real-world and mathematical problems.

Percents• Solve percent problems using both the percent proportions and percent equation and the use them to solve real world problems.

The Number System• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Geometry• Draw, construct and describe geometrical figures and describe the relationships between them.• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

What Problems do I have to do?Please allow enough time over the summer to complete the following sections of the

Please keep in mind that non-calculator problems need to be completed without the use of any type of calculator.

All answers must be justified by showing all work.

Your Class Next Year Course # Complete These Sections

Pre Algebra 282 AHonors Algebra 281 B DAccelerated Algebra 1 280 B C D

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department Statistics and Probability• Use random sampling to draw inferences about a population.• Draw informal comparative inferences about two populations.• Investigate chance processes and develop, use, and evaluate probability models.Checklist

I finished the sections listed for my class by showing all work I have a graphing calculator I circled the problems that I didn’t understand or couldn’t correct on my own. My name, last year’s class, and last year’s teacher are filled out on the next page I filled out this checklist

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department Name__________________________________ Class I took last year (circle) 270 271 NEW

Teacher I had last year _____________________

SECTION A NON-CALCULATOR : M282 Students Show all work to justify your answers. Circle any problems that you don’t understand.

I. The Number System

Operations with Rational Numbers- Completely simplify each numerical expression.1) 11[( 25 – 8.7 ) –14] = 2) -12.6 – 3.2 – ( -20.75) = 3)

Adding negative numbers

4) (-51.2) (1.06) (0.5) = 5) 6) Division of fractions

Rational and Irrational Numbers1) Identify all sets to which the following number belongs: Rational, Irrational, Whole, Integer

2) Which point on the number line shows ?

3) Which of the following shows the rational numbers in order from least to greatest?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

4) Which of the following show the fractions in order from greatest to least?

5) Which number belongs to the set of rational numbers and the set of integers?

6)

7)

Applications with Rational Numbers

1) Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to get to the same meeting. How many more miles did the business partner drive than Hector?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department 2) The gas tank of Ty’s truck holds 19.8 gallons. When the tank is empty, Ty fills it with gas that costs $3.65 per gallon. How much will it cost to fill the tank?

3) To simulate space travel, NASA’s Lewis Research Center in Cleveland uses a 430-foot shaft. The free fall of an object in the shaft takes 5 seconds to travel the 430 feet.(a) Write an integer to represent the change in the height of the object.

(b) On average, how far does the object travel each second?

4) A scuba diver is 120 feet below the water’s surface. She then ascends 83 feet. What is her current depth? Write an addition equation and then find the answer.

5) Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

6) Angela painted 3/8 of a room. Todd painted 2/5 of the same room. What part of the room has been painted?

7) A high school Family and Consumer Science class has cups of flour with which to

make soft taco shells. There are cups flour per shell. How many soft taco shells can they make?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

Terminating and Repeating Decimals- Write each rational number as a decimal. Identify if it is terminating or repeating.

8) 9) 10)

II. Ratios and Proportional Reasoning: Percents , Ratios , Proportions

1) The table shows the eye colors of the students in Mr. Lee’s class. Use the percent proportion to find the percent of students with blue eyes.

2) The bill for the Morgan family at a restaurant was $62.14. Mr. Morgan would like to leave their server a 20% tip. How much of a tip will the server receive?

3) In a community of 3200 homes, 72% of the households participate in the community recycling program. How many households is this?

4) Last year there were 43 science projects submitted by students at a science fair. This year there are 52 science projects. To the nearest tenth, what is the percent of change in the number of science projects submitted?

5) The table shows the prices of different sized jars of peanut butter. Which of the jars has the least unit price?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

III. Expressions and Equations Properties1) Name the property shown by each statement.

(a) 42 + 36 = 36 + 42________________________________

(b) 16 + 0 = 16 ________________________________________

(c) (19 • 15) • 2 = 19 • (15 • 2) _____________________________

(d) 33 • 0 = 0 _______________________________

(e) (7 + 9) + 6 = 7 + (9 + 6) ________________________________

(f) 25 • 1 = 25 ________________________________

2) Which expression can be written as 7(c + d)? Explain your reasoning. A. 7c • 7d B. (7 + c) • (7 + d) C. 7c + 7d D. (7 + c) + (7 + d)

distributive property

Evaluate and Simplify Expressions

3) Evaluate each expression if x = -3, y = 4 and z = 2 (Note: the bars are absolute values)

(a) 10 – | x | (b) | z | +19 (c) 2y - | x |

4) Simplify using exponents: a•a•a•b•a•b•b•a•b•a =

Translate into Algebraic Expressions, Equations or Inequalities

5) Karen made 5 less than 4 times the number of free throws that Kimi made. Write an expression in simplest form that represents the total number of free throws made by both players.

6) The product of a number and -6.5 is -58.5. Write and solve an equation to find the number.

7) The quotient of a number and 6 is -14. Write and solve an equation to find the

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department number.

8) What value of d makes the equation true? (Solve the equation)

9) Solve each equation and graph the solution on the number line.

IV. Geometry

Scale Drawings1) Suppose a model of a dragonfly has a wing length of 4 cm. If the length of the insect’s actual wing is 6 cm, what is the scale of the model?

2) Rebecca used a scale of 1 inch = 2 feet to construct a scale model of a kitchen. The kitchencountertop in the model has a length of 8 inches. What is the actual length of the countertop?

Geometric Formulas: Circles, 3-D figures1) A circular pool has a circumference of 40 meters. How long is the rope going across the pool?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

2) Find the area of the circle:

3)

Angles4) In the figure, line a is parallel to b, and q and r are transversals. Classify the relationship between the following angles: (a) <2 and <3

(b) <13 and <15

V. Statistics and Probability

1) Find the mean, median and mode of the set of data:

2) A bag contains 7 pink, 2 white, and 6 blue marbles. One marble is selected without looking. Find P(blue). Describe if this is impossible, unlikely, equally likely, likely or certain.

3) What is the probability of tossing a penny and landing on heads three times in a row?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

4) The spinner is spun twice. What is the probability that it will land on 8 after the first spin and on an odd number after the second spin?

VI. The Coordinate Plane

1) Write the ordered pair that names each point. A= B= C= D= E= F=

b) Which point(s) on the coordinate plane above are located in a) Quadrant IV? b) Quadrant II? c) Quadrant I? d) Quadrant III?

2) The table represents a relation.

a) Graph it.b) Select the equation that represents the relation.

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

IF YOU ARE A COURSE 282 STUDENT, YOU ARE DONE WITH YOUR SUMMER PACKET

SECTION B NON-CALCULATOR: M280 and M281 Students Show all work to justify your answers. Circle any problems that you don’t understand.

I. The Number System

Operations with Rational Numbers- Completely simplify each numerical expression.1) 11[( 25 – 8.7 ) –14] = 2) -12.6 – 3.2 – ( -20.75) = 3)

Adding negative numbers

4) (-51.2) (1.06) (0.5) = 5) 6) Division of fractions

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

7) 20 – (-1.34 + ) = 8) 9) 12 + 68 • – 2 • 42 =

10) 5[2(8 – 5) + 1.5 – 2.5] 11) 5(32 + 2) – 2(62 – 52)

Applications of Rational Numbers1) Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to get to the same meeting. How many more miles did the business partner drive than Hector?

2) The gas tank of Ty’s truck holds 19.8 gallons. When the tank is empty, Ty fills it with gas that costs $3.65 per gallon. How much will it cost to fill the tank?

3) To simulate space travel, NASA’s Lewis Research Center in Cleveland uses a 430-foot shaft. The free fall of an object in the shaft takes 5 seconds to travel the 430 feet.

(a) Write an integer to represent the change in the height of the object.

(b) On average, how far does the object travel each second?

4) A scuba diver is 120 feet below the water’s surface. She then ascends 83 feet. What is her current depth? Write an addition equation and then find the answer.

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

5) Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

6) Angela painted 3/8 of a room. Todd painted 2/5 of the same room. What part of the room has been painted?

7) A high school Family and Consumer Science class has cups of flour with which to

make soft taco shells. There are cups flour per shell. How many soft taco shells can they make?

Terminating and Repeating Decimals- Show that each decimal is a rational number by changing it to a mixed number or fraction.

1) 2) 3)

4) 0.6666… 5) 1. 6) 0.030303…..

II. Ratios and Proportional Reasoning: Discount/Tax/Tip

1) Isabella is shopping for clothes at a department store. Before tax, her bill is $95.

(a) She has a coupon to receive an additional 25% off her total purchase. What is the total cost of her items before tax?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

(b) After she receives the discount, how much will her total bill be if there is a 7.95% sales tax?

2) Marcus borrowed $4000 to buy a car. If his monthly payments are $184.17 for 2 years, what is the simple interest rate for the loan?

3) The table shows the heart rates of different animals.

(a) What is the ratio of a cat’s mass to its heart rate? Express the ratio as a fraction in simplest form.

(b) Order the animals from greatest mass to heart rate ratio to least mass to heart rate ratio.

(c) Which animal had the greatest ratio? Explain your reasoning.

4) Determine whether the number of legs are proportional to the number of spiders. If the relationship is proportional, identify the constant of proportionality. Explain your reasoning.

III. Expressions and Equations

Properties1) Name the property shown by each statement.

(a) 42 + 36 = 36 + 42________________________________

(b) 16 + 0 = 16 ________________________________________

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department (c) (19 • 15) • 2 = 19 • (15 • 2) _____________________________

(d) 33 • 0 = 0 _______________________________

(e) (7 + 9) + 6 = 7 + (9 + 6) ________________________________

(f) 25 • 1 = 25 ________________________________

2) Which expression can be written as 7(c + d)? Explain your reasoning. A. 7c • 7d B. (7 + c) • (7 + d) C. 7c + 7d D. (7 + c) + (7 + d)

distributive property

3) Admission to a science museum is d dollars and a ticket for the 3D movie is t dollars. Which expression represents the total cost of admission and a movie for p people? Explain your reasoning.A. dtp B. p(d + t) C. p + (dt) D. d(p + t)

Evaluate and Simplify Expressions

1) Evaluate each expression if x = -3, y = 4, and z = 2

(a) 10 – | x | (b) | z | +19 (c) 2y - | x |

(d) 3y + 3z + | x | (e) | 4yz | – 3 | x | (f) 2(z + y) – | x |

Translate into Algebraic Expressions, Equations

1) Karen made 5 less than 4 times the number of free throws that Kimi made. Write an expression in simplest form that represents the total number of free throws made by both players.

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

2) The quotient of a number and 6 is -14. Write and solve an equation to find the number.

3) April has saved $144 to buy a new car. If m is the monthly payment for one year, the expression $12m + $144 represents the total cost of the car.

a) Find the monthly payment by using the most efficient method if the total cost of the car is

$5,088.

Geometry:Scale Drawings

1) The blueprint of a skateboard ramp shows that its length is 11.4 inches. If the scale of the blueprint is 1 inch = 6 feet, what is the length of the actual skateboard ramp?

Geometric Formulas

3) A ferris wheel has a circumference of 226 meters. What is the radius of the ferris wheel?

4) A hockey rink is shown below. If the shaded region is called the neutral zone, find the area of the neutral zone.

Angles

2) Find the area of the circle:

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department 5) In the figure, line a is parallel to b, and q and r are transversals. Classify the relationship between the following angles: (a) <2 and <3

(b) <13 and <15

V. Statistics and Probability

1) Find the mean, median and mode of the set of data.

2) A bag contains 7 pink, 2 white, and 6 blue marbles. One marble is selected without looking. Find P(blue). Describe if this is impossible, unlikely, equally likely, likely or certain.

3) The average wait times for 10 different rides at an amusement park are 65, 21, 17, 52, 25, 17, 11, 22, 60, and 44 minutes. Would the park advertise the mean or median to show that the wait time for its rides are short? Explain.

4) Each number on the dart board has an equal amount of the circle’s section.

If a dart is thrown, find each of the probabilities of it landing on each:

(a) P(odd) (b) P(prime) (c) P(greater than 20)

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

IF YOU ARE A COURSE 281 STUDENT, YOU ARE DONE WITH YOUR SUMMER PACKET

SECTION C NON-CALCULATOR: M280 Students Show all work to justify your answers. Circle any problems that you don’t understand.

Ratios and Proportional Reasoning

1) The line graph shows Alicia’s and Jermaine’s average rates in a race.

(a) Express each person’s speed as a unit rate.

(b) How long would it take Alicia and Jermaine each to run 1 mile? (Hint: 1 mile = 5280 feet)

(c) Suppose Max runs at a rate of 5 feet per second. Predict where the line representing his speed would be graphed. Explain.

2) A cell phone store displayed the phone at the right on a poster. The length of the phone on the poster is 3 feet 4 inches. Write a ratio comparing the length of the actual cell phone to the length of the cell phone on the poster as a fraction in simplest form.

3) The cost for pounds of meat is $7.20. Find the constant of proportionality. Then write an equation relating cost to pounds. How much will 4 pounds cost?

4) The number of students on a school trip is proportional to the number of teachers as

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department shown on the graph.

(a) Find and interpret the constant of proportionality.

(b) Explain what the points (0, 0), (1, 25) and (4, 100) represent.

5) A bushel of apples will make approximately 3 gallons of apple cider. The table shows the relationship between the number of bushels of apples and the number of gallons of apple cider.

(a) Given b, the number of bushels needed, write an equation that can be used to find g, the number of gallons of apple cider.

(b) How many bushels are needed to make 54 gallons of cider?

III. Expressions and Equations

Properties

1) Insert grouping symbols in the expression so the value of the expression is 14. Show calculations to obtain the 14.

9 + 39 + 22 ÷ 11 – 9 + 3

Evaluate and Simplify Expressions2) Evaluate each at the variable value given.

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

Translate into Algebraic Expressions, Equations or Inequalities

3) Dean made a collage on a square sheet of poster board. The perimeter of the collage is (20x + 12) centimeters. What is the length of one side of the collage?

4) Kurt and four friends are eating in the food court at South Center Mall. They will divide the bill equally among the five of them. Two friends order hamburgers and two order pizza. All of them order soda. Kurt has only $3.75 with him. What can Kurt order so that each will pay only $3.75?

V. Statistics and Probability

1) The ages of the players on a volleyball team are 29, 25, 26, 31, 28, 23, 21, and 25. Suppose a new player joins the team. What must the age be of the new player to have a mean age of 27? Explain your reasoning.

2) A school committee consists of 4 girls and 6 boys. How many girls need to be added so that the probability of selecting a girl at random is 70%?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

SECTION D NON-CALCULATOR: M280 and M281 Students Show all work to justify your answers. Circle any problems that you don’t understand.

I. The Coordinate Plane 1) Write the ordered pair that names each point. A= B= C= D= E= F=

b) Which point(s) on the coordinate plane above are located in Quadrant IV?

2) Suppose Javier’s school represents the origin on a coordinate plane. If Javier leaves school and bikes four miles et and then two miles south to the recreation center, what is the location of the recreation center as an ordered pair?

3) The table represents a relation. Graph it and select the equation that represents the relation

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

II. Equation Solving

Solve each equation and graph its solution on the number line provided.

1. x – 4 = -2 2. x + 7 = -3 3. 3x = 70

4. 5. 2d – 3 = 9 6. 4(x – 2) = -4

7) Which operation should be performed first to solve the equation 2x + 4 = 8?

8) What value of d makes the equation true? (Solve the equation)

9) A shipping company charges $3.50 plus $0.85 per pound to ship a package. Janet shipped a package and the total charge was $8.60. Write and solve an equation to find the number of pounds she was charged for the package.

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

10) Tisa bought movie tickets for herself and two of her friends. She paid $8.50 for each ticket. If Tisa has $14.50 left, write and solve an equation to find how much money she had before she bought the movie tickets.

11) Write a proportion, an equation, and solve the following: A muffin recipe calls for 4 cups of sugar and yields 36 muffins. If Amelia only wants to make 24 muffins, how much sugar she will need?

12) The enrollment at a community college this year is 115% of last year’s enrollment. If there were 1240 students enrolled at the college last year, write and solve an equation to find how many students are enrolled this year.

III. Rational and Irrational Numbers1) Identify all sets to which the following number belongs: Rational, Irrational, Whole, Integer

2) Which point on the number line shows ?

3) Which of the following shows the rational numbers in order from least to greatest?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

4) Which of the following show the fractions in order from greatest to least?

5) Which number belongs to the set of rational numbers and the set of integers?

6)

7)

8) Constance wants to sew trim around the sleeves and collar of a gymnastics leotard. She needs a piece of trim that is 12.25 inched long for the sleeves and a piece that is 19¾ inches long for the collar. She buys a 4-foot piece of trim. How much trim will she have left once she finishes the leotard?

9) Simplify the following quotient:

10) Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to get to the same meeting. How many more miles did the business partner drive than Hector?

11) Last year there were 43 science projects submitted by students at a science fair. This year there are 52 science projects. To the nearest tenth, what is the percent of change in the number of science projects submitted?

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

12) The table shows the prices of different sized jars of peanut butter. Which of the jars has the least unit price?

Exponents1) Simplify the following expression using exponent notation: a•a•a•b•a•b•b•a•b•a

2) Simplify the following exponent problems: a) 2x•3x3 = b) -3a2• -4a3= c) (3x2y)3=

d) -2x2= e) (-2x)2= f) 2-3 = (simplify w/o neg exponent)

IV. Scientific Notation

1) The distance from Earth to the Sun is 92,900,000 miles. What is this number in scientific notation?

2) The table shows the area in square miles of certain states. Which state has the greatest area?

3) The distance from the Sun to Earth is about 1.5 x 1011 meters. Suppose light travels at a speed of 3 x 108 meters per second. About how long does it take light from the Sun to reach Earth? Compute and give your answer in Scientific Notation.

IV Geometry

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department

2) Find the volume of a soup can that has a height of 6 inches and a diameter of 5 inches.

Use 3.1 for π.

V Statistics and Probability1) What is the probability of tossing a penny and landing on heads three times in a row?

2) The spinner is spun twice. What is the probability that it will land on 8 after the first spin and on an odd number after the second spin?

VI Rate of Change

1)

Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015 DMS Mathematics Department 1) Amy earns $7 per hour for babysitting. Which of the following statements is true about the relationship

between

2) What is the rate of change of the relation in the table below? Is it proportional?

IF YOU ARE A COURSE 280 or 281 STUDENT, YOU ARE DONE WITH YOUR SUMMER PACKET

the number of hours Amy works and her earnings?