wccusd grade 7 math benchmark 2 study guide...wccusd grade 7 math benchmark 2 study guide page 2 of...

WCCUSD Grade 7 Math Benchmark 2 Study Guide

of 14 MCC@WCCUSD (WCCUSD) 01/06/16

1´ Given the graphed solution below: Which of the following statements are true?

7.EE.4b

1 Graph the inequality below. x < –2 The graph of an inequality shows all of its solutions. The solutions make the sentence true. To graph the boundary point, use an open circle for < and >. Use a closed circle for < and >. We will use a closed circle at –2 because the solution includes the point, –2. To determine which side of the boundary point makes the sentence true, substitute a number into the inequality. We will check the point x = 0

Let’s try a point on the other side of the boundary point. We will check the point x = –4 The sentence is true if we substitute –4 as the value for x, which means that all values on that side of the boundary point are true.

7.EE.4b

A) The solution includes 2. B) The solution includes –2. C) The solution includes 1. D) The solution includes –5. E) The solution includes 0.5. F) x < 1 matches the graph. G) x > 1 matches the graph. H) x < 1 matches the graph. I) x > 1 matches the graph.

Mark all correct answers.



2 Marco has at most $20 to spend on office supplies. He wants to buy a box of markers for $10 and spend the rest on binders. Each binder costs $4. Write, solve, and graph an inequality for the number of binders that Marco can purchase. Sample Solution: x = the number of binders Marco can buy How many binders can Marco buy without going over $20? Provide an explanation for your answer. Sample Response: Because Marco cannot purchase half of a binder, he can purchase a maximum of 2 binders before going over his $20 limit.

7.EE.4b

2a´ A restaurant charges a $50 flat fee for their party room and $6 for each person. Seraphina has no more than $215 to spend on the birthday party. A) Write, solve, and graph an inequality that represents the total number of people that can attend the party. B) How many people can attend the party without exceeding the limit? Provide an explanation for your answer.

7.EE.4b

2b´ Jaclyn wants to save at least $48 to buy a

new video game. She has $16 and will save $4 every week. How many weeks will it take Jaclyn to save up enough money to buy the video game? A) Write, solve, and graph an inequality that describes how many weeks it will take Jaclyn to save up for the video game. B) At least how many weeks will it take Jaclyn to save up for the game?

7.EE.4b



3 A basketball jersey is on sale for 30% off the original price of $90. How much is the sale price of the jersey? Method: Bar Model Method: Proportions Method: Direct Translation What is 70% of $90?

7.RP.3

3´ A tablet computer that regularly sells for $420 is on sale for 25% off. Which of the following expressions or methods could be used to find the sale price or discount?

7.RP.3

30% of $90 = $27 (discount)

$90 – $27 = $63 (final sale price)

A) B) C) 420 – 0.25 D) E)

F)

G) 420 – 25 H)

I)

J)




4 After a 40% discount, Manuel paid $75 for an mp3 player. What was the original price? Method: Bar Model The original price of the mp3 player is the discount ($50) plus the sale price ($75). ∴ The original price was $125 Method: Direct Translation The bar model shows us that the sale price of $75 is 60% of the original price. This reasoning can be expressed in an equation where x is the original cost of the mp3.

75= 0.60x Set up the equation75

0.60=

0.60x0.60

Divide both sides by 0.60

125= x Simplify

∴ The original price was $125

7.RP.3

4´ After a 35% discount, Heather paid $52 for a backpack. Which of the following equations or methods could be used to find the original price of the backpack?

7.RP.3

A) B) C) D) E) F)

G)




5 Attendance at Back to School Night rose from 120 parents last year to 180 parents this year. What is the percent increase in parent attendance? Method: Bar Model Method: Percent of Change Equation ∴ 60 more parents = 50% increase

7.RP.3

5´ Last week a baseball player had eight stolen bases. This week he only stole six. What is the percent decrease in his stolen bases?

7.RP.3



6 Compute the unit rate:

A scooter went 42 miles on 710

gallon.

42 mi.7

10 gal.

=427

10

miles per gallon

= 42÷ 710

miles per gallon

=421÷

710

miles per gallon

=421

• 107

miles per gallon

=42 •101• 7

miles per gallon

=6 • 7 •10

7 miles per gallon

= 60 miles per gallon

7.RP.1

6´ Compute the unit rate:

The sled dog team ran 3 miles in 14

hour.

7.RP.1



7 An airplane traveled 910

kilometer in

15

minute. What was its speed in kilometers

per minute?

7.RP.1

7´ A cheetah traveled 915

mile in 35

minute.

Which of the following represent OR could be used to find the cheetah’s average speed in miles per minute? 7.RP.1


A) average speed = miles per minute

B) average speed = 1 mile per minute

C) average speed =

D) average speed =

E) average speed =



8 Apples cost $4 for every 2 lbs. Make a line graph that demonstrates this relationship. How much will it cost for 21 lbs of apples? Graph: The graph shows that the cost of apples will rise $4 for every 2 lbs of apples. How much would it cost for 21 lbs of apples? Method 1: Table The table shows that the cost of apples per pound is twice the weight of the apples. ∴ the cost of 21 lbs of apples is $42. Method 2: Bar Model

7.RP.2

8´ Two pizzas cost $10. Make a line graph that shows the relationship between the number of pizzas purchased and the total cost. How much will it cost for 7 pizzas? How much will it cost for 17 pizzas? Graph:

7.RP.2

∴ if 1 pound of apples costs $2, then 21 pounds of apples costs $42.



9 Look at each relationship. For examples A, B and C, decide whether or not the relationship is proportional. If it is, identify the constant of proportionality. A) Yes, the relationship is proportional because the points would make a straight line that

goes through the origin. The slope is 43

so

the constant of proportionality is 43

.

B) y = 4x Yes, there is a direct relationship between x and y. Therefore, this is a proportional relationship. The constant of proportionality is 4. C) No, this does not indicate a proportional relationship because the money earned is not directly dependent on the number of hours worked. The point in the table (0, 15) would indicate that after zero hours of work, $15 would be earned. Although it looks like the constant of proportionality is 15, it does not work for zero hours. Therefore, there is no constant of proportionality.

7.RP.2a

9´ Look at each relationship. For each example, decide whether or not the relationship is proportional. If it is, identify the constant of proportionality. A) B) C) Walking to school, a student averages 6 blocks every 8 minutes.

7.RP.2a

End of Study Guide



You Try Solutions: 1´ Given the graphed solution below:

Which of the following statements are true?

7.EE.4b

2a´ A restaurant charges a $50 flat fee for their party room and $6 for each person. Seraphina has no more than $215 to spend on the birthday party. A) Write, solve, and graph an inequality that represents the total number of people that can attend the party.

6x + 50 ≤ 2156x + 50 ≤165+ 50

6x ≤1656x6≤1656

x ≤ 27.5

B) How many people can attend the party without exceeding the limit? Provide an explanation for your answer. Sample response: 27 people can attend the party without exceeding Seraphina’s limit of $215. If 28 people came, she would spend more than $215.

7.EE.4b

A) The solution includes 2. B) The solution includes –2. C) The solution includes 1. D) The solution includes –5. E) The solution includes 0.5. F) x < 1 matches the graph. G) x > 1 matches the graph. H) x < 1 matches the graph. I) x > 1 matches the graph.




2b´ Jaclyn wants to save at least $48 to buy a new video game. She has $16 and will save $4 every week. How many weeks will it take Jaclyn to save up enough money to buy the video game? A) Write, solve, and graph an inequality that describes how many weeks it will take Jaclyn to save up for the video game.

4x +16 ≥ 484x +16 ≥ 48+16 –16

4x ≥ 48 –164x ≥ 324x4≥324

x ≥ 8

B) At least how many weeks will it take Jaclyn to save up for the game? Sample response: It will take Jaclyn at least 8 weeks to save up for the game.

7.EE.4b

3´ A tablet computer that regularly sells for $420 is on sale for 25% off. Which of the following expressions or methods could be used to find the sale price or discount?

7.RP.3

A) B) C) 420 – 0.25 D) E)

F)

G) 420 – 25 H)

I)

J)




4´ After a 35% discount, Heather paid $52 for a backpack. Which of the following equations or methods could be used to find the original price of the backpack?

7.RP.3

5´ Last week a baseball player had eight stolen bases. This week he only stole six. What is the percent decrease in his stolen bases? Method: Bar Model Method: Percent of Change Equation ∴ 2 less bases = 25% decrease

7.RP.3

A) B) C) D) E) F)

G)




6´ Compute the unit rate:

The sled dog team ran 3 miles in 14

hour.

Method: Bar Model Method: Dividing Fractions

3 mi.14

hr.

=314

miles per hour

= 3÷ 14

miles per hour

=31÷

14

miles per hour

=31

• 41

miles per hour

=3• 41•1

miles per hour

=121

miles per hour

=12 miles per hour

7.RP.1

7´ A cheetah traveled mile in minute.

Which of the following represent OR could be used to find the cheetah’s average speed in miles per minute? 7.RP.1

915

35

12 miles = 1 hour ∴ The sled dog team’s unit rate is 12 miles per hour.

How many miles in 1 hour?


A) average speed = miles per minute

B) average speed = 1 mile per minute

C) average speed =

D) average speed =

E) average speed =



8´ Two pizzas cost $10. Make a line graph that shows the relationship between the number of pizzas purchased and the total cost. How much will it cost for 7 pizzas? How much will it cost for 17 pizzas? The graph shows that for every 2 pizzas, the cost will rise $10. How much will it cost for 7 pizzas? How much will it cost for 17 pizzas? Method 1: Bar Model Method 2: Table The table shows that the cost of any number of pizzas is calculated by the number of pizzas times five.

∴ the cost of 7 pizzas is $35 and the cost of 17 pizzas is $85.

7.RP.2

9´ Look at each relationship. For each example, decide whether or not the relationship is proportional. If it is, identify the constant of proportionality. A) Sample response: No, this is not a proportional relationship because a line connecting the points does not go through the origin. B) Sample response: Yes, this is a proportional relationship. Every shirt costs $5. There is no discount for ordering more shirts in this table. The constant of proportionality is 5. C) Walking to school, a student averages 6 blocks every 8 minutes. Sample response: Yes, this describes a proportional relationship. The number of blocks per

minute is 68

which simplifies to 34

. 7.RP.2a

∴ if 1 pizza costs $5, then 7 pizzas will cost $35 and 17 pizzas will cost $85.

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