Eureka Math Homework Helper 2015–2016 Grade 7 …

Eureka MathTM Homework Helper 2015?2016

Grade 7 Module 1 Lessons 1?22

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A Story of Ratios 7?1 2015-16

G7-M1-Lesson 1: An Experience in Relationships as Measuring Rate

Rate and Unit Rates

Find each rate and unit rate.

1. $8.96 for 8 pounds of grapefruit

.

=

.

Rate: . dollars per pound

Unit Rate: .

I determine the cost of one pound of grapefruit in order to find the rate. To do this, I divide the cost by the number of pounds.

2. 300 miles in 4 hours

=

Rate: miles per hour

Unit Rate:

The label explains the numerical value of the rate.

Ratios and Rates

3. Dan bought 8 shirts and 3 pants. Devonte bought 12 shirts and 5 pants. For each person, write a ratio to represent the number of shirts to the number of pants they bought. Are the ratios equivalent? Explain.

The ratio of the number of shirts Dan bought to the number of pants he bought is : .

The ratio of the number of shirts Devonte bought to the number of pants he bought is : .

The order of the ratios is important. In this case, it is stated that the ratio is shirts to pants, which means the first number in the ratio represents shirts and the second number represents pants.

The

ratios

are

not

equivalent

because

Dan's

unit

rate

is

or

,

and

Devonte's

unit

rate

is

or

.

I know these are not equivalent ratios because they do not have the same unit rate.

Lesson 1:

An Experience in Relationships as Measuring Rate

1

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Homework Helper

A Story of Ratios 7?1 2015-16

4. Veronica got hired by two different families to babysit over the summer. The Johnson family said they would pay her $180 for every 20 hours she worked. The Lopez family said they would pay Veronica $165 for every 15 hours she worked. If Veronica spends the same amount of time babysitting each family, which family would pay her more money? How do you know?

Calculating the unit rate helps compare different rates and ratios.

Veronica will earn $ per hour when she babysits for the Johnson family and will earn $ per hour when she babysits for the Lopez family. Therefore, she will earn more money from the Lopez family if she spends the same amount of time babysitting for each family.

Lesson 1:

An Experience in Relationships as Measuring Rate

2

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A Story of Ratios 7?1 2015-16

G7-M1-Lesson 2: Proportional Relationships

Proportional Quantities 1. A vegetable omelet requires a ratio of eggs to chopped vegetables of 2 to 7.

This means that I use 2 eggs and 7 chopped vegetables to make an omelet.

a. Complete the table to show different amounts that are proportional.

Number of Eggs

Number of Vegetables

b. Why are these quantities proportional?

Answers may vary, but I need to create ratios that are equivalent to the ratio 2: 7.

The number of eggs is proportional to the number of chopped vegetables since there exists a

constant number, , that when multiplied by any given number of eggs always produces the

corresponding amount of chopped vegetables.

2. The gas tank in Enrique's car has 15 gallons of gas. Enrique was able to determine that he can travel 35 miles and only use 2 gallons of gas. At this constant rate, he predicts that he can drive 240 more miles before he runs out of gas. Is he correct? Explain.

Once I calculate the unit rate, I use this to determine how many miles Enrique can travel with the gas remaining in his tank by multiplying both values by 15.

Gallons of Gas Used

Miles Traveled

.

.

Enrique can travel . more miles because has he can only travel . miles with gallons of gas, but he has already traveled miles. . - = . . Therefore, Enrique's prediction is not correct because he will run out of gas before traveling more miles.

Lesson 2:

Proportional Relationships

3

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A Story of Ratios 7?1 2015-16

G7-M1-Lesson 3: Identifying Proportional and Non-Proportional Relationships in Tables

Recognizing Proportional Relationships in Tables In each table, determine if is proportional to . Explain why or why not.

To determine if is proportional to , I determine if the unit rates, or value of each ratio, are equivalent.

1.

3

4

6

= = = =

8

5

10

No, is not proportional to because the values of all the ratios

6

11

: are not equivalent. There is not a constant where every

measure of multiplied by the constant gives the corresponding

measure in .

2. 6 9 12 15

2

= =

=

=

3

4

Yes, is proportional to because the values of the ratios :

5

are equivalent. Each measure of multiplied by this constant of

gives the corresponding measure in .

If

I

multiply

each

-value

by

1

,

the

outcome

3

will be the corresponding -value.

Lesson 3:

Identifying Proportional and Non-Proportional Relationships in Tables

4

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