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Ratios and Proportions

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Ratios and Proportions

Grades 6/7

Sara Anaya

AyşeŞahin

Diana White

- An example of how to introduce the notion of a ratio:
- Illustrative Mathematics6.RP.1 Task example:
- Games at recess

- Illustrative Mathematics6.RP.1 Task example:

Anaya, Şahin, White

- This recipe has a ratio of 3 cups of flour to 4 cups of sugar.
- How many cups of flour would you use for 1 cup of sugar?
- Answer this question using as many different methods as possible.

Anaya, Şahin, White

1 cup of flour

1 cup of flour

1 cup of flour

¾ cups of sugar

Author's Name IM&E CCSSM National PD

x 2

x 2

x 3

x 3

x 4

x 4

x ½

x ½

x¼

x¼

Author's Name IM&E CCSSM National PD

1

2

3

Cups

Cups

1

2

3

4

1

2

3

Cups of flour

Cups of sugar

1

2

3

4

Double number line representations don’t work as well when the units are the same.

Author's Name IM&E CCSSM National PD

Changing the problem slightly, a double number line becomes an appropriate representation:

This recipe calls for 3 tablespoons of butter for every 4 cups of sugar. How many tablespoons of butter would you use for 1 cup of sugar?

0 tbs

3 tbs

Tablespoons

Cups

4 c

0 c

Author's Name IM&E CCSSM National PD

Using double number lines we directly translate the problem into asking: what is 3 /4?

(Standard 5.NF.3) ¾ tbs of butter for every cup of sugar.

0 tbs

? tbs

3 tbs

Tablespoons

Cups

4 c

0 c

1 c

Author's Name IM&E CCSSM National PD

- This recipe has a ratio of 3 cups of flour to 4 cups of sugar.
- How many cups of sugar would you use for 1 cup of flour?
Solve this problem using a method you did not use for the previous question.

- How many cups of sugar would you use for 1 cup of flour?

Anaya, Şahin, White

This recipe calls for ¾ cup of flour for every ½ cup of sugar. How many cups of flour would you use for every 1 cup of sugar?

Answer this question using as many different methods as possible.

Anaya, Şahin, White

This recipe calls for ¾ cup of flour for every ½ cup of sugar. How many cups of flour would you use for every 1/4 cup of sugar?

Answer this question using as many different methods as possible.

Anaya, Şahin, White

Suppose Abby’s orange paint is made by mixing 1 cup red paint for every 3 cups yellow paint and Zack’s orange paint is made by mixing 3 cups red for every 5 cups yellow. Whose paint is yellower?

Anaya, Şahin, White

Suppose Abby makes orange paint by mixing 1 cup red paint for every 3 cups yellow paint. She can only find 100 cups of the red paint, and as much of the yellow paint as she likes. How many cups of orange paint can she make?

Answer this question using as many different methods as possible.

Anaya, Şahin, White