Ratios and proportions
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Ratios and Proportions. Grades 6/7. Sara Anaya Ayşe Şahin Diana White. An example of how to introduce the notion of a ratio: Illustrative Mathematics 6.RP.1 Task example: Games at recess. 6.RP.1: The language of ratio and proportion.

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Ratios and Proportions

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Ratios and proportions

Ratios and Proportions

Grades 6/7

Sara Anaya

AyşeŞahin

Diana White


6 rp 1 the language of ratio and proportion

  • An example of how to introduce the notion of a ratio:

    • Illustrative Mathematics6.RP.1 Task example:

      • Games at recess

6.RP.1: The language of ratio and proportion

Anaya, Şahin, White


6 rp 2 and 7 rp 1

  • 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.

6.RP.2 and 7.RP.1

Anaya, Şahin, White


Tape diagram representation

Tape Diagram Representation

1 cup of flour

1 cup of flour

1 cup of flour

¾ cups of sugar

Author's Name IM&E CCSSM National PD


Table

Table

x 2

x 2

x 3

x 3

x 4

x 4

x ½

x ½

Author's Name IM&E CCSSM National PD


Ratios and proportions

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


Ratios and proportions

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


Ratios and proportions

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


Ratios and proportions

  • 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.

Anaya, Şahin, White


7th grade unit rate problem

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.

7th Grade Unit Rate Problem

Anaya, Şahin, White


Ratios and proportions

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


6 rp 3 and 7 rp 3

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?

6.RP.3 and 7.RP.3

Anaya, Şahin, White


7 th grade extension

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.

7th Grade Extension

Anaya, Şahin, White


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