Looking Deeper Into Ratios

Tuesday March 20, 2012

Common Core Leadership in Mathematics (CCLM)

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

Learning Intentions

Review additive and multiplicative comparisons.

Use a variety of representations to solve ratio tasks.

Form ratios as measures of real-world attributes

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

Success Criteria

We will know we are successful when we can

Use and justify various strategies to solve ratio problems and make connections to CCSSM.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

Let’s review Standard 6RP1

Domain RP: Ratios and Proportional Relationships Cluster: Understand ratio concepts and use ratio

reasoning to solve problems. Standard 6RP1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

 

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

What happens at recess….

The students in Mr. Hill’s class played games at recess.

6 boys played soccer4 girls played soccer2 boys jumped rope8 girls jumped rope

Afterward, Mr. Hill asked the students to compare the boys and girls playing different games.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

And the class said

6 boys played soccer 2 boys jumped rope4 girls played soccer 8 girls jumped rope

Mika said, “Four more girls jumped rope than played soccer.”

Chaska said, “For every girl that played soccer, two girls jumped rope.”

Mr. Hill said, “Mika compared the girls by looking at the difference and Chaska compared the girls using a ratio.”

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

Your Turn

6 boys played soccer 2 boys jumped rope

4 girls played soccer 8 girls jumped rope

Compare the number of boys who played soccer and jumped rope using the difference. Write your answer as a sentence as Mika did.

Compare the number of boys who played soccer and jumped rope using a ratio. Write your answer as a sentence as Chaska did.

Compare the number of girls who played soccer to the number of boys who played soccer using a ratio. Write your answer as a sentence as Chaska did.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

Abby’s Paint Problem

Abby’s orange paint is made by

mixing 1 cup red paint for every

3 cups yellow paint.

Zach’s orange paint is made by mixing 3 cups red paint for every 5 cups yellow paint.

Whose mixture is ‘orangier’? Use ratio tables to prove your answer in at least two ways.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

Abby’s Paint Problem

Standard 6RP3

6RP3a Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

a)Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Refer to your work from Abby’s Paint Problem to illustrate the meaning of this standard.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

Ratio Wars: Who Has More Red?

Player 1: Ratio of 2 white to 6 red

Player 2: Ratio of 6 white to 4 red

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

Standards for Mathematical Practice

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

Connecting to the Practice Standards

MP #2: Reason abstractly and quantitatively

MP #3 Construct viable arguments and critique the reasoning of others

In what ways did our ratio work engage youin Math Practice #2 and #3?

Success Criteria

We will know we are successful when we can

Use and justify various strategies to solve ratio problems and make connections to CCSSM.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year