Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Ratio and

Proportional Relationships

Ratio and

Proportional Relationships

April 30, 2013Common Core Leadership in Mathematics2 (CCLM)

This material was developed for use by participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwaukee. Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source. Use by others is prohibited except by prior written permission.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Agenda• Welcome• Homework Debrief and Gears Revisited• RP Progression Reading• Understand composed units and multiplicative

comparisons• MKT Assessment

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Helping Students Make Transitions to Proportional Thinkers

Students need to make a transition from

•focusing on only one quantity to realizing that two quantities are important.

•making an additive comparison to forming a ratio between two quantities.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Gear Up! Part III

Consider one pair of gears. Determine when the two gears return to their starting position and then generate other rotation pairs for the gears.

Graph the ordered pairs.

At your table surface some important features of the graph.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Discussion

• As a table group, discuss the homework reading about Shift 1: From one quantity to two and Shift 2:From additive to multiplicative comparisons.

• On a sheet of paper, record three big ideas or ‘ahhas’ from your discussion.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Grade 6 Ratio and Proportional Relationship Domain

1. Read RP Progressions pp. 2-4Highlight as you read

* Important Idea? Some confusion

2. Read 6.RP.1Complete the organizer

–On one side, rephrase the standard. –On the other side, explain how this standard was illustrated in the gear problems.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

6.RP.1

Understand ratio concepts and use ratio reasoning to solve problems.1. 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, 2012 - 2013

Oh no! What’s the answer?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Strategies to Reason About Proportions

Strategies to Reason About Proportions

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Learning Intentions

We Are Learning To….• Analyze student thinking strategies to reason proportionally

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

What Do Students Know?

Middle School – Procedural Example Problem 1 Solve this Proportion

88% of Pre-Algebra students solved correctly

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

What Do Students Know?

Middle School – Application Example Problem 2 At a typical National Football League game, the ratio of males to females in attendance is 3:2. There are 75,000 spectators at an NFL game. How many of the spectators would you expect to be females?

How many Pre-Algebra students do you believe solved this problem correctly?

7% of Pre-Algebra students solved correctly

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Learning Intentions

• Analyze student reasoning in proportional situations

• Examine a progression of student strategies

• Summarize the CCSS related to reasoning about Proportions

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Anticipating Student Strategies

• Solve the four problems as though you are a 7th grader who does not yet know the cross multiplication algorithm.

• Represent at least one of your solutions visually.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

• Ellie estimates that it takes her 5 hours to walk 8 miles. How many hours would she walk if she walked 48 miles?

• Jane estimates that she takes 8 hours to go 12 miles. How many miles would she walk in 42 hours?

• Quinten is an extreme trail runner and estimates that he takes 3 hours to run 9 miles. How many hours would it take for him to run 24 miles?

• Sierra is also a trail runner. She estimates that she runs 8 miles in 3 hours. If she runs for 2 miles, how long has she run?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

Success Criteria

We will know we are successful when we can

Use various strategies to solve ratio and proportion problems.

Justify our thinking when solving problems involving ratio and proportion.

Clearly explain and provide examples for specific CCSS standards