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Ratio
and
Proportional Relationships
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.
April 30, 2013
Common Core Leadership in Mathematics2 (CCLM)
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. 2-4
Highlight as you read
* Important Idea
? Some confusion
2. Read 6.RP.1
Complete 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
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
Press Students
Conceptually
Address
Misconceptions
Take Students
Ideas Seriously
Building
Understanding
of
Proportional
Relationships
Focus on the
Structure of the
Mathematics
Encourage
Multiple
Strategies/Models
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
30 b
=
6 10
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
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013