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Using Artwork to Explore Proportional Reasoning

Sarah B. Bush, Karen S. Karp, Jennifer Nadler, and Katie Gibbons

By examining ratios in paintings and using a free educational app, students can size up artists' use of proportional reasoning in their creations.

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Solve It! Lemon Tea?

little problems with big solutions

Sherry L. Bair

To elicit creative student thinking, this open-ended problem asks solvers to calculate mixtures of lemon and tea.

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Solve It: Student Thinking: Lemon Tea?

Sherry L. Bair and JoAnn Cady

Solutions to a November 2013 Solve It problem are discussed, and the procedures used with problem solving are explored.

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Debunking Myths about the Standards for Mathematical Practice

Victor Mateas

Teachers can benefit from productive and manageable suggestions to align instruction to the intention of the Common Core's Standards for Mathematical Practice.

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Revisit Pattern Blocks to Develop Rational Number Sense

Joe Champion and Ann Wheeler

A classic manipulative, used since the 1960s, continues to offer opportunities for intriguing problem solving involving proportions.

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Gone Fishing: Science, Proportions, and Probability

Jill A. Cochran

An outdoor context can reel in two important mathematical ideas and catch students' misconceptions in the process.

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Proportioning Cats and Rats

Kimberly A. Markworth

This feline-rodent problem helps preservice teachers go beyond the cross-multiplication algorithm to think about proportional relationships.

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Strip Diagrams: Illuminating Proportions

Jessica S. Cohen

Use strip diagrams to model and solve problems requiring proportional reasoning.

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Develop Reasoning through Pictorial Representations

Wendy P. Ruchti and Cory A. Bennett

Solutions coupled with drawings can illustrate students' understandings or misunderstandings, particularly in the area of proportional reasoning.

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The Footprint Problem: A Pathway to Modeling

Kara L. Imm and Meredith D. Lorber

By exploring an open-ended investigation involving proportional reasoning, students were able to walk through both problem solving and modeling.