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## Solve It!: Parts of a Parallelogram

### little problems with big solutions

To elicit creative student thinking, this open-ended problem asks solvers to calculate the ratio of areas of a parallelogram.

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## Designing an Amusement Park Ride

iSTEM (Integrating Science, Technology, Engineering, and Mathematics) authors share ideas and activities that stimulate student interest in these integrated fields in K–grade 6 classrooms. This month, preservice teachers use Polydron® Revolution kits to design and create an amusement park ride that spins. The lesson integrates engineering design processes with mathematics to explore the concepts of proportional reasoning and least common multiple within the context of gears.

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## Solve It: Student Thinking: Lemon Tea?

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

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## Using Artwork to Explore Proportional Reasoning

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

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

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## Doing Mathematics with Spirograph

solve real-world and mathematical problems. Task 1.2, Task 1.3 (see table 3 ); Day 2 Tasks CCSS.MATH.CONTENT.6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities

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## Ratios, Rates, Unit Rates, and Debates!

Students work their way around four corners to reach mathematical consensus.

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## Gone Fishing: Science, Proportions, and Probability

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

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## Overcoming the “Run” Response

Strategies that foster self-awareness, help regulate emotions, and encourage problem-solving perseverance can turn mathematical fight or flight into re-engagement.

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## Examining Mistakes to Shift Student Thinking

During a lesson on ratios involving percentages of paint, four research-based criteria are used to evaluate students' mistakes. The takeaway is that painting all mistakes with the same brush can also be a blunder.