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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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## 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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## 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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## 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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## 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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## Improving Mathematics Discourse through Action Research

NCTM identified eight Mathematics Teaching Practices within its reform-oriented text, Principles to Actions: Ensuring Mathematical Success for All (2014). These practices include research-informed, high-leverage processes that support the in-depth learning of mathematics by all students. Discourse within the mathematics classroom is a central element in these practices. The goal of implementing the practice facilitate meaningful discourse is to give students the opportunity to “share ideas and clarify understandings, construct convincing arguments regarding why and how things work, develop a language for expressing mathematical ideas, and learn to see things from other perspectives” (NCTM 2014, p. 29). To further support implementing meaningful discourse, mathematics educators must become adept at posing questions that require student explanation and reflection, hence, pose purposeful questions, which is another of the eight practices. Posing purposeful questions allows “teachers to discern what students know and adapt lessons to meet varied levels of understanding, help students make important mathematical connections, and support students in posing their own questions” (NCTM 2014, pp. 35-36).

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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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## 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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## Revisit Pattern Blocks to Develop Rational Number Sense

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