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## Developing Property-Based Geometric Reasoning

Recognizing the complex nature of students’ geometric reasoning, we present guidelines and suggestions for implementing a Guess My Shape minilesson that focuses students’ attention on properties and attributes of geometric shapes.

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## Children’s Games and Games for Children

This article examines the mathematical activity of five-year-old Liam to explore the difference between the mathematics games designed for children and the children's games that emerge through playful activity. We propose that this distinction is a salient one for teachers observing mathematical play for evidence of mathematical sense making.

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## Mathematical Explorations: A New Twist on Collaborative Learning

Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).

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## Using KenKen to Build Reasoning Skills

Through KenKen puzzles, students can explore parity, counting, subsets, and various problem-solving strategies.

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## Improving Student Reasoning in Geometry

Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.

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## Thinking Like a Mathematician

The moves that mathematicians use to generate new questions can also be used by teachers and students to tie content together and spur exploration.

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## Pattern-block frenzy

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.

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## Informing Practice: Examples as Tools for Constructing Justifications

### research matters for teachers

Research explores how to help students build from, instead of building with, examples when justifying mathematical ideas.

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## A Super Way to Soak in Linear Measurement

After analyzing advertising claims regarding water shooters, students present their findings.

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## Tapering Timbers: Finding the Volume of Conical Frustums

Many everyday objects–paper cups, muffins, and flowerpots–are examples of conical frustums. Shouldn't the volume of such figures have a central place in the geometry curriculum?