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## Mathematical Explorations: A New Twist on Collaborative Learning

### classroom-ready activities

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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## The Cake Contest

Students used a pinch of this (a 3D printer and geometry software) and a cup of that (various volume formulas) to complete a tiered task.

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## Ship It!

U.S. Postal Service box dimensions are explored

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## Persevering with Prisms: Producing Nets

A scaling task that incorporates rectangular prisms can net an increase in students' geometric understanding.

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## Sharing Cookies: A Case Study

Gain insight into students' understanding of the concept of fraction as operator as well as their reliance on rote procedures to convert fractions to decimals.

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## Cartoon Corner: Easy as Pi? Infinitely Not!

A cartoon involving pi (or 3.14….) is coupled with a full-page activity sheet.

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## Math for Real: Packaging Golf Balls

### “when will I ever use this?”

A package of three golf balls provides the real-world scenario for this ratio and area activity.

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## The “Brick Wall” Graphic Organizer

Use this visual tool to plan lessons and assessments, diagnose gaps in students' conceptual knowledge, and help you and your students see connections within a particular lesson objective.

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## Representations and Rafts

Building a rod raft allows students to make mathematical connections among a model, a table, a formula, and a graph.

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## Geometry in A Box

Surface area and volume are explored with this cartoon, also containing an activity sheet.