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## Postscript: Knock 'em down

This simple dice game supports students' development of flexibility with numbers, the properties of the four operations (+, −, ×, ÷), and the order of operations. It requires only dice and a game board for each player.

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## Building Bridges to Spatial Reasoning

Three days of using building blocks significantly enriched second graders' thinking about multiple dimensions.

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## UDL for Geometric Length Measurement

A proactive preschool teacher differentiates instruction by using the Universal Design for Learning framework to decrease barriers that limit students' access to classroom learning.

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## Virtual manipulatives to assess understanding

Three preservice teachers used virtual manipulatives during clinical interviews with students of elementary school age. The technology exposed students' problem-solving strategies and mathematical understanding, promoting just-in-time teaching about the target content. The process of completing and reflecting on the interviews contributed to growth of the preservice teachers' technological pedagogical content knowledge.

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## An Appetite for Fractions

Using candy bars as models gives students a taste for learning to represent fractions whose denominators are factors of twelve.

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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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## Fractions and the funky cookie

A mathematics specialist has great success using a pattern-block configuration to help a small group of fifth graders understand that fractional parts of a whole unit must be equal in size. That's just the way the funky cookie crumbles.

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## A smorgasbord of assessment options

Presented with a variety of palatable, inquiry-based, creative learning choices in geometry, this teacher and her fifth graders found tremendous satisfaction in meeting target goals for reasoning skills and taking important “next steps” in learning.

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## Math by the Month: Sweet play

As part of her holiday preparations, Cathy decorates sugar cubes. Cathy's aunt, Ms. Betty, runs a bakery and likes to think of ways to make her store more attractive, especially for holidays. She enjoys cutting, arranging, and designing seasonal displays with her famous brownies almost as much as she enjoys baking them. And everyone loves the different sizes of Ms. Kate's chocolate sticks.