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Excerpts from discussion threads on the online MyNCTM community

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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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## Activities for Students: Soap and Slope: Mathematical Adventures in Fluid Dynamics

The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.

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## Radical Thoughts on Simplifying Square Roots

A geometric approach using exact square manipulatives can promote an understanding of the algorithm to dismantle radical expressions.

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## Using Disks as Models for Proofs of Series

Students use balls and disks to prove the general formulas for sums of squares and cubes.

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## Activities for Students: Filling Bottles with Water

In this activity, students gradually fill bottles of different shapes and graph the water level (height) versus the volume of water inside the bottles. Then they explore the relationship between the shape of a bottle and the resulting graph.