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• Author or Editor: Darin Beigie
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## Dare to Compare

Analyzing school cafeteria pizza, comparing the speeds of Usain Bolt and a cheetah, and pricing water versus gasoline were just a few of the unit rate and product comparisons that students investigated with enthusiasm.

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## Mathematical Exploration: Probability Experiments with Shared Spreadsheets

Probability Experiments with Shared Spreadsheets Probability experiments illustrate how apparently random events are ultimately governed by the laws of probability. A large number of trials are usually necessary for experimental data to converge to a theoretical prediction. Having students electronically combine their data into a shared spreadsheet provides an efficient and powerful way to collectively analyze a large amount of information. In this activity, seventh-grade students use a shared spreadsheet to collaboratively investigate what happens when they roll a pair of dice. They compare the case of two 6-sided dice with the case of a 4-sided die rolled with an 8-sided die.

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## Quick Reads: Slow-Cooker Questions in a Microwave World

### a good idea in a small package

Although technology places a premium on quick and efficient ways to answer questions, the author discusses extended-time, or “slow-cooker,” questions, as illustrated by a task on the Triangle Inequality theorem.

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## The Leap from Patterns to Formulas

Geometric problems help students progress from predicting numerical patterns to expressing algebraic generalizations.

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## No Child Left Unchallenged

Design lightbulb questions for your students using these six simple methods.

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## The Temptation of Risk

This classroom-tested exploration shows students the consequences of investments and saving money over time.

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## Traveling at the Speed of Light

Students use scientific notation to calculate how long it takes light to travel a variety of astronomical distances and then interpret the significance of their findings.

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## The Algebra Artist

Students create drawings with online software and are inspired to think holistically about graphing algebraic equations and inequalities.

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## Solving Optimization Problems with Spreadsheets

These classic activities usually reserved for calculus are recast in a highly visual approach as investigations with first-year algebra students.

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## Computer-Generated Fractal Art

Computer Software Can be a Powerful tool in both the study and creation of fractals. The Snowflake Fractal Generator (Shodor Education Foundation, www.shodor.org) is an appealing example of software that allows students to make fractals similar to the classic Koch snowflake (see fig. 1).