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The Problem With Problem Solving

By Jessica Smith
Meet the Author

"How do mathematicians communicate their ideas to each other and to the public? If math is just numbers and symbols, how can we talk about math?"

 Understandings & Objectives

Strategy: Organized list

 At A Glance

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Strategy: Organized list

Instructional Time: 1 hour a day for 2 days

Lin-Chuan presses his face up against the glass tank at the tropical fish store.  There are three types of fish for sale: a bright pink Gourami ($1.20), the nearly invisible Glass fish ($1.80), and the Neon Tetra ($.60) that has an electric blue band.  Lin-Chuan steps back and counts his money; he has $6.00.  How many different combinations of colorful tropical fish can Lin-Chaun buy with his $6.00?

One evening the small, furry, people-like Weebles, Wobbles, and Widgets hurried about in their secret underground caverns.  One particular Widget named Wally wandered off too far, and fell in a ravine.  Weebles, Wobbles, and Widgets ran over and tried to think of a way to save poor Wally, but no one had a long enough rope.  Then Wendell Wobble had an idea:  If they formed a furry chain, holding on to each other, maybe they could reach down the 40 inches to Wally.  The Weebles were 12 inches high, the Wobbles were 8 inches high, and the Widgets were 4 inches high.  How many different combinations of the small creatures would reach 40 inches high?

Lena is helping her father empty the coins from the commercial washing machines he services.  Lena’s father lets her count the coins in the machine with the smallest amount of money.  The washing machines take only 50-cent pieces, quarters, and dimes.  If Lena counts $2.00 in coins, how many different combinations of coins could Lena have counted?