Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Defining Problem Solving
 The Problem-Solving Standard | Organizing Data | Draw a Diagram or Make a Model | Organize the Data in a List, Diagram, Table, or Graph | Generate and Eliminate Candidates | Additional Problem-Solving Strategies | Low Threshold, High Ceiling Problems | Summary | Your Journal

After considering all the possibilities in an organized list, students are ready to arrange their data in a more structured format, such as a table or graph. When students are able to think of organized ways to represent their information, they are more likely to recognize patterns that will help them make generalizations that lead to the problem's solution.

Try the following problem, and be aware of how you organize the information.

Problem: The Millionaire

Mr. Lucky just won the state lottery -- \$1 million! He thinks about how he is going to spend this windfall and finally comes up with the following plan: He will spend \$1 the first day, \$2 the second day, \$4 the third day -- in other words, each day's amount is double the amount of the previous day. How long will it take Mr. Lucky to spend the entire million?

Solution: The Millionaire

A table similar to the following could be used:

Day Amount Spent Total Spent
1 \$1 \$1
2 \$2 \$3
3 \$4 \$7
4 \$8 \$15
5 \$16 \$31
6 \$32 \$63
7 \$64 \$127
8 \$128 \$255
9 \$256 \$511
10 \$512 \$1,023
11 \$1,024 \$2,047
12 \$2,048 \$4,095
13 \$4,096 \$8,191
14 \$8,192 \$16,383
15 \$16,384 \$32,767
16 \$32,768 \$65,535
17 \$65,536 \$131,071
18 \$131,072 \$262,143
19 \$262,144 \$524,287
20 \$524,288 \$1,048,575

This problem can be extended to introduce other mathematical concepts, such as: Operations in base-2, Graphic representations of 2x, and natural logarithms.

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