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|
Here are some other strategies that are helpful to students.
This strategy is best demonstrated using the following problem:
Problem: The Birthday Gift
My favorite aunt gave me some money for my birthday. I spent one-third of it on a new CD. I spent half the remainder to take my friend to the movies. Then I bought a magazine with half of what was left. When I went home, I still had $6. How much did my aunt give me for my birthday?
One way to solve this problem combines drawing a diagram and working backward.
Solution: The Birthday Gift
Questions to Consider: The Birthday Gift
To understand this strategy for organizing data, take a look at the problem and solution below:
Problem: My Favorite Number
My favorite number is a two-digit number, and it equals twice the sum of its digits. What is my favorite number?
Solution: My Favorite Number
Let's make x be the tens digit of the number and y be the ones digit. The value of the number is then 10x + y. The sum of the digits is x + y, and twice the sum is 2(x + y). These are equal, so we write 10x + y = 2(x + y), which becomes 10x + y = 2x + 2y. Then we collect the variables: 8x = y. Now we remember that both x and y are one-digit numbers. That means that x must be 1 and y is 8. The number is 18.
Solve a Simpler Problem
Watch a brief video segment (duration 0:22) to hear a reflection from Nan Sepeda, a middle school mathematics teacher, about using a simple problem to introduce a more difficult one.
In addition, here are some phrases that are commonly used to name techniques for solving problems:
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