6th Grade Math Textbook, Fundamentals

Problem-Solving Strategies

1.Guess and Test

2.Organize Data

3. Find a Pattern
   4.Make a Drawing
   5.Solve a Simpler Problem
   6.Reason Logically
   7.Adopt a Different Point of View
   8.Account for All Possibilities
   9.Work Backward
   10.Consider Extreme Cases

 &KDSWHU

Problem-Solving Strategy:

Find a Pattern

Objective To solve problems using the

strategyFind a Pattern

Problem 1:The stair-step design at the right, which is made
out of toothpicks, is said to be “4 rows deep.” A stair-step design
that is 10 rows deep would require how many toothpicks?

3-7

Read to understand what is being asked.

List the facts and restate the question.

Facts: You are given a stair-step arrangement

of squares made from toothpicks.

The pattern is 4 rows deep and uses

28 toothpicks.

Question:How many toothpicks are used to make

a stair-step pattern that is 10 rows deep?

Select a strategy.

You can use the strategy Find a Pattern. Examine

the designs that are 1, 2, 3, and 4 rows deep, and

find a pattern that you can use to extend to 10 rows.

Apply the strategy.

A design with 1 row is just a single small square of 4 toothpicks.

To create row 2, add 6 more toothpicks, for a total of 10 toothpicks.

To create row 3, add 8 more toothpicks, for a total of 18 toothpicks.

For row 4, add 10 more toothpicks, for a total of 28 toothpicks.

4 toothpicks Add 6 more Add 8 more Add 10 more

So each new row was created by adding two more toothpicks than were

added to create the previous row. To find the number of toothpicks in a

design with 10 rows, compute this sum:

4  6  8  10  12  14  16  18  20  22

You can find this sum easily by forming 5 sums of 26, as shown below.

So 5 • 26, or 130, toothpicks are required.

4  6  8  10  12  14  16  18  20  22