Problem Solving Strategy ~ Look for a Pattern ~

Content

 Process Problem 1 Process Problem 2 Process Problem 3 Problem Worksheet

Process Problem 1

A man was very overweight and his doctor told him to lose 36 kg. If he loses 11 kg the first week, 9 kg the second week, and 7 kg the third week, and he continues losing at this rate, how long will it take him to lose 36 kg? (Hint: Look for a pattern. Then complete the table.)

 Week Total Kilograms Lost 1 11 2 11 + 9 = 20 3 20 + 7 = 27 4 5

Understanding the Problem

· How much does the man need to lose? (36 kg)
· How much did he lose the first week? (11 kg)
· How much did he lose the second week? (9 kg)
· How much did he lose the third week? (7 kg)

Planning a Solution

· How much less does he lose the second week than the first week? (2 kg)
· How much less does he lose the third week than the secornd? (2 kg)

Finding the Answer

Make a Table/Look for a Pattern

 Week Total Kilograms Lost 1 11 2 11 + 9 = 20 3 20 + 7 = 27 4 27 + 5 = 32 5 32 + 3 = 35 6 35 + 1 = 36

Pattern: The number of kilograms lost decreases by 2 each week.

It will take the man 6 weeks to lose 36 kg.

Problem Extension

If the man gains his weight back at the rate of .2 kg the first week, 4 kg the second week, 6 kg the third week, and so on, in which week will he have gained back 36 kg? (the sixth)

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Process Problem 2

Jose used 6 blocks to build this staircase with 3 steps. How many blocks will Jose need to make a 6-step staircase? (Hint: Make a table and look for a pattern.)

Understanding the Problem

· How many blocks are used to build a 3-step staircase? (6)
· Do you know how many blocks are used to make a 6-step staircase? (No, that is what we are trying to find out.)

Planning a Solution

· How many blocks were used to build the first step? (1 )
· How many new blocks were used for the second step? (2)
· How many new blocks would be needed for the fourth step? (4) What would be the total number of blocks used to build a staircase with 4 steps? (10)

Finding the Answer

Make a TablelLook for a Pattern

 Steps in Staircase Blocks Needed to Build New Steps Total Blocks Needed 1 1 1 2 2 1 + 2 = 3 3 3 1 + 2 + 3 = 6 4 4 1 + 2 + 3 + 4 = 10 5 5 1 + 2 + 3 + 4 + 5 = 15 6 6 1 + 2 + 3 + 4 + 5 + 6 = 21

Pattern: The number of new blocks needed increases by 1 with eachnew step. The total number of blocks needed for nth step is the sum of the number 1 through n.

It would take 21 blocks to build a 6-step staircase.

Problem Extension

How many steps would there be in a staircase using 78 blocks? (12)

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Process Problem 3

Earl played a game using the figure below. First he covered the section numbered 1. Then he covered the sections numbered 1 and 2. Next he covered the sections numbered 1 and 4. What sections would he cover on his seventh round?

Understanding the Problem

· What numbers are in the circle? (1, 2, 4, 8)
· What number(s) did he cover first? (C') Second? (1, 2) Next? (1, 4)

Planning a Solution

· What is the sum of the numbers he covered first? (1)
· What is the sum of the numbers he covered second? (3) Next? (5)
· Make a table and look for a pattern. (See solution.)

Finding the Answer

Make a Table/Look for a Pattern

 Round Sum First 1 Second 1 + 2 = 3 Third 1 + 4 = 5 Fourth 1 + 2 + 4 = 7 Fifth 1 + 8 = 9 Sixth 1 + 2 + 8 = 11 Seventh 1 + 4 + 8 = 13

Pattern: The sum of the numbers increases by 2 in each round.

Earl would cover the 1, 4, and 8 on his seventh round.

Problem Extension

If he covered the 2 first, then the 4, then the 2 and the 4, what numbers would he cover on hisseventh round? (2, 4, 8)

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Process Worksheet: Look for a Pattern

1. Find the next 3 numbers in the following sequence.

2, 5, 11, 23, ____, _____, ______.

2. If this pattern was formed to make a cube, what numbers would appear where the question marks are?

3. The number of line segments joining a set of points increases as the number of points increases. Find how many line segments there will be when there are 8 points; 10 points.

4. For the hexagon with 42 dots, how many dots are there on each side?

5. Look for a common element in each of the following.

 This is a RUMDA. This is a not RUMDA. This is a RUMDA. Is this a RUMDA (A)? This is a RUMDA. Is this a RUMDA (B)? This is a not RUMDA.

6. If the figure on the left is continued, how many letters will be in the J row?

Which row will contain 27 letters?

A
BBB
CCCCC
DDDDDD

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