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Problem
Solving Strategy
~ Look for a Pattern ~ |
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Content
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. |
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This is a not RUMDA. |
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This is a RUMDA. |
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Is this a RUMDA (A)? |
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This is a RUMDA. |
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Is this a RUMDA (B)? |
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This is a not RUMDA. |
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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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