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UNDERLYING SKILLS AND CONCEPTS:
number patterns;
basic facts;
interpret variables
Find Number Patterns
a
K
ey Ide
To find a pattern in a series of numbers, check:
if the numbers increase by the same amount.
OR try to find a pattern in the amount by which they increase.
if the numbers decrease by the same amount.
OR try to find a pattern in the amount by which they decrease.
Once you find the pattern, you can write a rule to get the next number.
Sometimes the numbers are arranged in a table.
the 1st row of the table contains In numbers (called the x-numbers).
the 2nd row of the table contains Out numbers (called the y-numbers).
Look for a pattern in the Out numbers: How are they related to the In numbers?
Then write the rule to compute the Out number, given the In number.
1
Look at this pattern:
1,
2,
4,
7,
11, 16, 22,...
Do the numbers increase? Yes.
!1, !2, !3, !4, !5, !6
Is there a pattern in the increases? Yes, the difference between two numbers
increases by 1 each time.
What is the next number? It is 22 ! 7 " 29.
E x am p l E
2
Find the pattern.
x
y
0
7
1
8
2
9
3
10
x
y
0
7
1
8
2
9
3 4
10 11
Do the numbers increase? Yes
Do the numbers always increase by the same amount?
Yes. The next number is 1 more than the previous.
Find a pattern. Complete the table.
4
?
Is there a pattern between an x number
and the corresponding y number?
Yes. The y number is always 7 more than the x number.
The rule is “to get the y number, add 7 to the x number,” or simply “add 7.”
page 362
Chapter 31 – Lesson 1
D – © CSL Associates, Inc. All rights reserved.
E x am p l E
Name
P RAC T I C E
Write a rule to get from the In numbers to the Out numbers.
Complete each table.
1.
2.
3.
4.
5.
D – © CSL Associates, Inc. All rights reserved.
6.
x
y
0
0
1
3
2
6
3
9
4
x
y
0
4
1
5
2
6
3
7
4
x
y
2
0
3
1
4
2
5
3
6
the rule is:
Multiply by 3.
the rule is:
Add 4.
the rule is:
Subtract 2.
x
y
10 11 12 13 14
19 20 21 22
the rule is:
Add 9.
x
y
0
0
10 20 30 40
1
2
3
the rule is:
Divide by 10.
x
y
10 20 30 40 50
0 10 20 30
the rule is:
Subtract 10.
The Fibonacci sequence use the following rule to find the next number:
Add the two previous numbers together.
The sequence starts with: 1, 1, 2, 3, 5, 8,...
5+8
7. What expression gives the next number in the sequence?
13
8. What is the next number in the sequence?
18 13 21
9. What is the number after that?
Math
Reasoning
Patterns
10. This pattern uses two operations to get
from the In numbers to the Out numbers.
Write the rule and complete the table.
MR 1.1
x
y
1
2
2
5
3
8
4
Multiply by 3 and subtract 1.
Chapter 31 – Lesson 1
page 363
MCX94.HW.CL.G4.FM&Lesson.v211
8/2/04
19:17
Page 242
Name
…at home!
P RAC T I C E
1.
2.
3.
4.
5.
6.
x
y
0
0
1
4
2
8
3
12
4
x
y
0
6
1
7
2
8
3
9
4
x
y
3
0
4
1
5
2
6
3
7
the rule is:
Multiply by 4.
the rule is:
Add 6.
the rule is:
Subtract 3.
x
y
10 11 12 13 14
15 16 17 18
the rule is:
Add 5.
x
y
0
0
10 20 30 40
2
4
6
the rule is:
Divide by 5.
x
y
10 20 30 40 50
5 15 25 35
the rule is:
Subtract 5.
The Fibonacci sequence uses the following rule to find the next number:
Add the two previous numbers together.
The sequence starts with: 1, 1, 2, 3, 5, 8, 13, 21...
7. What expression gives the next number in the sequence?
8. What is the next number in the sequence?
21 34 55
9. What is the number after that?
Math
Reasoning
13 21
34
Patterns
10. This pattern uses two operations to get
from the In numbers to the Out numbers.
Write the rule and complete the table.
MR 1.1
x
y
1
3
2
8
3
13
4
Multiply by 5 and subtract 2.
page 242
Home Resource and Homework
Chapter 31 Lesson 1
D – © CSL Associates, Inc. All rights reserved.
Write each rule to get from the In numbers to the Out numbers.
Complete each table.
MCX94TEG4Ch01_32.v8.5.2 2/26/01 19:07 Page 667
Name
P RAC T I C E
Write a rule to get from the In numbers to the Out numbers.
Complete each table.
1.
2.
3.
4.
5.
D – © CSL Associates, Inc. All rights reserved.
6.
x
y
0
0
1
3
2
6
3
9
x
y
0
4
1
5
2
6
3
7
x
y
2
0
3
1
4
2
5
3
4
12
the rule is:
Multiply by 3.
the rule is:
Add 4.
the rule is:
Subtract 2.
4
8
6
4
x
y
10 11 12 13 14
19 20 21 22 23
the rule is:
Add 9.
x
y
0
0
10 20 30 40
1
2
3 4
the rule is:
Divide by 10.
x
y
10 20 30 40 50
0 10 20 30 40
the rule is:
Subtract 10.
The Fibonacci sequence use the following rule to find the next number:
Add the two previous numbers together.
The sequence starts with: 1, 1, 2, 3, 5, 8,...
5+8
7. What expression gives the next number in the sequence?
13
8. What is the next number in the sequence?
18 13 21
9. What is the number after that?
Math
Reasoning
Patterns
MR 1.1
10. This pattern uses two operations to get
from the In numbers to the Out numbers.
Write the rule and complete the table.
x
y
1
2
2
5
3
8
4
11
Multiply by 3 and subtract 1.
Chapter 31 – Lesson 1
Student Book Page
page 363
Name
…at home!
P RAC T I C E
Write each rule to get from the In numbers to the Out numbers.
Complete each table.
2.
3.
4.
5.
6.
x
y
0
0
1
4
2
8
3 4
12 16
the rule is:
Multiply by 4.
x
y
0
6
1
7
2
8
3
9
the rule is:
Add 6.
x
y
3
0
4
1
5
2
6
3
the rule is:
Subtract 3.
4
10
7
4
x
y
10 11 12 13 14
15 16 17 18 19
the rule is:
Add 5.
x
y
0
0
10 20 30 40
2
4
6 8
the rule is:
Divide by 5.
x
y
10 20 30 40 50
5 15 25 35 45
the rule is:
Subtract 5.
The Fibonacci sequence uses the following rule to find the next number:
Add the two previous numbers together.
The sequence starts with: 1, 1, 2, 3, 5, 8, 13, 21...
7. What expression gives the next number in the sequence?
8. What is the next number in the sequence?
21 34 55
9. What is the number after that?
Math
Reasoning
13 21
34
Patterns
10. This pattern uses two operations to get
from the In numbers to the Out numbers.
Write the rule and complete the table.
MR 1.1
x
y
1
3
2
8
3 4
13 18
Multiply by 5 and subtract 2.
page 242
Home Resource and Homework
Chapter 31 Lesson 1
D – © CSL Associates, Inc. All rights reserved.
1.