Patterns & Equations

Recognizing Patterns

100

Write the rule describing the pattern.

84, 80, 76, 72, 68, 64, 60, 56

Start at 84 and subtract 4 each time.

200

Identify the number pattern and fill in the missing numbers. 

48, 45, 42, 39, 36, ___, ____, ____, ____, ____

48, 45, 42, 39, 36, 33, 30, 27, 24, 21

Start at 48 and subtract 3 each time. 

300

What is the last number in the pattern before it begins to repeat? 

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 

The last number is 4

400

If the pattern continued to repeat, what would be the 12th number in the pattern?

5 6 7 8 5 6 7 8 

The 12th number would be 8.

5 6 7 8 5 6 7 8 5 6 7 8 

500

If the pattern continued to repeat, what would be the 25th number in the pattern? 

8  9  10  11  8  9  10  11  8  9   10   11

The 25th number would be 8.

Equalities

100

Find the missing number. 

5 - 4 = 20 - ___

19

5 - 4 = 20 - 19

200

Find  the missing number.

26 - 4 = 12 + ___

10

26 - 4 = 12 + 10

300

56 - ____ = 20 + 36

0 

56 - 0 = 20 + 36

400

100 - 47 = 60 - ____

7 

100 - 47 = 60 - 7

500

150 - 28 = 100 + ____ = 132 - ____

22, 10

150 - 28 = 100 + 22 = 132 - 10

Basic Equations

100

13 + 7 = 32 - x

13 + 7 = 32 - x

20 = 32 - x

x = 12

200

25 + 75 = 130 - x

25 + 75 = 130 - x

100 = 130 - x

x = 130 - 100

x = 30

300

x + 19 = 29 - 4

x + 19 = 29 - 4

x + 19 = 25

x = 25 - 19

x = 6

400

120 - 70 = 89 - x

120 - 70 = 89 - x

50 = 89 - x

x = 89 - 50

x = 39

500

The sum of 15 and x is equal to the difference between 19 and 45. What is the value of x?

15 + x = 45 - 19

15 + x = 26

x = 26 - 15

x = 11

Identifying Pattern

100

A  B A ___ A B A B A __ 

B

B

200

C C C  ___ H H H H ___

C

C

300

F  ___ H F  F H F F H

H

400

A B B C C C D D D D __ __ ___ ___ ___ ___ 

E E E E E F

500

Zz Yy Xx ___ ____ ____

Ww Vv Uu

Random

100

Look at the numbers. Write the rule describing each pattern. 

7, 13, 19, 25, 31, 37, 43, 49

Start at 7 and add 6 each time. 

200

Make the scales balance by using addition and subtraction to find the values of the variables.

b + 17 = 20 + 7

b = 10

300

Describe the pattern followed by the hops in the number line. 

Start at 5 and add 2 each time. 

400

Describe the pattern followed by the hops of the number line. 

What would be the next number after 150?

Start at 40 and add 30 each time. 

180

500

Describe the pattern followed by the hops of the number line. 

What would be the next number after 70?

Start at 118 and subtract 24 each time.

46