Algebra

Increasing & Decreasing Patterns

1

Add 2 Each Time

Fill in the missing numbers. The pattern adds 2 each time.

2
4
8
10
?
12
16
18
?
?
22
24
28
?
?
2

Add 2 — More Practice

Fill in the missing numbers.

30
32
36
38
?
44
48
50
?
?
56
58
62
?
?
3

Add 5 Each Time

Fill in the missing numbers. The pattern adds 5 each time.

5
10
20
25
?
30
40
45
?
?
55
60
70
?
?
4

Add 5 — More Practice

Fill in the missing numbers.

75
80
90
95
?
15
25
30
?
?
45
50
60
?
?
5

Add 10 Each Time

Fill in the missing numbers. The pattern adds 10.

10
20
40
50
?
50
70
80
?
?
110
120
140
?
?
6

Add 10 — Starting Big

Fill in the missing numbers.

200
210
230
240
?
350
370
380
?
?
510
520
540
?
?
7

What Is the Rule? (Adding)

Look at the pattern and circle the rule.

3, 6, 9, 12, 15

Add 2
Add 3
Add 5

4, 8, 12, 16, 20

Add 3
Add 4
Add 5

7, 14, 21, 28, 35

Add 5
Add 7
Add 8

10, 20, 30, 40, 50

Add 5
Add 10
Add 20
8

More Rules to Find (Adding)

Circle the rule for each pattern.

1, 3, 5, 7, 9

Add 1
Add 2
Add 3

6, 12, 18, 24, 30

Add 4
Add 5
Add 6

100, 110, 120, 130, 140

Add 5
Add 10
Add 20

8, 11, 14, 17, 20

Add 2
Add 3
Add 4
9

Growing Groups

Count the objects in each row. Notice the pattern!

?
?
?
?
10

Growing by 5s

Count the objects in each row. The pattern grows by 5!

?
?
?
?
11

Subtract 2 Each Time

Fill in the missing numbers. The pattern subtracts 2.

20
18
14
12
?
30
26
24
?
?
38
36
32
?
?
12

Subtract 2 — More Practice

Fill in the missing numbers.

50
48
44
42
?
26
22
20
?
?
14
12
8
?
?
13

Subtract 5 Each Time

Fill in the missing numbers. The pattern subtracts 5.

50
45
35
30
?
100
90
85
?
?
70
65
55
?
?
14

Subtract 5 — More Practice

Fill in the missing numbers.

80
75
65
60
?
45
35
30
?
?
90
85
75
?
?
15

Subtract 10 Each Time

Fill in the missing numbers. The pattern subtracts 10.

100
90
70
60
?
150
130
120
?
?
180
170
150
?
?
16

Subtract 10 — Starting Big

Fill in the missing numbers.

500
490
470
460
?
350
330
320
?
?
240
230
210
?
?
17

What Is the Rule? (Subtracting)

Look at the pattern and circle the rule.

25, 20, 15, 10, 5

Subtract 3
Subtract 5
Subtract 10

36, 33, 30, 27, 24

Subtract 2
Subtract 3
Subtract 4

80, 70, 60, 50, 40

Subtract 5
Subtract 10
Subtract 20

18, 16, 14, 12, 10

Subtract 2
Subtract 3
Subtract 4
18

More Decreasing Rules

Circle the rule for each pattern.

40, 36, 32, 28, 24

Subtract 3
Subtract 4
Subtract 5

50, 45, 40, 35, 30

Subtract 3
Subtract 5
Subtract 10

100, 90, 80, 70, 60

Subtract 5
Subtract 10
Subtract 20

30, 27, 24, 21, 18

Subtract 2
Subtract 3
Subtract 4
19

Match Rules to Sequences

Match each rule to the correct number pattern.

Add 3
Subtract 4
Add 6
Subtract 5
40, 35, 30, 25
2, 8, 14, 20
5, 8, 11, 14
32, 28, 24, 20
20

More Rules to Match

Match each rule to its pattern.

Add 2
Subtract 3
Add 10
Subtract 2
20, 18, 16, 14
3, 5, 7, 9
18, 15, 12, 9
10, 20, 30, 40
21

Add 3 Each Time

Fill in the missing numbers.

3
6
12
15
?
21
27
30
?
?
42
45
51
?
?
22

Add 4 Each Time

Fill in the missing numbers.

4
8
16
20
?
24
32
36
?
?
44
48
56
?
?
23

Subtract 4 Each Time

Fill in the missing numbers.

40
36
28
24
?
52
44
40
?
?
60
56
48
?
?
24

Growing Object Patterns

Continue the pattern by drawing the next group.

?
?
?
?
?
?
?
?
?
25

Shrinking Object Patterns

The pattern shrinks. Draw what comes next.

?
?
?
?
?
?
26

Increasing or Decreasing?

Is the pattern increasing or decreasing?

5, 10, 15, 20, 25

Increasing
Decreasing

30, 25, 20, 15, 10

Increasing
Decreasing

100, 200, 300, 400

Increasing
Decreasing

48, 44, 40, 36, 32

Increasing
Decreasing
27

Create Your Own Increasing Pattern

Create a pattern using the given rule. Write at least 6 numbers.

Start at 4, add 3 each time: 4, ___, ___, ___, ___, ___

Start at 7, add 5 each time: 7, ___, ___, ___, ___, ___

Start at 10, add 4 each time: 10, ___, ___, ___, ___, ___

28

Create Your Own Decreasing Pattern

Create a pattern using the given rule.

Start at 50, subtract 4 each time: 50, ___, ___, ___, ___, ___

Start at 100, subtract 10 each time: 100, ___, ___, ___, ___, ___

Start at 30, subtract 3 each time: 30, ___, ___, ___, ___, ___

29

Add 6 Each Time

Fill in the missing numbers.

6
12
24
30
?
36
48
54
?
?
66
72
84
?
?
30

Subtract 6 Each Time

Fill in the missing numbers.

60
54
42
36
?
72
60
54
?
?
30
24
12
?
?
31

Pattern Steps — How Much Between?

Work out the step size between each pair.

15
10
?
24
?
18
40
30
?
100
?
90
35
28
?
50
?
45
32

What Comes Next?

Circle the next number in the pattern.

3, 6, 9, 12, ___

14
15
16

50, 45, 40, 35, ___

25
30
35

4, 8, 12, 16, ___

18
20
22

100, 90, 80, 70, ___

50
55
60
33

More Next Numbers

Circle the next number.

7, 14, 21, 28, ___

30
33
35

60, 55, 50, 45, ___

35
40
42

8, 12, 16, 20, ___

22
24
26

200, 190, 180, 170, ___

150
155
160
34

Decreasing Groups

Count the objects. Notice the shrinking pattern!

?
?
?
?
35

Sort: Increasing or Decreasing?

Sort each pattern.

5, 10, 15, 20
40, 35, 30, 25
2, 4, 6, 8
100, 90, 80, 70
3, 6, 9, 12
50, 45, 40, 35
Increasing
Decreasing
36

Match Patterns to Their Rules

Match each pattern to its rule.

10, 15, 20, 25
36, 30, 24, 18
4, 8, 12, 16
100, 93, 86, 79
Subtract 7
Add 5
Add 4
Subtract 6
37

Describe the Pattern

Write the rule for each pattern.

2, 6, 10, 14, 18 — Rule: ___

45, 40, 35, 30, 25 — Rule: ___

3, 9, 15, 21, 27 — Rule: ___

38

Create and Extend

Continue each pattern for 3 more numbers.

5, 10, 15, 20, ___, ___, ___

80, 70, 60, 50, ___, ___, ___

3, 7, 11, 15, ___, ___, ___

48, 42, 36, 30, ___, ___, ___

39

Home Activity: Pattern Hunt

Find patterns that go up or down around your home!

  • 1Count steps as you walk upstairs. What is the pattern?
  • 2Stack blocks: 1, then 3, then 5. How many next?
  • 3Count backwards from 20 by 2s. Say the pattern out loud.
  • 4Make a growing pattern with pasta or buttons.
40

Trace Pattern Numbers

Trace these numbers used in number patterns.

3
6
9
12
15
18
21
24
41

Add 7 Each Time

Fill in the missing numbers.

7
14
28
35
?
42
56
63
?
?
21
28
42
?
?
42

Subtract 7 Each Time

Fill in the missing numbers.

70
63
49
42
?
35
21
14
?
?
56
49
35
?
?
43

Add 8 Each Time

Fill in the missing numbers.

8
16
32
40
?
48
64
72
?
?
24
32
48
?
?
44

Subtract 8 Each Time

Fill in the missing numbers.

80
72
56
48
?
40
24
16
?
?
64
56
40
?
?
45

Add 20 Each Time

Fill in the missing numbers.

20
40
80
100
?
120
160
180
?
?
240
260
300
?
?
46

Mixed Increasing and Decreasing

Fill in the missing numbers. Work out the rule first!

15
20
30
35
?
90
70
60
?
?
45
40
30
?
?
47

Growing by 3s

Count the objects in each row. The pattern grows by 3!

?
?
?
?
48

Shrinking by 4s

Count the objects in each row. The pattern shrinks by 4!

?
?
?
?
49

Object Patterns — Growing by 2

Continue each growing pattern.

?
?
?
?
?
?
50

Repeating Then Growing

Look at the pattern. Draw what comes next.

?
?
?
?
?
?
51

Compare Pattern Terms

For each pair, decide which value is bigger.

Add-5 pattern: which is bigger?

vs

Subtract-5 pattern: which is bigger?

vs

Are these equal?

vs

Subtract-10 pattern: which is bigger?

vs
52

Find the Mistake in the Pattern

Circle the number that does NOT fit the pattern.

5, 10, 15, 21, 25

5
21
25

20, 18, 16, 13, 12

16
13
12

3, 6, 9, 11, 15

9
11
15

100, 90, 80, 68, 60

80
68
60
53

What Number Comes Next?

Circle the next number in each pattern.

8, 12, 16, 20, ___

22
24
26

35, 30, 25, 20, ___

12
15
18

6, 12, 18, 24, ___

28
30
32

64, 56, 48, 40, ___

30
32
34
54

Match Patterns to Rules

Match each pattern to the rule used.

5, 10, 15, 20
30, 25, 20, 15
8, 16, 24, 32
40, 30, 20, 10
Subtract 10
Add 5
Add 8
Subtract 5
55

Group by Step Size

Sort these patterns by their step size.

2, 4, 6, 8
5, 10, 15, 20
9, 12, 15, 18
50, 40, 30, 20
7, 9, 11, 13
100, 90, 80, 70
Step of 2 or 3
Step of 5 or 10
56

Pattern Lengths

Record how many terms are in each pattern found.

ItemTallyTotal
4 terms
5 terms
6 terms
7+ terms
57

Explain the Rule

Look at each pattern and explain the rule in words.

4, 8, 12, 16, 20 Rule: ___

100, 93, 86, 79, 72 Rule: ___

1, 5, 9, 13, 17 Rule: ___

58

Create Your Own Patterns

Write a pattern with at least 6 terms. Write the rule below.

My increasing pattern: ___, ___, ___, ___, ___, ___ Rule: ___

My decreasing pattern: ___, ___, ___, ___, ___, ___ Rule: ___

A pattern that starts at 100: ___, ___, ___, ___, ___, ___ Rule: ___

59

Pattern Puzzle

Find the missing number in the middle of each pattern.

12, ___, 20, 24, 28 (pattern adds 4) → missing: ___

50, 43, ___, 29, 22 (pattern subtracts 7) → missing: ___

11, 22, ___, 44, 55 (pattern adds 11) → missing: ___