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Algebra

Missing Elements in Patterns

1

Find the Missing Number (Add 2)

Find the missing numbers in each pattern.

4
6
10
12
?
14
18
20
?
?
26
28
32
?
?
2

Find the Missing Number (Add 2) — More

Fill in the missing numbers.

6
8
12
14
?
18
22
24
?
?
34
36
40
?
?
3

Find the Missing Number (Add 5)

Find the missing numbers in each pattern.

5
10
20
25
?
10
20
25
?
?
35
40
50
?
?
4

Find the Missing Number (Add 5) — More

Fill in the missing numbers.

55
60
70
75
?
20
30
35
?
?
80
85
95
?
?
5

Find the Missing Number (Add 10)

Fill in the missing numbers.

10
20
40
50
?
30
50
60
?
?
80
90
110
?
?
6

What Goes in the Gap? (Easy)

Circle the number that fills the gap.

2, 4, ___, 8, 10

5
6
7

10, 20, ___, 40, 50

25
30
35

5, 10, 15, ___, 25

18
20
22

3, 6, 9, ___, 15

11
12
13
7

More Missing Number Gaps (Easy)

Circle the number that fills the gap.

4, 8, ___, 16, 20

10
12
14

100, 200, ___, 400, 500

250
300
350

1, 3, 5, ___, 9

6
7
8

6, 12, 18, ___, 30

22
24
26
8

What Comes Next in the Group?

The groups grow by 3. How many in each row?

?
?
?
?
9

Match Patterns to Missing Numbers

Match each pattern to the number that fills its gap.

2, 4, ___, 8
10, ___, 30, 40
15, 12, ___, 6
___, 8, 12, 16
4
6
20
9
10

Find the Missing Number (Subtract 2)

Find the missing numbers in each decreasing pattern.

20
18
14
12
?
30
26
24
?
?
16
14
10
?
?
11

Find the Missing Number (Subtract 5)

Find the missing numbers in each decreasing pattern.

40
30
25
20
?
50
45
35
?
?
85
80
70
?
?
12

Find the Missing Number (Subtract 5) — More

Fill in the missing numbers.

65
60
50
45
?
100
90
85
?
?
70
65
55
?
?
13

Find the Missing Number (Subtract 3)

Find the missing numbers.

30
27
21
18
?
24
18
15
?
?
42
39
33
?
?
14

Find the Missing Number (Subtract 10)

Fill in the missing numbers.

100
90
70
60
?
200
180
170
?
?
140
130
110
?
?
15

What Goes in the Gap? (Decreasing)

Circle the number that fills the gap.

20, 18, 16, ___, 12

13
14
15

50, 40, ___, 20, 10

25
30
35

100, 90, 80, ___, 60

65
70
75

36, ___, 24, 18, 12

28
30
32
16

More Decreasing Gaps

Circle the number that fills the gap.

45, 40, ___, 30, 25

33
35
37

60, ___, 40, 30, 20

45
50
55

28, 24, 20, ___, 12

14
16
18

90, 80, ___, 60, 50

65
70
75
17

Match Decreasing Patterns

Match each pattern to its missing number.

30, ___, 20, 15
40, 36, ___, 28
100, ___, 80, 70
___, 18, 15, 12
21
25
32
90
18

Fill in Missing Objects (Repeating)

What object comes next? Fill in the missing ones.

?
?
?
?
?
?
19

More Missing Objects

Fill in the missing objects.

?
?
?
?
?
?
20

Tricky Missing Numbers (Add 4)

Find all the missing numbers. Look carefully at the pattern!

4
12
16
?
?
28
32
40
?
?
8
16
24
?
?
21

Tricky Missing Numbers (Mixed)

Find all the missing numbers.

15
20
30
?
?
100
80
70
?
?
6
9
15
?
?
50
40
35
?
?
22

Find the Rule, Then the Missing Number

Work out the rule first, then circle the missing number.

7, 14, 21, ___, 35 (Rule: add ?)

25
28
30

60, 50, ___, 30, 20 (Rule: subtract ?)

35
40
45

8, 12, 16, ___, 24 (Rule: add ?)

18
20
22

45, ___, 35, 30, 25 (Rule: subtract ?)

38
40
42
23

Write the Rule and Find the Missing Number

Write what the rule is, then fill in the missing number.

Pattern: 7, 14, 21, ___, 35 Rule: ___ Missing number: ___

Pattern: 60, 50, ___, 30, 20 Rule: ___ Missing number: ___

Pattern: 8, 12, 16, ___, 24 Rule: ___ Missing number: ___

24

Find Missing Numbers (Add 3)

Fill in the missing numbers.

3
6
12
15
?
18
24
27
?
?
33
36
42
?
?
25

Find Missing Numbers (Subtract 4)

Fill in the missing numbers.

40
36
28
24
?
56
48
44
?
?
32
28
20
?
?
26

Find Missing Numbers (Add 6)

Fill in the missing numbers.

6
12
24
30
?
36
48
54
?
?
18
24
36
?
?
27

What Number Is Missing? (Mixed Rules)

Work out the rule and circle the missing number.

9, 12, 15, ___, 21

17
18
19

40, 35, ___, 25, 20

28
30
32

8, 16, ___, 32, 40

20
22
24

100, ___, 80, 70, 60

85
90
95
28

More Mixed Missing Numbers

Circle the missing number.

6, 9, ___, 15, 18

11
12
13

50, 45, 40, ___, 30

33
35
37

4, 8, 12, 16, ___

18
20
22

70, ___, 50, 40, 30

55
60
65
29

Match Missing Numbers to Patterns

Match each pattern to its missing number.

4, 8, ___, 16, 20
50, ___, 30, 20, 10
6, 12, 18, ___, 30
100, 90, ___, 70, 60
80
12
40
24
30

Pattern Bonds — What Goes in the Gap?

Use your knowledge of patterns to fill in the missing part.

20
12
?
30
?
15
45
30
?
50
?
25
36
24
?
60
?
40
31

Object Pattern — Find the Missing One

What comes next in the pattern?

?
?
?
?
?
?
32

Growing Object Pattern

The groups are getting bigger. Draw the next group.

?
?
?
?
?
?
?
?
?
33

Sort Patterns by Rule

Sort these patterns by whether they increase or decrease.

5, 10, 15, 20
30, 25, 20, 15
4, 8, 12, 16
100, 90, 80, 70
3, 6, 9, 12
50, 40, 30, 20
Increasing
Decreasing
34

Two Missing Numbers at Once

Find BOTH missing numbers in each pattern.

10
15
20
?
?
14
12
10
?
?
8
12
16
?
?
90
80
70
?
?
35

Three Missing Numbers!

Find all the missing numbers. This is tricky!

6
12
?
?
?
40
20
?
?
?
8
16
?
?
?
36

Write the Rule and Find the Missing Number (Hard)

Work out the rule, then find the missing number.

Pattern: 11, 22, ___, 44, 55 Rule: ___ Missing number: ___

Pattern: 84, 72, 60, ___, 36 Rule: ___ Missing number: ___

Pattern: 15, ___, 35, 45, 55 Rule: ___ Missing number: ___

37

Create a Pattern Puzzle

Create your own pattern with a missing number. Write the answer on the back!

My increasing pattern: ___, ___, ___, ___, ___ The rule is: ___

My decreasing pattern: ___, ___, ___, ___, ___ The rule is: ___

38

Home Activity: Pattern Puzzles

Create pattern puzzles for your family to solve!

  • 1Write a number pattern on paper but leave one number blank. Can someone find it?
  • 2Make a bead or button pattern with a missing piece. Ask someone to fill it in.
  • 3Write the numbers 1 to 50 but leave out the multiples of 5. What's missing?
  • 4Take turns making patterns for each other to solve.
39

Trace Numbers Used in Patterns

Trace these numbers that often appear as missing elements.

15
25
35
45
55
65
75
85
40

Missing Elements — Add 3

Fill in the missing numbers.

9
15
18
21
?
27
30
36
?
?
33
36
42
?
?
41

Missing Elements — Subtract 3

Fill in the missing numbers.

30
27
21
18
?
21
18
12
?
?
48
45
39
?
?
42

Missing Elements — Bigger Numbers

Fill in the missing numbers. Find the pattern first!

200
250
350
400
?
175
200
250
?
?
500
600
650
?
?
43

Missing Group — How Many?

The groups grow by 5 each time. How many in the missing group?

?
?
?
×10
×10
?
44

Which Group is Missing?

The groups grow by 3 each time. Write the missing count.

?
?
?
?
45

Which Number Is Missing?

Circle the missing number for each pattern.

10, 20, ___, 40, 50

25
30
35

5, ___, 15, 20, 25

8
10
12

100, 95, 90, ___, 80

82
84
85

7, 14, 21, ___, 35

26
28
30
46

Find the Rule Then Fill In

Work out the rule, then circle the missing number.

3, 6, ___, 12, 15. Rule: add ___?

Add 2 → 8
Add 3 → 9
Add 4 → 10

40, 35, ___, 25, 20. Rule: subtract ___?

Subtract 3 → 32
Subtract 4 → 31
Subtract 5 → 30

8, 16, ___, 32, 40. Rule: add ___?

Add 6 → 22
Add 8 → 24
Add 9 → 25

60, ___, 44, 36, 28. Rule: subtract ___?

Subtract 7 → 53
Subtract 8 → 52
Subtract 9 → 51
47

Match Missing Numbers to Patterns

Match each missing number to the correct pattern.

3, ___, 9, 12
20, 16, ___, 8
50, 55, ___, 65
30, 27, 24, ___
21
60
12
6
48

Match Patterns to Their Missing Middle

Match each pattern to the number that belongs in the middle.

10, ___, 30, 40, 50
3, 6, ___, 12, 15
50, ___, 30, 20, 10
8, 10, ___, 14, 16
9
12
40
20
49

Sort: Add Pattern or Subtract Pattern?

Sort these patterns by whether they are increasing or decreasing.

6, ___, 12, 15
20, ___, 12, 8
100, ___, 80, 70
3, ___, 9, 12
50, 55, ___, 65
24, 21, ___, 15
Increasing (adding)
Decreasing (subtracting)
50

Sort by Step Size

Sort these patterns by how much they go up or down by.

2, ___, 6, 8
4, ___, 12, 16
10, ___, 30, 40
9, ___, 15, 18
5, ___, 15, 20
100, ___, 120, 130
Step size 2–3
Step size 4–5
Step size 10+
51

Pattern Puzzle Results

Record how many students solved each type of missing-element puzzle.

ItemTallyTotal
Easy add
Easy subtract
Hard add
Hard subtract
52

Write a Pattern with Two Missing Numbers

Fill in two missing numbers for each pattern.

Pattern (add 4): 4, ___, 12, ___, 20 Missing: ___ and ___

Pattern (subtract 6): 60, ___, 48, ___, 36 Missing: ___ and ___

Pattern (add 9): 9, ___, 27, ___, 45 Missing: ___ and ___

53

Mystery Patterns

There are two numbers missing. Find the rule and fill them in.

___, ___, 21, 28, 35 (add 7) → missing: ___ and ___

80, ___, ___, 56, 48 (subtract 8) → missing: ___ and ___

___, 15, ___, 25, 30 (add 5) → missing: ___ and ___

54

Missing Part in a Bond

Find the missing number in each number bond.

50
30
?
75
?
25
100
60
?
45
?
15
80
50
?
35
?
20
55

Explain Your Strategy

Explain how you find the missing number in a pattern.

3, ___, 9, 12, 15 I found the missing number by: ___

50, 45, ___, 35, 30 I found the missing number by: ___

What strategy do you use to find missing numbers? ___

56

What Is the Missing Element?

Circle the number that belongs in the blank.

5, 10, ___, 20, 25

12
15
14

100, 90, ___, 70, 60

75
85
80

3, 6, 9, ___, 15

11
12
13

50, 45, 40, ___, 30

38
35
37
57

Sort Patterns by Rule Type

Sort these patterns by their rule.

2, 4, ___, 8, 10 (add 2)
20, 15, ___, 5 (subtract 5)
10, 13, ___, 19 (add 3)
30, ___, 20, 15 (subtract 5)
7, ___, 21, 28 (add 7)
40, 36, ___, 28 (subtract 4)
Add rule
Subtract rule
58

Match Patterns to Their Missing Numbers

Match each pattern to the number that fills the blank.

4, 8, ___, 16
25, ___, 15, 10
7, ___, 21, 28
90, 80, ___, 60
20
12
70
14
59

Count Objects in Patterns

Count the objects. Identify the pattern rule.

?
?
?
60

Ten Frames — Missing Dots

How many dots are missing from each ten frame? Write the rule.

?
?
?
?
61

Pattern Graph — Counting by 3

Read the picture graph. How many objects in each row?

Row 1
Row 2
Row 3
Row 4
1

What is the pattern rule?

2

How many circles would be in row 5?

3

How many circles altogether?

62

Which Patterns Did You Find Easiest?

Record which pattern type students found easiest.

ItemTallyTotal
Add 2
Add 5
Subtract 3
Subtract 10
63

Compare Pattern Totals

Which pattern produces larger numbers? Circle it.

Add 4 pattern vs add 5 pattern?

vs

Which rule gives 20?

vs

Count by 4 or count by 6?

vs

Which is the bigger jump?

vs
64

Mixed Missing Elements

Find the rule and fill in the missing numbers.

7
14
28
35
?
40
30
10
?
?
11
33
44
?
?
65

My Own Missing Element Pattern

Create your own pattern with a missing element.

My pattern rule is: add ___ My pattern: ___, ___, ___, ___, ___ The missing element is: ___

My pattern rule is: subtract ___ My pattern: ___, ___, ___, ___, ___ The missing element is: ___

66

Pattern Shapes

Trace these shapes used in visual patterns.

Circle0 corners
Square4 sides
Triangle3 sides
Diamond4 sides
67

Pattern Detectives

Be a pattern detective! Explain how you found each missing number.

4, ___, 12, 16 → Missing: ___ I found it by ___

55, 50, ___, 40 → Missing: ___ I found it by ___

What's your best strategy for finding missing pattern elements? ___

What to do next

Measurement

Measuring with Informal Units

Measure and compare shapes and objects using uniform informal units