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Algebra

Unknown Values: Addition & Subtraction

1

Find the Missing Number (Addition)

What number goes in the blank?

15
?
8
18
9
?
23
?
15
20
12
?
25
?
17
30
14
?
2

More Missing Addends

What number goes in the blank?

12
?
5
16
7
?
19
?
11
22
13
?
27
?
18
14
6
?
3

What Goes in the Box?

Circle the number that makes the sentence true.

___ + 6 = 14

6
7
8

9 + ___ = 17

6
7
8

___ + 12 = 20

7
8
9

15 + ___ = 22

5
6
7
4

More Missing Numbers

Circle the correct number.

___ + 8 = 15

5
6
7

11 + ___ = 20

8
9
10

___ + 14 = 25

10
11
12

7 + ___ = 19

11
12
13
5

Match Sentences to Missing Numbers

Draw a line to match.

___ + 5 = 13
7 + ___ = 16
___ + 9 = 20
6 + ___ = 18
12
8
11
9
6

Write the Missing Number

Fill in the blank.

___ + 7 = 15. Missing number = ___

8 + ___ = 22. Missing number = ___

___ + 13 = 25. Missing number = ___

16 + ___ = 30. Missing number = ___

7

Find the Missing Number (Subtraction)

What number goes in the blank?

20
?
7
25
16
?
30
?
12
18
11
?
35
?
19
22
13
?
8

More Subtraction Unknowns

What number goes in the blank?

28
?
15
32
17
?
24
?
9
40
23
?
19
?
11
33
20
?
9

What Goes in the Box? (Subtraction)

Circle the number that makes the sentence true.

___ − 5 = 13

17
18
19

24 − ___ = 16

6
7
8

___ − 9 = 21

28
29
30

30 − ___ = 18

10
11
12
10

More Subtraction Boxes

Circle the correct number.

___ − 7 = 15

20
21
22

35 − ___ = 20

13
14
15

___ − 12 = 18

28
29
30

28 − ___ = 19

7
8
9
11

Match Sentences to Missing Numbers

Draw a line to match.

___ + 8 = 20
25 − ___ = 17
14 + ___ = 23
___ − 6 = 19
25
12
8
9
12

More Matching

Match each sentence to the missing number.

___ − 5 = 25
18 + ___ = 30
40 − ___ = 28
___ + 11 = 35
12
30
24
12
13

Write Unknowns

Find the missing number.

___ + 15 = 32. Missing number = ___

45 − ___ = 28. Missing number = ___

___ − 13 = 27. Missing number = ___

19 + ___ = 41. Missing number = ___

14

Addition or Subtraction?

What operation do you need to find the missing number?

___ + 8 = 20. To find ___ you...

Subtract 8 from 20
Add 8 to 20
Multiply

30 − ___ = 18. To find ___ you...

Subtract 18 from 30
Add 18 and 30
Multiply

___ − 15 = 25. To find ___ you...

Add 15 and 25
Subtract 15 from 25
Divide
15

Find the Unknown (Bigger Numbers)

Work out the missing number. Show your thinking.

___ + 35 = 72. Missing number = ___

84 − ___ = 49. Missing number = ___

___ + 28 = 65. Missing number = ___

93 − ___ = 57. Missing number = ___

16

More Big Number Unknowns

Find the missing number.

___ + 46 = 81. Missing number = ___

72 − ___ = 35. Missing number = ___

___ − 29 = 54. Missing number = ___

17

Word Problems with Unknowns

Write a number sentence and solve.

Tom has some marbles. He gets 15 more and now has 38. How many did he start with? Number sentence: ___ + 15 = 38 Answer: ___

A jar had 50 lollies. Some were eaten and now there are 32. How many were eaten? Number sentence: 50 − ___ = 32 Answer: ___

18

Check Your Work

Is the missing number correct?

___ + 17 = 45. Answer: 28

Correct
Incorrect

60 − ___ = 35. Answer: 25

Correct
Incorrect

___ + 23 = 50. Answer: 37

Correct
Incorrect

82 − ___ = 46. Answer: 36

Correct
Incorrect
19

Home Activity: Mystery Numbers

Create mystery number puzzles for your family!

  • 1Write a number sentence with a blank: ___ + 15 = 32. Ask someone to solve it.
  • 2Play 'I'm thinking of a number': I add 8 and get 25. What's my number?
  • 3Make 5 different number sentences with blanks. Swap with a partner and solve.
  • 4Use subtraction too: I subtract 7 and get 18. What did I start with?
20

Missing Addends — Two-Digit

Fill in the missing number.

41
?
16
63
27
?
55
?
28
78
35
?
90
?
47
82
54
?
21

Missing Subtrahends — Two-Digit

Fill in the missing number.

50
?
23
74
46
?
61
?
33
85
59
?
40
?
18
92
64
?
22

Missing Numbers — Three-Digit

Find the unknown.

250
?
130
480
290
?
370
?
190
560
340
?
430
?
210
700
450
?
23

Find the Unknown — Set A

Circle the number that makes the sentence true.

___ + 24 = 50

24
26
28

47 + ___ = 80

31
33
35

___ + 38 = 75

35
37
39

52 + ___ = 100

46
48
50
24

Find the Unknown — Set B

Circle the number that makes the sentence true.

___ − 14 = 30

42
44
46

70 − ___ = 38

30
32
34

___ − 27 = 45

70
72
74

90 − ___ = 56

32
34
36
25

True or False — Unknowns

Circle True or False.

If ___ + 9 = 20, then ___ = 11

True
False

If 35 − ___ = 20, then ___ = 25

True
False

If ___ + 16 = 40, then ___ = 26

True
False

If 50 − ___ = 17, then ___ = 33

True
False
26

Match Number Sentences to Unknowns — Set A

Match each sentence to the missing number.

___ + 19 = 45
60 − ___ = 22
___ + 33 = 70
80 − ___ = 49
37
38
26
31
27

Match Number Sentences to Unknowns — Set B

Match.

___ + 47 = 90
65 − ___ = 28
___ − 39 = 50
72 + ___ = 100
89
43
37
28
28

Find Unknowns — Set A

Show your working.

___ + 43 = 90. Working: ___ Answer: ___

75 − ___ = 48. Working: ___ Answer: ___

___ + 28 = 65. Working: ___ Answer: ___

29

Find Unknowns — Set B

Show your working.

100 − ___ = 63. Working: ___ Answer: ___

___ − 25 = 46. Working: ___ Answer: ___

84 − ___ = 29. Working: ___ Answer: ___

30

Number Sentence Creation — Set A

Write a number sentence with an unknown for each situation.

I start with some money. I earn $15 more. Now I have $40. Number sentence: ___ Unknown: ___

I have some stickers. I give away 12. I have 25 left. Number sentence: ___ Unknown: ___

31

Number Sentence Creation — Set B

Write a number sentence with an unknown.

A bag had some apples. 9 fell out. Now there are 23. Number sentence: ___ Answer: ___

Ben collected some cards. He gave 17 to a friend. He has 38 left. Number sentence: ___ Answer: ___

32

Word Problems with Unknowns — Set A

Write a number sentence and solve.

Anna read some pages. She read 45 more. She has read 82 in total. Sentence: ___ Pages at start: ___

A jar had some lollies. 30 were eaten. 55 remain. Sentence: ___ Lollies at start: ___

33

Word Problems with Unknowns — Set B

Write a number sentence and solve.

There were some people at a concert. 24 left early. 76 stayed. Sentence: ___ Total at start: ___

Sam scored ___ points in a game. Then lost 18 points. He now has 43 points. Sentence: ___ Starting points: ___

34

Two-Step Unknowns

Find the unknown in each two-step problem.

___ + 10 + 15 = 40. The unknown is: ___

50 − ___ − 12 = 20. The unknown is: ___

___ + 20 − 8 = 30. The unknown is: ___

35

Sort: Add or Subtract to Find Unknown?

Sort each strategy needed.

___ + 15 = 30
50 − ___ = 20
___ + 28 = 60
80 − ___ = 45
70 + ___ = 100
___ − 12 = 38
Add to find the unknown
Subtract to find the unknown
36

Sort: Is the Unknown the Start, Change, or Result?

Identify the unknown type.

___ + 8 = 20
15 + ___ = 22
30 + 14 = ___
___ − 9 = 16
25 − ___ = 11
40 − 23 = ___
Unknown is the start
Unknown is the change
Unknown is the result
37

Unknown Values Solved

Count how many unknowns each student found.

ItemTallyTotal
Group A
Group B
Group C
Group D
38

Puzzle Creation

Write your own number sentences with unknowns for a partner to solve.

Addition puzzle: ___ + ___ = ___ (Make one part unknown)

Subtraction puzzle: ___ − ___ = ___ (Make one part unknown)

Word problem puzzle: ___

39

Reflect on Unknown Values

Write about what you have learnt.

When we have an unknown in an addition sentence, we can find it by: ___

When we have an unknown in a subtraction sentence, we can find it by: ___

Which type of unknown problem do you find hardest? Why? ___

40

Challenge Unknowns

These are harder! Show all your working.

___ + ___ = 40 where both unknowns are equal. What are they? ___

___ + 15 = 2 × 25. What is the unknown? ___

100 − ___ = 3 × 20. What is the unknown? ___

41

Unknown Values — Speed Round A

Fill in the missing number quickly!

50
?
23
75
48
?
100
?
37
60
28
?
85
?
56
42
17
?
42

Unknown Values — Speed Round B

Fill in the missing number.

200
?
85
300
170
?
500
?
345
400
230
?
250
?
190
350
120
?
43

Unknown in the Middle — Set A

Find the unknown.

10 + ___ + 5 = 20

3
4
5

30 − ___ − 8 = 17

4
5
6

25 + ___ − 10 = 30

13
14
15

50 − ___ + 5 = 25

28
30
32
44

Number Sentences with Unknowns — Set C

Find each unknown.

3 × ___ = 24. Unknown = ___

___ × 5 = 45. Unknown = ___

40 ÷ ___ = 8. Unknown = ___

___ ÷ 7 = 6. Unknown = ___

45

Balance the Scale

Find the unknown to balance each side.

15 + ___ = 8 + 14. Unknown = ___

30 − ___ = 12 + 6. Unknown = ___

___ + 9 = 3 × 8. Unknown = ___

50 − ___ = 4 × 9. Unknown = ___

46

Match Unknowns to Solutions

Match each number sentence to the unknown value.

___ + 45 = 100
60 − ___ = 25
___ − 38 = 42
75 + ___ = 100
25
35
80
55
47

Write Your Own Unknowns

Create number sentences with unknowns for each type.

Unknown at the start: ___ + ___ = ___

Unknown in the middle: ___ + ___ + ___ = ___

Unknown at the end: ___ + ___ = ___

Swap with a friend and solve each other's problems!

48

Home Activity: Mystery Number Games

Play mystery number games at home!

  • 1Think of a number. Add 10 and tell your partner. Can they find your starting number?
  • 2Write 5 equations with blanks. Leave overnight. Solve them fresh the next day.
  • 3Make a 'guess my number' game: give two clues, e.g. 'I add 7 to get 20' and 'I'm bigger than 10'.
  • 4Use objects: put some in a bag, add 4 more. Total is 13. How many were in the bag?
49

Find the Unknown — Addition

Find the missing number.

25
13
?
42
?
19
60
37
?
84
?
46
100
63
?
75
?
38
50

Find the Unknown — Subtraction

Find the missing number.

30
18
?
50
?
23
70
42
?
90
?
57
100
71
?
85
?
36
51

Find the Missing Number in Sequence

Find what comes in the blank.

10
30
40
50
?
100
90
70
60
?
15
20
25
35
?
52

Increasing Pattern with Rule

Find the rule and fill the missing number.

4
8
12
20
?
3
6
12
15
?
11
22
44
55
?
53

Solve for the Unknown — Set A

Circle the correct value.

___ + 14 = 30. The unknown is...

14
16
44

25 + ___ = 40. The unknown is...

10
15
65

___ − 8 = 17. The unknown is...

9
25
26

50 − ___ = 23. The unknown is...

27
73
23
54

Solve for the Unknown — Set B

Circle the correct value.

35 + ___ = 60. The unknown is...

20
25
95

___ + 47 = 100. The unknown is...

43
53
147

82 − ___ = 50. The unknown is...

32
42
132

___ − 25 = 45. The unknown is...

20
70
75
55

Which Symbol? — Set A

Circle the correct symbol to make the sentence true.

45 ___ 20 = 25

+
−
×

12 ___ 8 = 20

+
−
×

50 ___ 30 = 20

+
−
×

4 ___ 9 = 36

+
−
×
56

Which Symbol? — Set B

Circle the correct symbol.

100 ___ 35 = 65

+
−
×

7 ___ 8 = 56

+
−
×

72 ___ 9 = 8

−
÷
+

5 ___ 6 = 30

+
÷
×
57

Match Unknown Equations to Answers

Match.

___ + 16 = 30
45 − ___ = 20
___ + 28 = 50
60 − ___ = 37
22
25
23
14
58

Match Story to Equation

Match each story to the correct equation with an unknown.

Sam had some apples and gave away 5. He has 8 left.
Mia had 7 books and got some more. She has 15 now.
Jake started with 20 coins. He lost some and has 13.
Zoe had some jellybeans. She ate 6 and has 11 left.
? − 6 = 11
20 − ? = 13
7 + ? = 15
? − 5 = 8
59

Sort: Unknown at Start or End?

Sort each equation.

___ + 7 = 15
8 + ___ = 20
___ − 5 = 13
25 − ___ = 10
___ + 12 = 35
40 + ___ = 65
Unknown at the start
Unknown at the end
60

Sort: True or False?

Evaluate and sort.

3 + ? = 10 where ? = 7
20 − ? = 8 where ? = 8
? + 15 = 30 where ? = 15
? − 9 = 21 where ? = 12
40 + ? = 60 where ? = 20
? + 6 = 14 where ? = 9
True
False
61

Find the Unknown — Two-Step Problems

Solve these two-step unknown problems.

If ___ + 5 = 20 and ___ × 2 = ?, what is ? ___

If 30 − ___ = 15 and ___ + 10 = ?, what is ? ___

62

Mystery Number Riddles

Solve each riddle.

I add 12 to a mystery number and get 35. The mystery number is: ___

I subtract 18 from a mystery number and get 27. The mystery number is: ___

I double a mystery number and get 48. The mystery number is: ___

63

Write Your Own Missing Number Problems

Create 4 missing number problems of your own.

___ + ___ = ___ ___ − ___ = ___ ___ + ___ = ___ ___ − ___ = ___

Swap with a friend and solve each other's problems. Were the answers correct? ___

64

Balance the Scale

Make both sides equal by finding the missing value.

15 + ___ = 20 + 5 → ___ = ___

30 − ___ = 10 + 5 → ___ = ___

___ + 8 = 25 − 7 → ___ = ___

100 − ___ = 40 + 20 → ___ = ___

65

Using Inverse to Find Unknowns

Use the inverse operation to solve.

___ + 34 = 80. Use subtraction: 80 − 34 = ___

60 − ___ = 22. Use addition: 60 − 22 = ___

___ × 5 = 35. Use division: 35 ÷ 5 = ___

48 ÷ ___ = 6. Use multiplication: 6 × ___ = 48

66

Tally: Types of Unknowns Solved

Record how many of each type you solved.

ItemTallyTotal
Unknown at start
Unknown in middle
Unknown at end
67

Unknown Values Quiz Results

How many students solved each type correctly?

___ + n = total
total − n = ___
n × ___ = total
total ÷ ___ = n
1

Which type did students find easiest?

2

How many students solved subtraction correctly?

3

How many students were tested?

68

Write About Unknown Values

Reflect on solving equations with unknowns.

What does an 'unknown value' mean in mathematics? ___

What strategy do you use to find unknowns? ___

Why is it useful to find unknown values? Give a real-life example: ___

69

Home Activity: Number Sentence Hunt

Find and create equations with unknowns at home!

  • 1Look at a recipe. If it serves 4, how many does half the recipe serve? Write as an equation.
  • 2Think of your age. How many years until you are 18? Write as ___ + ___ = 18.
  • 3Make up 5 mystery number riddles. Share them with your family.
  • 4Draw a balance scale and show 3 balanced equations.
70

True or False Equations

Circle True or False for each equation.

___ + 14 = 30; the unknown is 16

True
False

45 − ___ = 27; the unknown is 17

True
False

___ + 38 = 70; the unknown is 32

True
False

100 − ___ = 63; the unknown is 47

True
False
71

Fill the Balance Scale

Fill in the missing value to balance each equation.

15
30
?
42
70
?
25
100
?
60
95
?
72

Unknown in Addition

Find the missing number in each addition bond.

52
?
27
81
36
?
100
?
44
130
75
?
200
?
87
73

Match: Equation to Solution

Match each equation to its correct solution.

___ + 23 = 50
60 − ___ = 34
___ + 45 = 100
75 − ___ = 48
26
27
55
27
74

Write the Equation from the Story

Turn each word problem into an equation with an unknown.

Sam had some stickers. He gave away 18 and now has 35. Write the equation: ___ − 18 = ___

A bag has some apples. 23 more are added and the total is 61. Equation: ___ + 23 = 61

Solve both unknowns and show your working:

75

Make Your Own Balanced Equations

Create 4 equations where each side is equal.

___ + ___ = ___ + ___ (all different numbers)

___ − ___ = ___ − ___ (all different numbers)

Explain how you checked both sides are equal:

76

Sort: Addition or Subtraction Unknown?

Sort each equation by the operation needed to find the unknown.

___ + 15 = 40
70 − ___ = 30
___ + 33 = 80
50 − ___ = 22
___ + 48 = 100
90 − ___ = 54
Need addition
Need subtraction
77

Fill the Frame — Find the Unknown

How many more counters needed to fill each frame?

?
?
?
?
?
78

Equations Solved Correctly

This graph shows how many equations each student solved correctly.

Anna
Blake
Cara
Dean
1

Who solved the most equations?

2

How many did Anna and Blake solve together?

3

How many would all four students score in total?

79

Home Activity: Equation Builder

Build equations with unknowns using household items!

  • 1Put some pasta in one cup and 12 in another. How many total? Write as ___ + 12 = total.
  • 2Use a kitchen scale: put some weight on one side. How much is needed to balance to 500 g?
  • 3Play 'guess my number': I add 25 and get 61. What's my number?
  • 4Make 5 equation cards for a family member to solve.
80

Unknown in Multiplication

Circle the correct unknown.

___ × 4 = 24

5
6
7

5 × ___ = 35

6
7
8

___ × 8 = 56

6
7
8

9 × ___ = 81

8
9
10
81

Growing Pattern Sequences

Find the pattern and fill in the missing term.

3
6
9
15
?
7
14
21
35
?
4
8
16
32
?
82

Unknown in Two-Step Problems

Find the unknown value.

50
?
18
100
63
?
75
?
38
120
47
?
200
?
85
83

Match Equation Type to Strategy

Match each type of unknown equation to the best strategy.

___ + 24 = 60
70 − ___ = 42
___ × 5 = 45
36 ÷ ___ = 9
Think: 45 ÷ 5
Think: 60 − 24
Think: 36 ÷ 9
Think: 70 − 42
84

Write Two-Step Equations

Create two-step equations with unknowns.

___ + 15 − 8 = 27. Find the unknown: ___ Show steps:

(___ × 4) + 6 = 30. Find the unknown: ___ Show steps:

85

Sort: Can This Be Solved with Addition or Subtraction?

Sort each equation by what operation solves it.

___ + 23 = 50
75 − ___ = 30
___ × 6 = 42
___ + 48 = 100
90 − ___ = 45
___ × 9 = 72
Solved by addition
Solved by subtraction
Solved by multiplication
86

Puzzle: Find the Three Numbers

Three numbers: A, B, C. A + B = 20. B + C = 30. A + C = 22.

Hint: add all three equations. A + B + C = ___

Use A + B + C to find each value: A = ___ B = ___ C = ___

Check: does A + B = 20? ___ B + C = 30? ___ A + C = 22? ___

87

Home Activity: Unknown Number Newspaper

Create a one-page unknown number newspaper!

  • 1Write 5 headlines using unknown numbers: 'Mayor earns ___ dollars if she earns $100 and spends $37.'
  • 2Create 3 puzzles for your family to solve using unknown values.
  • 3Find a pattern in nature and write it as an equation.
  • 4Design a 'Guess the Number' game for younger students using what you know about unknowns.

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