All Worksheets
Report a Mistake
Algebra

Unknown Values in Equations

1

Find the Missing Part – Addition (Set A)

Find the missing number in each equation.

45
18
?
72
?
35
100
53
?
150
?
86
200
127
?
2

Find the Missing Part – Addition (Set B)

Find the missing number.

30
12
?
55
?
28
80
45
?
125
?
67
250
143
?
3

Find the Missing Part – Addition (Set C)

Find the missing number.

60
?
25
90
37
?
110
?
58
175
89
?
300
?
162
4

Find the Missing Part – Subtraction (Set A)

Find the missing number. Total minus one part gives the other.

90
?
34
125
67
?
200
?
88
300
145
?
500
?
276
5

Find the Missing Part – Subtraction (Set B)

Find the missing number.

75
32
?
100
?
41
160
78
?
250
?
123
400
215
?
6

What Goes in the Box? (Set A)

Circle the number that makes each equation true.

___ + 24 = 61

33
37
41

85 − ___ = 39

44
46
48

___ + 156 = 200

34
44
54

300 − ___ = 178

112
122
132
7

What Goes in the Box? (Set B)

Circle the number that makes each equation true.

___ + 35 = 82

43
47
57

100 − ___ = 63

37
47
57

___ + 250 = 400

140
150
160

500 − ___ = 285

205
215
225
8

What Goes in the Box? (Set C)

Circle the correct number.

___ + 19 = 50

29
31
39

75 − ___ = 48

23
27
33

___ + 88 = 200

102
112
122

1000 − ___ = 725

265
275
285
9

Match Equations to Answers (Set A)

Draw a line from each equation to the value of the unknown.

___ + 15 = 42
63 − ___ = 28
100 − ___ = 47
___ + 88 = 150
53
27
62
35
10

Match Equations to Answers (Set B)

Draw a line from each equation to the unknown value.

___ + 34 = 80
120 − ___ = 55
200 − ___ = 137
___ + 75 = 200
63
46
125
65
11

True or False? (Equations)

Circle TRUE or FALSE.

25 + 75 = 100

TRUE
FALSE

If ___ + 30 = 80, then ___ = 40

TRUE
FALSE

If 100 − ___ = 35, then ___ = 65

TRUE
FALSE

If ___ + 48 = 100, then ___ = 62

TRUE
FALSE
12

True or False? (Equations – Set B)

Circle TRUE or FALSE.

If 50 − ___ = 23, then ___ = 27

TRUE
FALSE

If ___ + 64 = 100, then ___ = 46

TRUE
FALSE

If 200 − ___ = 85, then ___ = 115

TRUE
FALSE

If ___ × 4 = 20, then ___ = 6

TRUE
FALSE
13

Find the Unknown (Addition – Set C)

Find the missing number.

60
25
?
80
?
37
90
56
?
75
?
48
120
65
?
14

Find the Unknown (Addition – Set D)

Find the missing number.

150
83
?
200
?
127
500
245
?
300
?
178
1000
634
?
15

Find the Unknown (Set C)

Circle the value that makes the equation true.

___ + 36 = 80

34
44
54

90 − ___ = 53

37
43
47

___ + 125 = 200

65
75
85

300 − ___ = 187

103
113
123
16

Find the Unknown (Set D)

Circle the correct answer.

___ × 5 = 45

7
8
9

36 ÷ ___ = 9

3
4
5

___ × 8 = 56

6
7
8

72 ÷ ___ = 8

8
9
10
17

Find the Unknown (Set E – Multiplication)

Circle the value that makes it true.

___ × 6 = 42

6
7
8

___ × 3 = 27

8
9
10

4 × ___ = 48

10
11
12

___ × 7 = 63

8
9
10
18

Match Equations to Answers (Set C)

Draw a line from each equation to the unknown value.

___ + 45 = 100
80 − ___ = 33
___ × 6 = 54
48 ÷ ___ = 8
6
47
55
9
19

Match Equations to Answers (Set D)

Draw a line to match.

___ + 77 = 150
200 − ___ = 138
___ × 9 = 81
56 ÷ ___ = 7
8
62
73
9
20

Sort Equations by Operation

Sort each equation by the operation needed to solve it.

___ + 15 = 40
___ × 4 = 36
100 − ___ = 63
54 ÷ ___ = 6
___ + 88 = 200
___ × 7 = 49
Addition/Subtraction
Multiplication/Division
21

Write Your Own Equations

Write equations with unknown values, then solve them.

Write an addition equation where the answer is 50. Leave one number blank. Solve it.

Write a subtraction equation where the answer is 25. Leave one number blank. Solve it.

Write a multiplication equation with an unknown. Solve it.

22

Equations in Context

Write an equation for each problem, then solve it.

I had some stickers. I gave away 15 and have 23 left. How many did I start with? Equation: ___ − 15 = 23

I shared biscuits equally among 6 friends. Each got 8. How many did I have? Equation: ___ ÷ 6 = 8

I bought some books at $7 each and spent $42. How many books? Equation: ___ × 7 = 42

23

Equation Patterns

Find the pattern and continue.

10
20
30
40
?
?
?
5
10
20
40
?
?
?
24

Multiplication Unknowns

Find the missing factor. Total = partA × partB.

36
4
?
48
?
8
63
7
?
54
?
6
72
8
?
25

Larger Unknown Values (Set A)

Find the missing number.

500
234
?
750
?
418
1000
567
?
1200
?
735
26

Larger Unknown Values (Set B)

Find the missing number.

600
?
275
850
493
?
1000
?
382
1500
876
?
27

Solve the Equations (Set A)

Find the unknown value. Show your working.

___ + 234 = 500. The unknown is ___

375 − ___ = 198. The unknown is ___

___ + 167 = 400. The unknown is ___

600 − ___ = 347. The unknown is ___

28

Solve the Equations (Set B)

Find the unknown. Show working.

___ + 456 = 900. The unknown is ___

800 − ___ = 525. The unknown is ___

___ + ___ = 100 (find two different numbers that add to 100)

1,000 − ___ = 637. The unknown is ___

29

Word Problems with Unknowns (Set A)

Write an equation with an unknown, then solve.

I think of a number. I add 35 and get 82. What was my number?

I think of a number. I subtract 47 and get 53. What was my number?

30

Word Problems with Unknowns (Set B)

Write an equation and solve.

A bag has some marbles. 25 are added and now there are 68. How many were there at the start?

A jar has 150 lollies. Some are eaten and 87 are left. How many were eaten?

31

Which Equation Matches? (Set A)

Circle the correct equation for each problem.

I add 45 to a number and get 100.

___ + 45 = 100
___ − 45 = 100
45 × ___ = 100

I subtract a number from 80 and get 35.

80 + ___ = 35
80 − ___ = 35
___ − 80 = 35

A number plus 67 equals 200.

67 − ___ = 200
200 + ___ = 67
___ + 67 = 200
32

Which Equation Matches? (Set B)

Circle the correct equation.

250 minus a number equals 175.

250 − ___ = 175
175 − ___ = 250
___ + 250 = 175

A number added to 89 equals 150.

89 − ___ = 150
___ + 89 = 150
150 + ___ = 89

500 take away something gives 312.

500 + ___ = 312
312 − ___ = 500
500 − ___ = 312
33

Match Word Problems to Equations

Draw a line from each problem to its equation.

15 more than a number is 40
A number less 20 is 55
Double a number is 48
Half a number is 12
___ − 20 = 55
___ + 15 = 40
___ ÷ 2 = 12
___ × 2 = 48
34

Two-Step Equations

Solve these two-step problems. Show your working.

I think of a number, double it, and add 10. I get 50. What was my number?

I think of a number, subtract 15, and then add 8. I get 43. What was my number?

35

Challenge: Balance Puzzles

Both sides must be equal. Find the unknown.

___ + 25 = 40 + 10. What is ___?

100 − ___ = 35 + 15. What is ___?

___ + ___ + ___ = 60 (all three numbers are the same). What is each number?

36

Create Your Own Equations

Write your own equations with unknowns. Then give them to someone to solve!

Write an addition equation with an unknown:

Write a subtraction equation with an unknown:

Write a word problem that uses an unknown:

37

Home Activity: Mystery Number Games

Practise finding unknowns at home!

  • 1Play 'I'm thinking of a number.' Give clues like 'add 25 and you get 60'. Can your family guess?
  • 2Write equations on cards with one number missing. Race to solve them!
  • 3Think of your age. What do you add to get 100? What do you subtract to get 0?
  • 4Make a set of balance puzzles using household items and a ruler balance.
38

Find the Unknown (Multiplication, Set A)

Find the missing factor in each equation.

48
6
?
72
?
9
56
7
?
63
?
7
81
9
?
39

Find the Unknown (Multiplication, Set B)

Find the missing factor.

84
?
4
90
10
?
96
?
8
108
9
?
120
?
12
40

Find the Unknown Value (Set A)

Circle the correct value for the unknown.

□ + 47 = 93

46
140
36

158 − □ = 79

79
237
69

□ × 8 = 64

7
8
9

72 ÷ □ = 9

6
7
8
41

Find the Unknown Value (Set B)

Circle the correct value for the unknown.

□ + 136 = 250

114
124
386

300 − □ = 174

126
136
474

□ × 7 = 98

13
14
15

132 ÷ □ = 12

10
11
12
42

Equations with Unknowns on Both Sides

Find the value that makes each equation true.

□ + 18 = 35 + 12. What is □?

72 − □ = 40 + 8. What is □?

3 × □ = 2 × 18. What is □?

□ ÷ 4 = 5 × 3. What is □?

43

Match Equation to Its Unknown Value

Draw a line from each equation to the correct value of □.

□ + 28 = 65
90 − □ = 37
□ × 6 = 54
84 ÷ □ = 7
9
53
37
12
44

Sort: Equations with Addition or Subtraction Unknown

Sort each equation by which operation you use to find the unknown.

□ + 34 = 80
95 − □ = 47
□ × 9 = 63
□ + 123 = 200
144 ÷ □ = 12
78 − □ = 29
Use subtraction to find □
Use addition to find □
Use multiplication or division
45

Two-Step Equations

Solve each two-step equation.

2 × □ + 5 = 21. What is □?

□ ÷ 3 − 4 = 8. What is □?

3 × (□ + 4) = 30. What is □?

(□ − 7) ÷ 4 = 5. What is □?

46

Equations Form Sequences

Fill in the missing values in the pattern of equations.

5
10
20
25
?
100
90
80
60
?
3
9
27
243
?
47

Write Your Own Equations

Create equations with unknowns for each situation.

A number plus 47 equals 85. Write and solve the equation.

A number multiplied by 8 equals 96. Write and solve the equation.

75 minus a number equals 28. Write and solve the equation.

48

Word Problems with Unknowns (Set A)

Write an equation and solve each problem.

A bag of apples has an unknown number. Add 14 more and there are 30. How many were there at first?

A number is divided by 6 and the answer is 9. What is the number?

49

Word Problems with Unknowns (Set B)

Write an equation and solve each problem.

A baker makes some pies. After selling 23, there are 45 left. How many were made?

There are 6 equal groups of students. There are 78 students altogether. How many in each group?

50

True, False or Open? (Set A)

Circle whether each equation is always TRUE, always FALSE, or OPEN (depends on □).

□ + 5 = 10

Always TRUE
Always FALSE
OPEN

6 × 7 = 42

Always TRUE
Always FALSE
OPEN

□ × 0 = 100

Always TRUE
Always FALSE
OPEN

□ + □ = 2 × □

Always TRUE
Always FALSE
OPEN
51

Equation Types Tally

Count how many unknowns are in the addition, subtraction, multiplication and division positions.

ItemTallyTotal
Unknown in addition
Unknown in subtraction
Unknown in multiplication
Unknown in division
52

Algebra Reasoning

Answer each question about equations.

If □ + 50 = 150, what is □ + 60? Explain without solving from scratch.

If 3 × □ = 60, what is 6 × □? Explain the relationship.

Write an equation where □ = 12. Make it tricky!

53

Challenge: Inequalities

Find values that make each statement true.

□ + 30 > 50. List 4 possible values for □.

□ × 5 < 30. List all whole number values for □.

100 − □ ≥ 60. What values can □ be?

What to do next

Algebra

Algorithms & Number Patterns

Follow and create algorithms that generate sets of numbers and identify emerging patterns