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Algebra

Finding Unknown Values

1

Find the Missing Factor (A)

Find the missing number. Example: 6 × ___ = 42, answer is 7.

36
4
?
56
7
?
45
5
?
72
9
?
2

Find the Missing Factor (B)

Find the missing number.

63
?
7
48
?
6
32
?
4
81
?
9
3

Find the Missing Factor (C)

Find the missing number.

42
6
?
54
?
6
35
5
?
64
?
8
4

Match Equations to Answers (A)

Draw a line from each equation to the missing number.

___ × 8 = 64
7 × ___ = 49
___ × 6 = 54
9 × ___ = 54
9
8
7
6
5

Match Equations to Answers (B)

Draw a line from each equation to the missing number.

___ × 5 = 40
3 × ___ = 27
___ × 7 = 77
4 × ___ = 48
12
8
9
11
6

What Is the Missing Number? (A)

Circle the correct answer.

___ × 6 = 30

4
5
6

7 × ___ = 56

7
8
9

___ × 9 = 63

6
7
8

8 × ___ = 72

8
9
10
7

What Is the Missing Number? (B)

Circle the correct answer.

___ × 4 = 36

8
9
10

5 × ___ = 45

7
8
9

___ × 3 = 27

7
8
9

6 × ___ = 42

6
7
8
8

Missing Factor Practice (A)

Find the missing number in each equation.

___ × 7 = 49. Missing number: ___

8 × ___ = 64. Missing number: ___

___ × 6 = 48. Missing number: ___

9 × ___ = 54. Missing number: ___

9

Missing Factor Practice (B)

Find the missing number.

___ × 5 = 60. Missing number: ___

4 × ___ = 52. Missing number: ___

___ × 8 = 96. Missing number: ___

3 × ___ = 78. Missing number: ___

10

Sort: Missing Number Greater or Less Than 10?

Work out the missing number and sort it.

___ × 6 = 48 → 8
___ × 5 = 75 → 15
___ × 4 = 36 → 9
___ × 3 = 42 → 14
___ × 7 = 84 → 12
___ × 9 = 72 → 8
Missing number < 10
Missing number ≥ 10
11

Find the Missing Number — Division (A)

Circle the correct answer.

___ ÷ 5 = 12

50
60
70

72 ÷ ___ = 9

6
7
8

___ ÷ 8 = 7

48
56
64

96 ÷ ___ = 12

6
8
9
12

Find the Missing Number — Division (B)

Circle the correct answer.

___ ÷ 6 = 15

80
90
96

108 ÷ ___ = 12

8
9
10

___ ÷ 7 = 11

70
77
84

144 ÷ ___ = 16

8
9
10
13

Solve Division Equations (A)

Find the unknown value in each equation.

5 × ___ = 85. So ___ = ___

___ ÷ 6 = 15. So ___ = ___

___ × 7 = 98. So ___ = ___

144 ÷ ___ = 12. So ___ = ___

14

Solve Division Equations (B)

Find the unknown value.

___ ÷ 9 = 13. So ___ = ___

8 × ___ = 104. So ___ = ___

___ ÷ 4 = 25. So ___ = ___

156 ÷ ___ = 12. So ___ = ___

15

Match Equations to Unknown Values

Draw a line from each equation to the unknown value.

___ ÷ 8 = 9
___ × 6 = 90
96 ÷ ___ = 12
7 × ___ = 91
8
72
13
15
16

Multiplication and Division Link

If the total is the product, one part is a factor. Find the other factor.

84
7
?
108
9
?
96
6
?
132
11
?
150
5
?
168
8
?
17

Relate Multiplication and Division

Write the related multiplication and division facts.

If 12 × 8 = 96, then 96 ÷ 8 = ___ and 96 ÷ 12 = ___

If 15 × 6 = 90, then 90 ÷ 6 = ___ and 90 ÷ 15 = ___

If ___ × 7 = 91, then 91 ÷ 7 = ___ and 91 ÷ ___ = 7

18

Unknown Value Word Problems (A)

Write an equation and solve.

I think of a number, multiply it by 6 and get 78. What is my number? Equation: ___ × 6 = 78. Answer: ___

I think of a number, divide it by 5 and get 17. What is my number? Equation: ___ ÷ 5 = 17. Answer: ___

19

Unknown Value Word Problems (B)

Write an equation and solve.

48 lollies are shared equally and each person gets 8. How many people? Equation: 48 ÷ ___ = 8. Answer: ___

Some boxes hold 9 oranges each. There are 108 oranges. How many boxes? Equation: ___ × 9 = 108. Answer: ___

20

Two-Step Equations (A)

Find the unknown value. Show your working.

3 × ___ + 5 = 32. What is the missing number?

Draw here

___ × 4 − 10 = 30. What is the missing number?

Draw here

60 ÷ ___ + 8 = 20. What is the missing number?

Draw here
21

Two-Step Equations (B)

Find the unknown value.

5 × ___ − 7 = 38. What is the missing number?

Draw here

___ ÷ 3 + 12 = 20. What is the missing number?

Draw here

2 × ___ + 15 = 45. What is the missing number?

Draw here
22

Two-Step Equations (C)

Solve each equation step by step.

(___ + 4) × 3 = 27. Step 1: ___ × 3 = 27 so ___ = ___. Step 2: ___ + 4 = ___ so ___ = ___.

Draw here

(30 − ___) ÷ 5 = 4. What is the missing number?

Draw here
23

Two-Step: Choose the Answer

Circle the correct answer.

4 × ___ + 3 = 19. ___ = ?

3
4
5

___ × 5 − 6 = 24. ___ = ?

5
6
7

36 ÷ ___ + 2 = 8. ___ = ?

4
6
8

2 × ___ + 10 = 26. ___ = ?

6
7
8
24

Balance the Equation

Both sides must be equal. Find the missing number.

5 × 8 = ___ × 10. Missing: ___

72 ÷ 9 = 48 ÷ ___. Missing: ___

6 × 7 = ___ × 3. Missing: ___

___ × 4 = 12 × 5. Missing: ___

25

Two-Step Word Problems (A)

Write an equation and solve.

I buy 5 identical items and pay $2 for a bag. The total cost is $37. How much is each item?

Draw here

A number is multiplied by 4 then 10 is added. The result is 50. What is the number?

Draw here
26

Two-Step Word Problems (B)

Write an equation and solve.

I share some money equally among 6 friends and have $3 left over. I started with $45. How much did each friend get?

Draw here

A box of chocolates is shared among some children. Each gets 8 chocolates and 4 are left over. There were 52 chocolates. How many children?

Draw here
27

Write Your Own Equations

Create equations for others to solve.

Write a one-step multiplication equation with a missing number. Then give the answer.

Write a one-step division equation with a missing number. Then give the answer.

Write a two-step equation with a missing number. Then give the answer.

28

Find the Missing Factor (D)

Find the missing number.

24
3
?
54
6
?
42
7
?
35
5
?
64
8
?
27
9
?
29

Find the Missing Factor (E)

Find the missing number.

30
?
5
48
?
8
56
?
7
40
?
10
18
?
2
72
?
8
30

Find the Missing Number (A)

Circle the correct answer.

___ × 6 = 48

6
7
8

9 × ___ = 63

6
7
8

___ × 4 = 36

8
9
10

7 × ___ = 49

6
7
8
31

Find the Missing Number (B)

Circle the correct answer.

___ ÷ 5 = 8

35
40
45

72 ÷ ___ = 9

6
7
8

___ ÷ 3 = 12

33
36
39

56 ÷ ___ = 7

7
8
9
32

Missing Numbers in Multiplication (A)

Find the missing number.

___ × 8 = 64. Missing number: ___

5 × ___ = 45. Missing number: ___

___ × 12 = 60. Missing number: ___

7 × ___ = 84. Missing number: ___

33

Missing Numbers in Division (A)

Find the missing number.

___ ÷ 4 = 9. Missing number: ___

63 ÷ ___ = 7. Missing number: ___

___ ÷ 8 = 7. Missing number: ___

96 ÷ ___ = 12. Missing number: ___

34

Match Equations to Answers (A)

Draw a line.

___ × 7 = 35
54 ÷ ___ = 9
8 × ___ = 72
___ ÷ 5 = 11
9
6
5
55
35

Match Equations to Answers (B)

Draw a line.

___ × 3 = 27
80 ÷ ___ = 10
___ × 6 = 42
100 ÷ ___ = 25
4
9
8
7
36

Missing Numbers in Mixed Operations

Find the missing number.

___ × 5 + 3 = 28. Missing number: ___

4 × ___ − 6 = 26. Missing number: ___

(___ + 3) × 4 = 36. Missing number: ___

(50 − ___) ÷ 5 = 6. Missing number: ___

37

Which Equation Matches? (A)

A number times 6 equals 42. Circle the equation.

A number times 6 equals 42

n + 6 = 42
n × 6 = 42
n − 6 = 42

48 divided by a number equals 8

48 ÷ n = 8
48 × n = 8
48 − n = 8

Triple a number is 27

n + 3 = 27
3n = 27
n ÷ 3 = 27
38

Which Equation Matches? (B)

Circle the equation.

A number divided by 4 gives 9

n ÷ 4 = 9
4 ÷ n = 9
n × 4 = 9

5 times a number minus 2 equals 23

5n − 2 = 23
5 + n − 2 = 23
5(n − 2) = 23

A number multiplied by itself equals 49

n + n = 49
n × 2 = 49
n × n = 49
39

Word Problems to Equations (A)

Write an equation and solve.

I think of a number. I multiply it by 8. I get 56. What is the number? Equation: ___ Answer: ___

I divide a number by 7 and get 9. What is the number? Equation: ___ Answer: ___

3 bags of marbles contain 45 marbles total. Equation: ___ Marbles per bag: ___

40

Word Problems to Equations (B)

Write equations and solve.

A rectangle has an area of 48 cm². Its width is 6 cm. Length: ___ Equation: ___

Stickers are shared equally among 9 children. Each gets 7. Total stickers: ___ Equation: ___

A class of children makes 5 teams. Each team has 6 players. Total children: ___ Equation: ___

41

Sort: Multiplication or Division Equation?

Sort each problem.

___ × 4 = 32
48 ÷ ___ = 6
7 × ___ = 63
___ ÷ 9 = 5
12 × ___ = 96
81 ÷ ___ = 9
Needs multiplication
Needs division
42

Two-Step Problems (C)

Solve these two-step equations.

3 × ___ + 7 = 31. Missing number: ___. Show working.

___ × 4 − 10 = 22. Missing number: ___. Show working.

(60 ÷ ___) + 5 = 17. Missing number: ___. Show working.

43

Two-Step Problems (D)

Solve.

5 × (___ − 3) = 40. Missing number: ___

(100 ÷ ___) × 3 = 60. Missing number: ___

44

Inverse Operations

Circle the inverse operation to solve.

To solve n × 8 = 56, use...

56 + 8
56 − 8
56 ÷ 8

To solve n ÷ 5 = 12, use...

12 × 5
12 ÷ 5
12 + 5

To solve 7n = 91, use...

91 × 7
91 − 7
91 ÷ 7

To check n × 6 = 54, verify that...

54 ÷ 6 = n
54 + 6 = n
54 × 6 = n
45

Challenge Equations

Solve these challenging equations.

___ × ___ = 36 (find all pairs of whole numbers)

n × n = 81. What is n? ___

If n × 5 = 35 and n × m = 56, what is m? ___

46

Match Equation to Solution

Draw a line.

n × 7 = 56
n ÷ 4 = 12
3 × n = 45
n + 15 = 40
50 − n = 21
n = 25
n = 8
n = 15
n = 48
n = 29
47

Unknown Value Bonds (B)

Find n in each equation: n × a = total.

72
8
?
63
9
?
84
7
?
96
8
?
110
11
?
78
6
?
48

Correct Equation (B)

Circle the equation that is TRUE.

n = 6 in which equation?

n × 8 = 56
n × 7 = 42
n × 9 = 72

n = 12 in which equation?

n ÷ 3 = 3
n ÷ 4 = 3
n ÷ 6 = 3

n = 25 in which equation?

n + 5 = 15
n − 5 = 20
n × 5 = 20

n = 7 in which equation?

3n = 28
4n = 28
5n = 28
49

Sort Equations by Operation Needed

Sort to show which operation solves the equation.

n × 6 = 48
n ÷ 5 = 9
n + 17 = 30
n − 11 = 23
8n = 104
n/7 = 12
Use division
Use multiplication
Use subtraction
Use addition
50

Write Your Own Equations

Create equations with a missing value.

Write an equation where n = 9 using multiplication: ___

Write an equation where n = 24 using division: ___

Write a two-step equation: n = 5. ___

Ask a partner to solve your equation and check their answer:

51

Equations in Real Life (B)

Write and solve equations for these situations.

Packs of pencils cost $4 each. Total cost is $32. How many packs? Equation: ___ Solution: ___

A number divided by 7 gives 12. Write the equation and solve it.

Three equal groups with 2 left over total 23. Write the equation.

52

Multiplication Sequences

Continue each sequence.

3
9
27
81
?
?
2
6
18
54
?
?
4
12
36
108
?
?
53

Equations Solved per Student

Class results for a missing value worksheet.

Group A
Group B
Group C
Group D
Group E
1

Total equations solved?

2

Average per group?

3

Which group solved the most?

4

How many more did Group E solve than Group B?

54

Types of Equations Practised

Tally of equation types practised by students.

ItemTallyTotal
n × a = b
n ÷ a = b
a × n + b = c
Other
55

Compare Missing Value Problems

Estimate which is harder.

n × 6 = 42 vs n + 6 = 42 — which is harder to solve?

vs

n × 7 = 63 vs 7n + 7 = 63 — which is a two-step problem?

vs
56

Generalise the Pattern

Look at these equations: 2 × 5 = 10, 2 × 50 = 100, 2 × 500 = 1,000.

What pattern do you notice?

Use the pattern: 2 × 5,000 = ___ and 2 × 50,000 = ___

Does the same pattern work for division? Give an example:

57

Order of Operations (B)

Apply order of operations (BODMAS).

3 × (4 + 2) = ___. Without brackets: 3 × 4 + 2 = ___

10 − 2 × 3 = ___. (10 − 2) × 3 = ___

Why do brackets change the answer?

58

Balance Problems

Use balancing to find unknowns.

If n + 5 = 13, then n = ___. If n + 5 + 3 = 13, then n = ___

A balance has 3 weights of n grams on the left and 45 grams on the right. What is n? ___

The left has n + 8 grams. Right has 27 grams. What is n? ___

59

Patterns and Rules (B)

Find the rule and complete the pattern.

In/Out table: 2→10, 3→15, 4→20, 5→25, n→___ Rule: ___

In/Out table: 6→2, 9→3, 12→4, 15→5, n→___ Rule: ___

In/Out table: 1→3, 2→5, 3→7, 4→9, n→___ Rule: ___

60

Sort Equations by Complexity

Sort from simplest to most complex.

n × 4 = 28
3n + 7 = 22
n ÷ 5 = 8
(n + 3) × 4 = 32
5n − 12 = 18
One step
Two steps
More complex
61

Real-Life Equations (C)

Create equations from situations.

A market stall sells items for $n each. Total for 7 items is $56. Write and solve the equation:

A ribbon is cut into 5 equal pieces and 3 cm is left over. Total ribbon is 28 cm. Write and solve the equation for piece length:

Create your own real-life equation where n = 8:

62

Checking Solutions (B)

Check if the value makes the equation true.

Is n = 9 a solution to 4n − 7 = 29? Show: ___

Is n = 12 a solution to 3(n − 4) = 24? Show: ___

63

Equation Vocabulary (B)

Match each term to its definition.

Variable
Coefficient
Equation
Expression
Solution
the answer that makes the equation true
a letter representing an unknown
a statement saying two things are equal
no equals sign, just terms
number multiplying a variable
64

Unknown Values (Multiplication)

Find the missing value using division.

72
8
?
91
7
?
132
11
?
96
12
?
65

Which Value Solves the Equation?

Circle the correct solution.

5n = 45, n = ?

8
9

n + 13 = 31, n = ?

18
19

n ÷ 7 = 6, n = ?

42
43

3n − 4 = 17, n = ?

6
7
66

Sort by Operation Needed to Solve

Sort equations by the operation needed to isolate n.

n − 15 = 23
n × 6 = 54
n + 18 = 40
n ÷ 9 = 7
Use addition
Use subtraction
Use multiplication
Use division
67

Solve Two-Step Equations

Solve these equations showing all steps.

2n + 5 = 19. Step 1: 2n = ___. Step 2: n = ___

3n − 7 = 14. Step 1: 3n = ___. Step 2: n = ___

n/4 + 3 = 9. Step 1: n/4 = ___. Step 2: n = ___

68

Word Problems Using Equations (B)

Write an equation, then solve.

Tickets cost $n each. 6 tickets total $42. Equation: ___. Solution: n = ___

A bag has n apples. 4 are eaten and 7 remain. Equation: ___. n = ___

Double a number then subtract 3 gives 15. Equation: ___. Number: ___

69

Number Rules and In/Out Tables (B)

Find the rule and complete.

3
6
9
12
?
?
1
4
9
16
?
?
100
90
80
70
?
?
70

Equations from Diagrams

Write an equation for each balance diagram.

Left side: n + n + 3. Right side: 15. Equation: ___. Solve: n = ___

Left: 4n. Right: n + 18. Equation: ___. Solve: n = ___

Draw your own balance diagram where n = 5:

Draw here
71

Compare Unknown Values

Which equation has the larger solution?

3n = 24 (n=8) vs 4n = 36 (n=9) — which is larger?

vs

n + 9 = 15 (n=6) vs n + 5 = 12 (n=7) — which is larger?

vs
72

Equations Solved Correctly (Class)

Tally how many students got each type of equation right.

ItemTallyTotal
One-step add/subtract
One-step multiply/divide
Two-step equations
Equations with brackets
73

Algebra Puzzles (B)

Solve these algebra puzzles.

If a = 5 and b = 3, find: a + b = ___, a × b = ___, 2a − b = ___, a² − b² = ___

If p + q = 20 and p − q = 4, find p = ___ and q = ___

74

True or False: Equations (B)

Circle TRUE or FALSE.

If 3n = 15, then n = 5

TRUE
FALSE

n + n = 2n (for any value of n)

TRUE
FALSE

3 + n = n + 3 (always true)

TRUE
FALSE

2(n + 1) = 2n + 1

TRUE
FALSE
75

Home Activity: Equation Detective

Create and solve equations at home!

  • 1Write 5 multiplication equations with a missing number. Challenge a family member to solve them.
  • 2If 8 packets of biscuits contain 96 biscuits total, write and solve an equation to find how many are in each packet.
  • 3Think of your own two-step equation and see if someone at home can solve it.
  • 4Use counters or blocks to model: ___ groups of 7 = 42.
76

Trace Unknown Values (A)

Trace each value. These are answers to missing-number equations.

3
4
5
6
7
77

Match Equations to Solutions (C)

Draw a line from each equation to its solution.

___ × 9 = 99
144 ÷ ___ = 12
___ × 11 = 154
195 ÷ ___ = 15
13
12
11
14
78

Match Equations to Solutions (D)

Match each equation to its solution.

n × 8 = 200
n ÷ 7 = 14
12 × n = 180
n ÷ 13 = 10
25
15
98
130
79

Find the Missing Number (C)

Circle the correct answer.

___ × 8 = 96

11
12
13

144 ÷ ___ = 16

8
9
10

___ × 7 = 91

11
12
13

156 ÷ ___ = 12

11
12
13
80

Find the Missing Number (D)

Circle the correct value of n.

5n = 65, n = ?

11
13
15

n ÷ 6 = 15, n = ?

80
90
100

8n = 104, n = ?

12
13
14

n ÷ 9 = 11, n = ?

90
99
110
81

Find the Missing Factor (F)

Find the missing factor.

130
10
?
165
11
?
168
12
?
182
13
?
210
14
?
240
15
?
82

Missing Numbers in Multiplication (B)

Find the missing number and check.

___ × 13 = 156. Missing: ___. Check: ___ × 13 = ___

14 × ___ = 196. Missing: ___. Check: 14 × ___ = ___

___ × 15 = 225. Missing: ___. Check: ___ × 15 = ___

83

Missing Numbers in Division (B)

Find the missing number.

234 ÷ ___ = 13. Missing: ___

___ ÷ 12 = 15. Missing: ___

256 ÷ ___ = 16. Missing: ___

___ ÷ 11 = 21. Missing: ___

84

Sort: Multiplication or Division Needed?

Sort each equation type.

n ÷ 6 = 12
___ × 7 = 98
n × 8 = 128
144 ÷ n = 12
n × 11 = 121
n ÷ 14 = 6
Multiplication to find n
Division to find n
85

Three-Step Problems (A)

Solve these multi-step equations.

(___ × 6) + 12 = 60. Show working.

(n ÷ 8) − 4 = 7. What is n?

4 × (n + 5) = 52. What is n?

86

Three-Step Problems (B)

Solve.

3n + 2n = 60. What is n?

n × 6 = n × 4 + 20. What is n?

2 × (3n − 4) = 28. What is n?

87

Word Problems to Equations (C)

Write an equation then solve.

A number when tripled then reduced by 5 equals 19. Find the number.

Eggs are packed in boxes. If 144 eggs fill some boxes with 12 each, how many boxes?

88

Word Problems to Equations (D)

Write equations and solve.

A rectangular garden has an area of 120 m². Its length is 15 m. Find the width.

A bag of rice weighs n kg. 8 bags weigh 56 kg. Find n.

A factory makes n items per hour. In 9 hours it makes 1,008 items. Find n.

89

Inverse Operations (B)

Use inverse operations to solve.

To solve ___ × 12 = 180, divide ___

180 by 12
180 by 180
12 by 180

To solve n ÷ 14 = 7, multiply ___

7 by 7
7 by 14
14 by 14

To check 13 × 12 = 156, verify ___

156 ÷ 12 = 13
156 ÷ 13 = 12
both of the above
90

Match Word Problems to Equations (A)

Draw a line from each problem to the correct equation.

12 teams with n players, 96 total
n books at $8 each cost $104
A number halved is 35
n rows of 15 chairs, 225 total
n = 225 ÷ 15
n = 104 ÷ 8
n × 12 = 96
n = 35 × 2
91

Equations Solved Per Student

Count equations solved by each student.

Ali
Beth
Carl
Dee
1

Who solved the most equations?

2

How many in total?

3

If each equation has a missing value n, how many n values did Ali find?

4

What is the mean number solved?

92

Types of Equations Tally

Count how many equations of each type were solved.

ItemTallyTotal
n × ? = ?
? × n = ?
? ÷ n = ?
n ÷ ? = ?
93

Pattern Problems with Unknown Values (A)

Find the pattern and the unknown.

4, 8, ___, 16, ___. The rule is ×2. Missing values: ___

n, 2n, 3n, 4n — if 3n = 24, what is n? What is 4n? ___

A pattern: 5, 10, 20, 40... Next term: ___. Rule: ___. If the 6th term is k, k = ___

94

Create Your Own Equations (B)

Write equations and challenge someone to solve them.

Write 3 equations with a missing factor. Solutions: ___, ___, ___

Write a two-step word problem involving a missing value. Solve it.

Draw here
95

Compare Equation Solutions (A)

Compare the solutions to each pair of equations.

n × 7 = 56 vs n × 8 = 72: are the solutions the same?

vs

48 ÷ n = 8 vs 54 ÷ n = 9: same solution?

vs

What to do next

Algebra

Patterns in Factors & Multiples

Create and use algorithms to identify patterns in factors and multiples