Unknown Values & Combined Operations
Find the Missing Number (Addition)
Write the number that makes each equation true.
___ + 15 = 27
___ + 34 = 50
23 + ___ = 41
___ + 48 = 75
Find the Missing Number (Subtraction)
Write the number that makes each equation true.
36 − ___ = 19
50 − ___ = 28
___ − 14 = 33
72 − ___ = 45
Find the Missing Number (Multiplication)
Write the number that makes each equation true.
___ × 6 = 42
___ × 8 = 56
9 × ___ = 63
___ × 12 = 84
Find the Missing Number (Division)
Write the number that makes each equation true.
56 ÷ ___ = 8
___ ÷ 5 = 9
72 ÷ ___ = 6
___ ÷ 7 = 11
Pick the Missing Number
Circle the value that makes each equation true.
___ + 18 = 35
42 − ___ = 15
___ × 7 = 49
60 ÷ ___ = 12
Match Equations to Unknowns
Draw a line to match each equation to the value of the unknown.
More Equation Matching
Draw a line to match each equation to its answer.
Write the Equation
Write an equation for each word problem, using ___ for the unknown. Then solve it.
I think of a number and add 12. The answer is 31. Equation: ___. The number is ___.
I think of a number and multiply by 5. The answer is 45. Equation: ___. The number is ___.
I think of a number and subtract 18. The answer is 24. Equation: ___. The number is ___.
Two-Step Equations
Find the unknown value. Work backwards! Example: 3 × ___ + 5 = 20 → 3 × ___ = 15 → ___ = 5.
4 × ___ + 3 = 19. The unknown is ___.
5 × ___ − 7 = 18. The unknown is ___.
2 × ___ + 10 = 24. The unknown is ___.
6 × ___ − 4 = 32. The unknown is ___.
More Two-Step Equations
Find the unknown value. Show your working.
3 × ___ + 8 = 29. The unknown is ___.
___ × 7 − 10 = 25. The unknown is ___.
8 × ___ + 6 = 46. The unknown is ___.
___ ÷ 4 + 3 = 8. The unknown is ___.
Which Value Makes It True?
Circle the value that makes the equation true.
3 × ___ + 2 = 14
24 ÷ ___ − 1 = 5
___ × 7 − 3 = 25
5 × ___ + 8 = 33
More Two-Step Choices
Circle the value that makes the equation true.
2 × ___ + 9 = 21
___ × 8 − 12 = 20
10 × ___ + 5 = 75
36 ÷ ___ + 2 = 8
Two-Step Word Problems
Write an equation and solve each problem.
I think of a number, double it and add 7. The answer is 23. What is the number?
I think of a number, multiply by 5 and subtract 3. The answer is 32. What is the number?
I think of a number, divide by 3 and add 4. The answer is 9. What is the number?
Order of Operations
Calculate each expression using the correct order of operations (multiplication/division before addition/subtraction).
3 + 4 × 5 = ___
20 − 3 × 4 = ___
6 × 3 + 8 ÷ 2 = ___
15 − 2 × 3 + 4 = ___
More Order of Operations
Calculate each expression. Remember: brackets first, then × and ÷, then + and −.
(3 + 4) × 5 = ___
24 ÷ (8 − 2) = ___
2 × (10 + 5) − 6 = ___
(18 − 6) ÷ 3 + 7 = ___
Order of Operations Check
Circle the correct answer.
8 + 2 × 3 = ?
(8 + 2) × 3 = ?
12 ÷ 4 + 2 = ?
12 ÷ (4 + 2) = ?
Add Brackets to Make It True
Insert brackets to make each equation true.
2 + 3 × 4 = 20 (add brackets): ___
10 − 2 × 3 = 24 (add brackets): ___
6 + 8 ÷ 2 = 7 (add brackets): ___
5 × 3 + 7 = 50 (add brackets): ___
Challenge Equations
Find the unknown and explain your reasoning.
(2 × ___) + (3 × ___) = 25, where both blanks are the same number. The number is ___.
(___ + 3) × 4 = 28. The unknown is ___.
100 − (___ × ___) = 51, where both blanks are the same number. The number is ___.
Home Activity: Equation Detective
Create and solve equations at home!
- 1Think of a number, double it, add 6. The answer is 22. What was the number? Write the equation.
- 2Make up 3 two-step equations for a family member to solve.
- 3Use playing cards: flip 3 cards and try to make an equation using +, −, × or ÷.
- 4Write a word problem that involves finding an unknown value.
- 5Create a 'guess my rule' game with a family member using input-output tables.
Using Pronumerals
Use a pronumeral (letter) to write each equation, then solve.
A number x plus 14 equals 29. Equation: ___. x = ___
A number n multiplied by 8 equals 72. Equation: ___. n = ___
A number y minus 17 equals 43. Equation: ___. y = ___
A number p divided by 6 equals 12. Equation: ___. p = ___
Evaluating Expressions
Evaluate each expression for the given value.
3x + 2, when x = 5:
4n − 1, when n = 7:
2(p + 3), when p = 4:
(m − 2) × 5, when m = 8:
Substitution Practice
Substitute the given value and evaluate each expression.
5x − 3, when x = 4: ___
2n + 7, when n = 9: ___
3(y − 2), when y = 6: ___
10 − 2p, when p = 3: ___
(a + 4) × 3, when a = 5: ___
Match Equation to Solution
Draw a line to match each equation to its solution.
Forming Algebraic Expressions
Write an algebraic expression for each description.
A number increased by 8: ___
Twice a number decreased by 5: ___
A number divided by 4, then add 3: ___
Three times the sum of a number and 2: ___
Solving Equations Systematically
Use inverse operations to solve each equation. Show each step.
3x + 8 = 26. Step 1: ___. Step 2: ___. x = ___
4n − 9 = 27. Step 1: ___. Step 2: ___. n = ___
2(y + 5) = 22. Step 1: ___. Step 2: ___. y = ___
Sort: Which Operation to Use First?
Sort each equation by the inverse operation to use first.
Order of Operations Problems
Calculate using the correct order of operations (BOMDAS).
5 + 3 × 4 − 2 = ___
(7 + 3) × (8 − 5) = ___
4² + 3 × 5 − 10 = ___
48 ÷ (2 + 4) × 3 = ___
3 × (6 − 2)² + 5 = ___
Writing Equations from Word Problems
Write an equation and solve it.
A box holds n books. 5 boxes hold 35 books. Write and solve: ___
Ali is x years old. 3 times his age minus 4 is 20. Write and solve: ___
After spending $25, Mia has y dollars left. She now has $48. Write and solve: ___
True or False: Order of Operations
Circle TRUE or FALSE.
2 + 3 × 4 = 20
(2 + 3) × 4 = 20
8 ÷ 2 + 6 = 1
8 ÷ (2 + 6) = 1
Algebraic Number Bonds
Find the missing value in each equation.
Input-Output Tables
Complete each input-output table.
Algebraic Problem Solving
Use algebra to solve each problem.
Theo is 3 times as old as Sam. Together they are 40. How old is each? ___
The perimeter of a square is 64 cm. Use 4s = 64 to find the side length: ___
Two numbers add to 57. The larger is 9 more than the smaller. Find both: ___
Combined Operations with Fractions and Decimals
Solve each combined operation problem.
3.5 × ___ + 4 = 18. The unknown = ___
___ ÷ 4 − 2.5 = 5. The unknown = ___
½ × ___ + 6 = 15. The unknown = ___
Generalising with Algebra
Write a general algebraic rule for each pattern.
Pattern: 4, 8, 12, 16 (for n = 1, 2, 3, 4). Rule: term = ___
Pattern: 5, 8, 11, 14. Rule: term = ___
Pattern: 1, 4, 9, 16. Rule: term = ___
Checking Solutions
Check if each given value solves the equation. Write YES or NO and show checking.
Does x = 4 solve 3x − 2 = 10? ___
Does n = 7 solve 2n + 5 = 19? ___
Does p = 3 solve 4(p + 2) = 24? ___
Equations with Negative Integers
Solve each equation involving negative integers.
x + 5 = -3. x = ___
n − 4 = -7. n = ___
2p + 1 = -5. p = ___
3y − 2 = -11. y = ___
Unknown Values — Summary Challenge
Solve these mixed equation challenges.
Find x: 5(x − 3) + 4 = 19. x = ___
Find n: 48 ÷ n − 2 = 6. n = ___
Write your own two-step equation and solve it: ___