Use knowledge of the order of operations to solve equations | Maths

Starter quiz

For the following equation, which operation should we undertake first? 29 + 34 − 3 × 4 =
- Addition
- Subtraction
- Multiplication ✓
Match the square numbers to the correct expression.
- $4^2$
  
  ⇔
  
  16 ✓
- $8^2$
  
  ⇔
  
  64 ✓
- $10^2$
  
  ⇔
  
  100 ✓
- $12^2$
  
  ⇔
  
  144 ✓
Match the equivalent equations.
- 2 + 5 × 5 =
  
  ⇔
  
  2 + 25 = ✓
- (2 + 8) × 3 =
  
  ⇔
  
  10 × 3 = ✓
- (6 − 2) × 9 =
  
  ⇔
  
  4 × 9 = ✓
Tick the greatest equation.
- 4 × 6 + 3 =
- 4 × (6 + 3) = ✓
- 4 × (6 − 3) =
- 4 × 6 ÷ 3 =
Match the equations to the correct solutions.
- 5 + 18 ÷ 2 =
  
  ⇔
  
  14 ✓
- (12 + 13) ÷ 5 =
  
  ⇔
  
  5 ✓
- 36 + 10 ÷ 2 =
  
  ⇔
  
  41 ✓
- (30 + 30) ÷ 10 =
  
  ⇔
  
  6 ✓
There are six tables in a classroom. Sam shares out 18 workbooks equally and Jun shares out 12 textbooks equally. How many books are there on each table? There are ______ books.
- '5' ✓

Exit quiz

Tennis balls are stored in packs of four. Jun has 12 balls to put away and Sam has 16 balls to put away. How many packs are put away in total? ______ packs are put away.
- '7' ✓
Sam buys six chocolate eggs at £2 each. A week later, the same eggs are reduced to £1.50 each. How much would Sam have saved if she had bought the eggs a week later? £______
- '3' ✓
What is the missing number? ______ + $2^3$ = 21
- '13' ✓
Match the missing numbers with the correct equation.
- 8 + ___ × 2 = 12
  
  ⇔
  
  2 ✓
- 5 × ___ − 7 = 8
  
  ⇔
  
  3 ✓
- ___ ÷ 2 + 6 = 10
  
  ⇔
  
  8 ✓
Solve the equation. $6^2$ − 5 × 4 = ______
- '16' ✓
Match the expressions to their results.
- 5 + 5 + 5 + 5
  
  ⇔
  
  20 ✓
- 5 + 5 × 5 + 5
  
  ⇔
  
  35 ✓
- (5 + 5) × 5 + 5
  
  ⇔
  
  55 ✓
- (5 + 5) × 5 ÷ 5
  
  ⇔
  
  10 ✓
- (5 + 5 + 5) ÷ 5
  
  ⇔
  
  3 ✓

Worksheet

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Lesson Details

Key learning points

When there are no brackets, multiplication and division are completed before addition and subtraction.
Where there is a common factor, the other factors can be added or subtracted before the final multiplication.
Where there is a common divisor, the dividends can be added or subtracted before the final division.
Any part of an equation that is in brackets should be calculated first.
In an equation, powers have priority over multiplication and division.

Common misconception

Children may forget to use the order of operations and revert back to working from left to right.

Encourage them to identify all the operations in an equation before they begin to solve it so that they can apply their knowledge of the order of operations.

Keywords

Order of operations - The distributive law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.
Distributive law - The order of operations is a set of rules that tell you which operations have priority over others in an equation.