Understand why the order of addition and subtraction steps can be chosen | Maths

Starter quiz

How can Izzy reorder this equation so it has the same value? 45 + 30 = 75
- 75 − 45 = 30 ✓
- 45 = 75 − 30 ✓
- 35 + 40 = 75
- 30 = 75 − 45 ✓
The equation 20 + 18 = 38 has been reordered in different ways. Match up the parts of the equations to make them correct.
- 20 =
  
  ⇔
  
  38 − 18 ✓
- 18 =
  
  ⇔
  
  38 − 20 ✓
- 38 =
  
  ⇔
  
  18 + 20 ✓
Find the missing part. 42 + $\square$ = 62
- '20' ✓
What is the missing number? $\square$ = 50 + 14
- '64' ✓
What is 12 + 4 + 4? = ______
- '20' ✓
Izzy and Lucas are collecting conkers. Izzy has 14 conkers and Lucas has 8 conkers. They find another 6 conkers. How many do they have altogether?
- '28' ✓

Which expression would give the same answer as 10 + 5 − 3?
- 10 − 5 + 3
- 12 − 3 + 5
- 10 − 3 + 5 ✓
True or false? 11 + 1 – 3 is equal to 11 – 3 + 1
- True ✓
- False
True or false? 11 + 4 – 5 is equal to 11 – 2 + 1
- True ✓
- False
Match the expressions which have the same answer.
- 8 + 2 − 3
  
  ⇔
  
  8 − 3 + 2 ✓
- 8 + 3 − 2
  
  ⇔
  
  8 − 2 + 3 ✓
- 8 − 4 + 2
  
  ⇔
  
  8 + 2 − 4 ✓
There are 8 people on a bus. At the next stop, 3 people get on the bus and 4 people get off. How many people are on the bus? Which calculation would give the correct answer?
- 8 − 3 + 4 =
- 4 + 8 − 3 =
- 8 − 4 + 3 = ✓
- 8 + 4 − 3 =
What step needs to be added to make this correct? 14 + 6 − 5 is equal to 14 − 5 ___
- + 6 ✓
- − 6
- + 5
- − 5

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Addition and subtraction can be done in any order
If you do the addition and subtraction in a different order, the answer will be the same
Problems can have equal answers even when different numbers are added and subtracted.

Pupils may reorder the numbers but forget to reorder the operations too.

Model the problems using tens frames and number lines, ensuring that pupils understand that both the numbers and operations need to be reordered.