Know that addition and subtraction are inverse operations | Maths

Starter quiz

Does this story show addition or subtraction?
- Addition ✓
- Subtraction
What has been added in this story?
- 2 apples
- 5 apples ✓
- 7 apples
What has been subtracted in this story?
- 6 counters
- 5 counters ✓
- 1 counter
Which equation could represent this story?
- 6 + 3 = 9
- 3 - 6 = 9
- 3 + 6 = 9 ✓
Write an equation to represent this story. First, 10 friends were playing a matching game together. Then, 2 left to play another game. Now, 8 friends are playing the matching game together.
- '10 - 2 = 8 ' ✓
What is missing from this story?
- 9 counters ✓
- 4 counters
- 5 counters

Exit quiz

What amount would we subtract to undo the addition? Use the cubes to help you.
- '3' ✓
What amount would we add to undo the subtraction?
- '6' ✓
How would we undo the change in this story? First, I had 9 pencils. Then, 2 pencils were taken. Now, I have 7 pencils. 9 − 2 = 7
- 7 + 2 = 9 ✓
- 9 − 7 = 2
- 9 − 2 = 7
Match each addition equation with the subtraction equation that can undo it.
- 4 + 3 = 7
  
  ⇔
  
  7 − 3 = 4 ✓
- 5 + 1 = 6
  
  ⇔
  
  6 − 1 = 5 ✓
- 0 + 3 = 3
  
  ⇔
  
  3 − 3 = 0 ✓
Which of these pictures represent the inverse of 3 + 4 = 7
Which of these number pairs would complete this story?
- 3 and 8 ✓
- 2 and 4
- 4 and 10

Worksheet

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Presentation

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Lesson Details

Key learning points

Addition is the inverse of subtraction. Addition can 'undo' subtraction.
Subtraction is the inverse of addition. Subtraction can 'undo' addition.
When a given amount is added to the start of a story, to 'undo' the change, we must subtract the same amount.
When a given amount is subtracted from the start of a story, to 'undo' the change we must add the same amount.

Common misconception

Children may not understand the importance of the order of the numerals in equations, so may not understand that the amount added or subtracted is of key importance when undoing a change made.

Present errors to discuss and correct. Encourage children to use practical equipment to demonstrate how they know they are right or to show why an error made cannot be correct.

Keywords

Add - o find the total, or sum, by combining two or more parts (addends), or to increase an amount by adding another.
Subtract - To partition one part from another (the subtrahend from the difference), or to decrease an amount by taking an amount away.
Inverse - Inverse means the opposite in effect; the reverse of.