Primary 4 maths · Operations · About 12 minutes
A transfer changes the difference
Work backwards from a transfer and a final difference to find a starting amount
Start the interactive lesson →Practise: Beads in the top tray
What you will learn
- Work backwards from a transfer and a final difference to find a starting amount
Models used: tables, bar models, number sentences, stories.
Before you start
Two changes in one move
The top starts with twice the bottom. Move 8 beads down; the top then has 14 more. Find the starting top.
Keep the original comparison, move and final gap visible.
The information from this question Clue Information At first Top has twice the bottom Moved from top to bottom 8 beads Final difference 14 more in top Moving 8 changes each side of the gap by 8.
8 + 8 = 16
The information from this question Clue Information At first Top has twice the bottom Moved from top to bottom 8 beads Final difference 14 more in top Add that change back to the final gap to recover the starting gap.
14 + 16 = 30
The information from this question Clue Information At first Top has twice the bottom Moved from top to bottom 8 beads Final difference 14 more in top At first the top was two parts and the bottom one part. Their gap was one part, so the top was two parts.
30 × 2 = 60
The information from this question Clue Information At first Top has twice the bottom Moved from top to bottom 8 beads Final difference 14 more in top
Worked example: Work backwards together
The top starts with twice the bottom. Move 9 beads down; the top then has 14 more. Find the starting top.
| Clue | Information |
|---|---|
| At first | Top has twice the bottom |
| Moved from top to bottom | 9 beads |
| Final difference | 14 more in top |
The top loses 9 and the bottom gains 9.
The information from this question Clue Information At first Top has twice the bottom Moved from top to bottom 9 beads Final difference 14 more in top By how many beads did the difference shrink?
18
Add that change back to the final difference of 14.
The information from this question Clue Information At first Top has twice the bottom Moved from top to bottom 9 beads Final difference 14 more in top What was the starting difference?
32
The starting top was two equal parts and the bottom was one. Their difference is one part.
The information from this question Clue Information At first Top has twice the bottom Moved from top to bottom 9 beads Final difference 14 more in top How many beads were in the top tray at first?
64
Check both trays after the move.
64 − 9 = 55; 32 + 9 = 41; 55 − 41 = 14
The information from this question Clue Information At first Top has twice the bottom Moved from top to bottom 9 beads Final difference 14 more in top
Common mistakes to discuss
- Count only one side of the transfer. The top loses and the bottom gains, so both changes affect the difference.
- Double the final difference. Find the starting difference before using the original twice-as-many clue.
Check your understanding
- Track the loss and gain in a transfer.
- Work back to the starting difference.
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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