GuideMath · P5 / P6Problem Sums
Constant Difference / Constant Total Guide
Spot the unchanged relationship before solving.
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Bar model
Draw the parts, then the whole.
1
Constant Difference
Both people gain or lose the same amount. The gap between them never changes.
2
Constant Total
One person's gain equals another person's loss. The total never changes.
3
How to Spot It
Ask: is money moving between them (constant total) or is each getting/losing separately (constant difference)?
Common Mistakes
- Assuming the total is constant when it isn't
- Using the wrong 'before' ratio for the difference
- Skipping the check-in question
Teaching Team Tip
Write 'DIFFERENCE stays' or 'TOTAL stays' at the top of your working before drawing bars.
Worked Example
Try it, then check the steps
Question
Amy and Bala each save $5 more per week. If the ratio was 3 : 5 and later becomes 2 : 3, find their original amounts.
Steps
- 1Difference is constant (both gain $5, gap unchanged)
- 2Before: 5u − 3u = 2u ; After: 3p − 2p = 1p
- 3So 2u = 1p → use to solve for original amounts
What to do next
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