Math · Stage 4
Solve difference and equalising problems using constant totals/gaps
Two secret rules of Olympiad problem sums: when BOTH sides change the same way the GAP stays fixed, and when things only MOVE from one side to the other the TOTAL stays fixed.
✦ Math📘 Stage 4 · S4⏱ ~11 min🧒 Ages 8–9★ Free to start
I can solve difference and equalising problems using constant totals/gaps.
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Kavi's Two Unchanging Rules ⚖️
Ann has 9 sweets and Ben has 5 🍬. "I know two secrets," hoots Kavi. "If they both get 2 more, the gap stays 4 — the difference never changes! And if Ann just gives some to Ben, the total stays 14 — nothing is lost. Spot what stays the same and the puzzle solves itself ⚖️."
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What your child will learn
1When BOTH change the same → the GAP staysIf two amounts both go up by the same number (or both go down the same), the difference between them never changes. Ann is 10 and Ben is 7 — the gap is 3. Tap each card.
2When things only MOVE → the TOTAL staysIf nothing is added and nothing is thrown away — one side just gives to the other — then the total stays exactly the same. Ann has 9 🍬 and Ben has 5, so the total is 14. Tap each card.
3Equalising: split the fixed total in halfTo make two amounts equal, share the fixed total into two equal parts — each side ends with total ÷ 2. Here the total is 14, so each equal part is 14 ÷ 2 = 7. Tap more ▶ and ◀ less.
4Does the GAP stay or the TOTAL stay?
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A peek inside
Ann is 10 and Ben is 7 🎂. In 5 years, how much older will Ann be than Ben?
both ages grow by 5, so the gap is unchanged: 10 − 7 = 3
Try this at home: Gap stays: Ann 12, Ben 5 → the gap is __ . In 4 years the gap is __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 4 · S4 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.