Math · Stage 5

Solve deduction, working-backwards and invariant problems

Three olympiad detective powers: reason from clues (deduction), start at the end and undo each step (work backwards), and find the gap or total that never changes (invariant).

✦ Math📘 Stage 5 · S5⏱ ~12 min🧒 Ages 9–10★ Free to start

I can solve deduction, working-backwards and invariant problems.

Start the free lesson →⬇ Printable PDF

📖

Detective Kavi on the Case 🔍

A locked puzzle lands on Kavi's desk: a mystery number, a trail of steps, two children swapping sweets. "No guessing!" hoots Kavi, tightening the detective hat. "Every hard problem cracks open with the right power — deduction to reason from clues, work backwards to undo the trail, and invariant to spot what never changes."

🎓

What your child will learn

1Three detective powersA problem that looks impossible usually just needs the right strategy. Tap each one to hear it.

2Start at the end, walk backA secret number was tripled, then had 5 added, and ended at 26. Tap each card.

3Find what never changesMira is 15 and Leo is 9. Their age GAP is 15 − 9. Tap Step →.

4Reason until one answer is leftClue 1: Ana is taller than Ben. Clue 2: Ben is taller than Cam. Tap to deduce the order.

🔍

A peek inside

A number was tripled, then 7 added, and the result was 34. What was the number? (work backwards)

undo +7 → 34 − 7 = 27 · undo ×3 → 27 ÷ 3 = 9 · check 9 × 3 + 7 = 34 ✓

Try this at home: Work backwards: a number was doubled, then 5 added, giving 19. Undo: 19 − 5 = __, then __ ÷ 2 = __

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

Start the free lesson →⬇ Download PDF

Part of Math · Stage 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.