Math · Stage 3

Use the excess-and-shortage method to find quantities

Share one way and some is left over, share a bigger way and you fall short — the two gaps together reveal exactly how many sharers there are.

✦ Math📘 Stage 3 · S3⏱ ~10 min🧒 Ages 7–8★ Free to start

I can use the excess-and-shortage method: from two sharing attempts (one with a surplus, one with a shortage) find the number of people as (surplus + shortage) / (difference per person), then the total.

Start the free lesson →⬇ Printable PDF

📖

Kavi Shares the Acorns 🌰

Kavi has a basket of acorns for the squirrel friends. "If I give 3 acorns to each squirrel, I'll have 4 left over," hoots Kavi. "But if I give 5 acorns to each, I'll be 6 short!" One share leaves a surplus, the other leaves a shortage — and Kavi knows a clever trick to turn those two gaps into the exact number of squirrels, without any guessing.

🎓

What your child will learn

1Two shares, two gapsSame squirrels, same basket — Kavi just tries two different shares. Tap each card and read what happens to the acorns.

2Add the surplus and the shortageLine up the two attempts. The first leaves 4 acorns spare; the second needs 6 more than Kavi has. The whole swing from 'have-spare' to 'need-more' is the surplus plus the shortage.

3Share the gap, two at a timeThe gap of 10 extra acorns gets handed out 2 to each squirrel (the difference per person). Hop along the line in twos — each hop of 2 is one more squirrel found.

4Both shares give the same totalThe real total never changes — the two attempts just describe it two ways. From our 5 squirrels: 5 × 3 + 4 = 19 and 5 × 5 − 6 = 19. Same 19 acorns, every time.

🔍

A peek inside

Kavi gives each squirrel 3 acorns and has 4 left over; giving 5 acorns each would leave Kavi 6 short 🌰. How many squirrels, and how many acorns?

difference per squirrel = 5 − 3 = 2 · gap = surplus + shortage = 4 + 6 = 10 · squirrels = 10 ÷ 2 = 5 · acorns = 5 × 3 + 4 = 19 · check: 5 × 5 − 6 = 19 ✓

Try this at home: Give 2 pencils each → 6 left over. Give 4 pencils each → 4 short. How many children, and how many pencils?

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 3 · S3 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.