Math · Stage 3
Sum consecutive numbers by pairing ends (Gauss)
Add 1 + 2 + … + n the fast way — pair the ends into equal totals, then use n × (n + 1) ÷ 2.
✦ Math📘 Stage 3 · S3⏱ ~12 min🧒 Ages 7–8★ Free to start
I can find the sum of consecutive counting numbers 1 + 2 + ... + n by pairing the ends into equal totals, and use the rule n x (n + 1) / 2.
📖
Kavi's Lightning Add 🦉⚡
The class is told to add 1 + 2 + 3 + … + 10. Everyone starts adding one at a time — but Kavi hoots the answer in a flash! "I didn't add them in a row," winks Kavi. "I paired the ends: 1 + 10, 2 + 9… every pair makes the same 11!"
🎓
What your child will learn
1A row of counting numbersWe want to add every number from 1 to 10 in order — these are consecutive counting numbers. Adding them one by one is slow… there must be a smarter way!
2Pair the ends → equal totalsFold the row in half. The smallest meets the biggest: 1 + 10 = 11. Tap more ▶ to slide the split: 2 + 9 = 11, 3 + 8 = 11… every pair of ends makes the same 11!
3Every pair makes 11Look down the list: 1 + 10, 2 + 9, 3 + 8, 4 + 7, 5 + 6 — five pairs, each a tidy 11. (Ignore the 0-rows: we only pair 1 to 10.)
🔍
A peek inside
Add 1 + 2 + 3 + … + 10 the fast way.
pair ends: 1+10, 2+9, 3+8, 4+7, 5+6 → each = 11 · 5 pairs → 5 × 11
Try this at home: Pair the ends of 1…10: 1 + 10 = __ · 2 + 9 = __ · 5 + 6 = __ · how many pairs? __ · sum = __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 3 · S3 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.