Math · Stage 3
Count shortest lattice paths by Pascal's rule
Walk a grid going only right and down — the paths to each corner are the paths from above PLUS the paths from the left.
✦ Math📘 Stage 3 · S3⏱ ~12 min🧒 Ages 7–8★ Free to start
I can count shortest lattice paths on a grid by adding, at each corner, the paths from above and from the left (Pascal's rule).
📖
Kavi's Grid Walk 🗺️
Kavi's house is at the top-left corner of a block-grid, and the park is at the bottom-right 🗺️. "I want the shortest walk — only right and down, never back," hoots Kavi. "But how many different short ways are there?" Kavi finds the olympiad trick: at every corner, add the ways from above and the ways from the left!
🎓
What your child will learn
1Shortest means right & down onlyA shortest path on a grid never wastes a step — it only goes right ▶ or down ▼, never back or up. Tap each card to see the difference.
2Pascal's rule: above + leftHere is the magic. To reach any corner you must arrive either from above ▼ or from the left ▶. So the paths to a corner = paths from above + paths from the left. Tap the bond: 1 from above + 1 from the left = 2.
3Fill the far cornerOn a 2 × 2 grid, filling corners by the rule gives 1, 2, 3 along the middle row (and the middle column), and the far corner is fed by a 3 from above and a 3 from the left. Add them — tap Step →.
4Guess the gridUse the rule to predict how many shortest paths cross each grid. Tap your answer, then check.
🔍
A peek inside
A corner can be reached by 1 path from above and 1 path from the left. By Pascal's rule, how many shortest paths reach it?
above + left → 1 + 1
Try this at home: Pascal's rule — a corner gets 1 from above and 1 from the left: 1 + 1 = __ paths
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.