Math · Stage 3
Slide the steps — perimeter of a staircase shape
A staircase shape has the same perimeter as the rectangle that boxes it in: slide every step out to the edge, then P = 2 × (length + width).
✦ Math📘 Stage 3 · S3⏱ ~10 min🧒 Ages 7–8★ Free to start
I can find the perimeter of a rectilinear staircase shape by sliding its steps out to the edges of its bounding rectangle, so P = 2 × (length + width).
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Kavi's Staircase Fence 🪜
Kavi must fence a garden shaped like stairs 🪜 — step, step, step! "That is a LOT of little edges to add," hoots Kavi. "But here is the olympiad trick: if I slide every step out to the edge, the stairs turn into a neat rectangle — and the fence is exactly the same length!"
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What your child will learn
1First, box it inEvery staircase shape fits snugly inside one rectangle — its bounding box. The box touches the highest point and the widest point. A rectangle's perimeter is easy: two long sides + two short sides. Tap the shapes.
2Slide every step outHere is the magic move. Tap each card to see what happens to the edges.
3Add length + width, then doubleA staircase fits in a bounding box that is 6 cm long and 4 cm wide. Add one long + one short first — tap Step →.
4Stairs yes — dents noThe sliding trick works for staircases that only step one way. Watch out for a shape with a dent cut in. Tap each card.
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A peek inside
A staircase shape fits exactly inside a bounding rectangle that is 6 cm long and 4 cm wide. What is its perimeter?
slide the steps out → it becomes the 6 × 4 box → 2 × (6 + 4)
Try this at home: A staircase fits in a 6 cm by 4 cm box. Slide the steps out: perimeter = 2 × (6 + 4) = __
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.