Math PicnicFree printable practice

The counting principle worksheets

Four shirts and three pairs of shorts make twelve outfits, not seven. These free printable worksheets count the outcomes of a choice made in stages — the multiplication rule behind every sample space.

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The counting principle
The counting principle worksheet — Two or three stages, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The one idea is that independent choices MULTIPLY. Each of the four shirts can go with each of the three shorts, so the outfits are 4 × 3, not 4 + 3 — and adding is the mistake the sheet is built around. A child who pictures every shirt paired with every pair of shorts sees why it is a product.

Why this sheet works

Three stages are the same idea one step further: 3 mains, 2 sides and 4 drinks make 3 × 2 × 4 = 24 meals. The walk does it two at a time — the mains-and-sides first, then times the drinks — so the “each one with each one” stays visible instead of collapsing into a single long multiplication.

How this one works

One question from this sheet, worked through a step at a time.

8 frames and 7 wheels. How many different bikes can you make?

87
8×7=56
  1. Each of the 8 frames can go with every one of the 7 wheels, so the choices multiply — they do not add.
  2. 8 × 7 = 56.

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