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A Square and A Cube

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A tiler fixes tiles on floors. He lays 9 tiles in a 3 by 3 patch. A shop packs 27 cubes into a cube-shaped box.

A square counts flat. A cube counts a filled space.

This is Part I, Chapter 1: A Square and A Cube.

What you will learn

  • A square number — the tile count of a square.
  • The odd staircase — each new layer is the next odd number.
  • A test that says no — the last digit rules some numbers out.
  • Square roots — the side a square came from.
  • Pairing primes — find a square root without guessing.
  • In between — a number that sits between two squares.
  • A cube number — the count of unit cubes in a cube.
  • Cube patterns — odd numbers add up to cubes.
  • Grouping in threes — find a cube root.
  • Flat or filled — which count a job needs.

Each lesson has a lab, apart from the checkpoints, summary and quiz. Tap it or slide it, and watch.

Jump to lesson

This track

  1. 0 Start here
  2. 1 A number you can draw as a square
  3. 2 Each new layer is the next odd number
  4. 3 A test that can only say no
  5. 4 Going back to the side you started from
  6. 5 Pairing the primes finds the side
  7. 6 Checkpoint: squares, the staircase and roots
  8. 7 When no whole number fits
  9. 8 A cube number counts real cubes
  10. 9 What cubes end in, and what they add up to
  11. 10 Grouping the primes in threes
  12. 11 Which count is the job asking for
  13. 12 Checkpoint: in between, cubes and cube roots
  14. 13 The big picture
  15. 14 Track quiz

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