Multiplication and division puzzles

Groups, arrays, factors and sharing out — and several boards where multiplying is something you do to a position rather than to a pair of numbers on a page.

Disco Balls takes a product apart into primes and draws the result. Mondrian Puzzle, Picasso Brush and Galaxea each make a rectangle the unit of play, so every move is a multiplication you have to do before you know what you have made. Gozen forces the next number on you and lets you choose only where it stands, so shared factors decide whether it survives the turn. Zebra and Balanced Zebra multiply your own herd sizes together, which is where the useful surprise is: three threes beat one nine, and a stone standing alone is worth nothing at all.

9 puzzles

• Stained GlassSkip-counting turned into a picture: the pattern each times table draws across a hundred square. · grades 1–6
• Disco BallsPrime factors made visible: a product becomes circles inside circles, so multiplication reads as structure. · grades 2–6
• Fractured FractionsOne point cuts the whole picture at once, and every piece has to come out holding the fraction written on it. · grades 3–5
• GalaxeaTwo of the three dice are the sides of a rectangle — and the game is which two, and where to hang it. · grades 3–6
• Mondrian PuzzleEvery rectangle painted is a multiplication, and the score is the gap between the biggest one and the smallest. · grades 2–6
• Picasso BrushA stroke is only as long as one end number divided by the other, so covering the paper is a hunt for factors. · grades 2–6
• Balanced ZebraBoth colours have to multiply out to the same number, and then to the largest that shape allows. · grades 3–6
• GozenYour next number is forced, so a prime is always coming — and on a prime only a square nobody watches will do. · grades 4–6
• ZebraHerds multiply together, so three threes beat one nine — and a stone left on its own throws itself away. · grades 3–6