A game for 2 players. The winner is the player with most points at the end.

Starter (optional)

- Play a game with the 13x table. This is almost completely unfamiliar and the kids will be intrigued. The KEY fact is that 7×13=91 because 91 is a terribly prime-looking number but it isn’t. Pupils who are confident with their other tables will, by learning this factorisation, have completed the full set of skills in factorising numbers under 100.

- Make sure the players can factorise a number using their calculator. On the CASIO fx-83gt PLUS this is done by entering the number, pressing equals, SHIFT and
**., ,,,**(this has “FACT” written above it in yellow). The Prime Factor Form is displayed as the answer.

Each turn:

- Roll 2 (or 3) dice, and choose which number to build. For example, a 5 and a 1 could be 15, 51 or 6. Factorise your chosen number. The score is the number of prime factors. eg 15 would score 2 for 3×5. 8 would score 3 because it is 2 cubed. 24 scores 4 because it is 2x2x2x3. 71 scores 1 because it is prime. ** You may need to explain the “Index Form” that the calculator displays. This is a very important notation anyway, which a lot of students misunderstand.

What Maths is learned:

- To choose the best number, ideally the players have to mentally factorise both numbers. They will make repeated use of the standard divisibility tests (for 2, 3, 5 and 9) and probably invent a few more (this evening my pupil realised 357 and 217 must both be in the 7x table, just by looking at them.)
- Once they know a number will divide, they have to actually DO it mentally. Practice makes perfect here!
- A printed tables sheet may be a help.
- In their enthusiasm to win they are stretching their own mental maths to the limit. If they don’t fully factorise both numbers, they may miss a high score!
- A younger pupil may want to try all the possible numbers with the calculator – this is good practice anyway and reinforces the correct factorisations.
- An enthusiastic player will start to memorise some of the factorisations – this is really helpful knowledge.