Factorising Race

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.

Introduction:

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.