You will need:
2 dice and a pen and paper.
Take in turns to:
 Throw the dice
 From the dice, construct 2 or perhaps 3 numbers. For example, if you throw a two and a three, you can make 5, 23 and 32 (3+2=5, two followed by three is 23 and three followed by two is 32)
 Score one point for each prime number you have made (so this example scores one for the 5 and one for the 23, scoring two points in total).
 If you need to use a calculator, then a Casio fx83GT PLUS can tell you whether a number is prime. This is *not* cheating – students will soon start to recognise the primes they need, rather than having to check using the calculator!
The Winner Is:
The person who has the most points.
Things to discuss:
 Why are two even numbers always such bad news? (even+even=even and the only even prime number is two)
 Is it possible to score three points with one throw?
 If there is a six in your throw, what happens?
This sample space diagram may help:

Sample Space Diagram for 2 Dice


1

2

3

4

5

6

1

(1,1)

(2,1)

(3,1)

(4,1)

(5,1)

(6,1)

2

(1,2)

(2,2)

(3,2)

(4,2)

(5,2)

(6,2)

3

(1,3)

(2,3)

(3,3)

(4,3)

(5,3)

(6,3)

4

(1,4)

(2,4)

(3,4)

(4,4)

(5,4)

(6,4)

5

(1,5)

(2,5)

(3,5)

(4,5)

(5,5)

(6,5)

6

(1,6)

(2,6)

(3,6)

(4,6)

(5,6)

(6,6)

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On the CASIO fx83gt PLUS factorising is done like this:
 Entering the number,
 press equals,
 SHIFT and ., ,,, (this has “FACT” written above it in yellow).
 The Prime Factor Form is displayed as the answer.
 If the number is Prime, then the number itself is displayed.
This is a natural way to introduce what indices mean, because the CASIO gives the answers in index form eg 3^{4} rather than 3x3x3x3
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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 primelooking 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 fx83gt 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.
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Bespoke Maths uition for struggling pupils