1. Multiples and Factors

2. Multiples A multiple is a number that is in the times tables. A multiple is a number that is in the times tables. Multiples of 6 are Multiples of 6 are 6, 12, 18, 24, 30… Multiples of 20 are Multiples of 20 are 20, 40, 60, 80, 100…

3. What are the multiples of… 4 4, 8, 12, 16, 20… 4, 8, 12, 16, 20…9 9, 18, 27, 36, 45… 9, 18, 27, 36, 45…30 30, 60, 90, 120, 150… 30, 60, 90, 120, 150…

4. Factors A factor is a number that divides exactly into another number. A factor is a number that divides exactly into another number. Factors of 6 are Factors of 6 are 1, 2, 3 and 6 Factors of 20 are Factors of 20 are 1, 2, 4, 5, 10 and 20

5. What are the factors of… 15 1, 3, 5, 15 1, 3, 5, 1528 1, 2, 4, 7, 14, 28 1, 2, 4, 7, 14, 2850 1, 2, 5, 10, 20, 25, 50 1, 2, 5, 10, 20, 25, 50

6. Factor exploration Start with any number: Start with any number: Write down all its factors: Write down all its factors: Add all but the largest: Add all but the largest: Write down the factors of the new number: Write down the factors of the new number: Add all but the largest: Add all but the largest: … and so on … 9 1, 3, 9 1+3 = 4 1, 2, 4 1+2 = 3 1, 3 =1

7. 9  4  3  1 This is called the factor chain for 9. Draw factor chains for these numbers: (a) 16(b) 29(c) 12(d) 6 (e) a number of your choice (f) Challenge: 102 (this is long!)

8. Play “Juniper Green” A game for 2 players, played on a grid like this: A game for 2 players, played on a grid like this: 12345678910 11121314151617181920 21222324252627282930 31323334353637383940

9. Play “Juniper Green” The first player puts a counter on an even number. The first player puts a counter on an even number. After that, players take turns, putting a counter on either a factor or a multiple of the last number covered. After that, players take turns, putting a counter on either a factor or a multiple of the last number covered. The first player who is unable to cover a number loses. The first player who is unable to cover a number loses.

10. Play “Juniper Green” Show that this is a first player game by finding the winning strategy for the first player. Show that this is a first player game by finding the winning strategy for the first player. Try playing on different sized grids. Try playing on different sized grids. Juniper Green is named after the school where it was invented. Thanks!

11. JRElse 2004