1. Half-time Scores The full-time score in a game of hockey was 3 – 4. What could the score have been at half-time? Work with a friend and write down as many different half-time scores as you can on the blank cards provided.

2. Half-time Scores 0 - 0 0 - 1 0 - 2 1 - 01 - 1 1 - 4 1 - 3 2 - 0 2 - 1 2 - 4 2 – 3 2 - 2 3 - 0 3 - 1 3 - 4 3 - 3 3 - 2

3. Half-time Scores 1 - 0 1 - 4 1 - 3 2 - 0 2 - 1 2 - 4 2 – 3 0 - 0 1 - 1 2 - 2 3 - 3 3 - 0 3 - 1 3 - 4 0 - 2 0 - 1 DRAWS 2 - ?1 - ? 0 - ? 3 - ?

4. Half-time Scores 0 - 4 0 - 3 1 - 0 1 - 4 1 - 3 1 - 2 2 - 0 2 - 1 2 - 4 2 – 3 0 - 0 1 - 1 2 - 2 3 - 3 3 - 0 3 - 1 3 - 4 3 - 2 0 - 2 0 - 1 DRAWS 2 - ?1 - ? 0 - ? 3 - ?

5. Half-time Scores 0 - 4 0 - 3 1 - 0 1 - 4 1 - 3 1 - 2 2 - 0 2 - 1 2 - 4 2 – 3 0 - 0 1 - 1 2 - 2 3 - 3 3 - 0 3 - 1 3 - 4 3 - 2 0 - 2 0 - 1 DRAWS 2 - ?1 - ? 0 - ? 3 - ?

6. Half-time Scores 0 - 4 0 - 3 1 - 0 1 - 4 1 - 3 1 - 2 2 - 0 2 - 1 2 - 4 2 – 3 0 - 0 1 - 1 2 - 2 3 - 3 3 - 0 3 - 1 3 - 2 3 - 4 0 - 2 0 - 1 DRAWS 2 - ?1 - ? 0 - ? 3 - ?

7. Half-time Scores 0 - 0 0 - 1 1 - 0 0 - 2 1 - 1 2 - 0 0 - 3 1 - 2 2 - 1 3 - 0 0 - 4 1 - 3 2 - 2 3 - 1 3 - 4 2 - 4 3 - 3 3 - 2 1 - 4 2 - 3 Sum of the scores

8. Half-time Scores 0 - 4 0 - 3 1 - 4 3 - 0 0 - 2 1 - 3 2 - 0 2 - 4 3 - 1 0 - 0 1 - 1 2 - 2 3 - 3 0 - 1 1 - 0 1 - 2 2 - 1 2 – 3 3 - 4 3 - 2 0 diff 2 diff 3 diff 4 diff 1 diff

9. Half-time Scores 0 - 00 - 10 - 4 0 - 3 0 - 21 - 01 - 11 - 4 1 - 3 1 - 22 - 02 - 12 - 4 2 – 3 2 - 23 - 03 - 13 - 4 3 - 3 3 - 24 - 04 - 14 - 4 4 - 3 4 - 2

10. Half-time Scores 0 - 00 - 10 - 4 0 - 3 0 - 21 - 01 - 11 - 4 1 - 3 1 - 22 - 02 - 12 - 4 2 – 3 2 - 23 - 03 - 13 - 4 3 - 3 3 - 24 - 04 - 14 - 4 4 - 3 4 - 2

11. Half-time Scores 0 - 00 - 10 - 4 0 - 3 0 - 21 - 01 - 11 - 4 1 - 3 1 - 22 - 02 - 12 - 4 2 – 3 2 - 23 - 03 - 13 - 4 3 - 3 3 - 24 - 04 - 14 - 4 4 - 3 4 - 2

12. Half-time Scores 0 - 00 - 10 - 4 0 - 3 0 - 21 - 01 - 11 - 4 1 - 3 1 - 22 - 02 - 12 - 4 2 – 3 2 - 23 - 03 - 13 - 4 3 - 3 3 - 24 - 04 - 14 - 4 4 - 3 4 - 2

13. Half-time Scores 0 - 00 - 10 - 4 0 - 3 0 - 21 - 01 - 11 - 4 1 - 3 1 - 22 - 02 - 12 - 4 2 – 3 2 - 23 - 03 - 13 - 4 3 - 3 3 - 24 - 04 - 14 - 4 4 - 3 4 - 2

14. Half-time Scores 0 - 00 - m 1 - 0 n - 0 n - 1 n - m Number of half-time scores = (n+1)(m+1) 1 -m 0 - 1 0 - 2

15. Half-time Scores Here is a clown’s hat. It has 3 pom-poms on the front and each pom-pom can be one of 3 colours, red, blue or green. How many different clowns hats can be made? Clowns’ Hats

16. Half-time Scores Clowns’ Hats

17. Half-time Scores Clowns’ Hats Red tops Green tops Blue tops

18. Half-time Scores Clowns’ Hats Blue tops

19. Half-time Scores Clowns’ Hats Blue tops Two blue at the top Two blue one at the top one at the bottom One blue at the top and the other the same One blue at the top and the others different

20. Half-time Scores Clowns’ Hats One colour Three colours Two Colours

21. Half-time Scores Clowns’ Hats All same All different Red and Blue Red and Green Blue and Green