1. DARTBOARD MATHS ALGEBRA - generating simple equations Dave Carden Liverpool Maths Team

2. 1 X = 2 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 X + 5 = 7

3. 2 X = 6 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 X + 2 = 8

4. 3 y = 4 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 y + 4 = 8

5. 4 k = 8 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 k + 3 = 11

6. 5 m = 9 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 m + 11 = 20

7. 6 m = 3 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 2m + 5 = 11

8. 7 m = 5 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 3m + 5 = 20

9. 8 m = 10 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 2m + 2 = 22

10. 9 X = 5 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 2X + 5 = 15

11. 10 K = 5 x 2 5 1 3 y 2 m 3 m 8 1 1 2m 7 5 k 2 y 2 x y 20 x 4 2 2K + 11 = 21

12. In these simple equations, x is either 1, 2, 3, 4 or 5 X + 2 = 5 so x = X - 1 = 4 so x = X + 4 = 8 so x = 7 – X = 5 so x = 4 - X = 0 so x = X - 3 = 1 so x = X + 3 = 7 so x = X + 1 = 6 so x = 8 – X = 5 so x = X - 2 = 1 so x = A

13. In these simple equations, x is either 1, 2, 3, 4 or 5 X + 2 = 5 so x = X - 1 = 4 so x = X + 4 = 8 so x = 7 – X = 5 so x = 4 - X = 0 so x = X - 3 = 1 so x = X + 3 = 7 so x = X + 1 = 6 so x = 8 – X = 5 so x = X - 2 = 1 so x = 3 4 4 5 5 4 3 4 3 2 A

14. In these simple equations, x is either 1, 2, 3, 4 or 5 2X + 1 = 5 so x = 2X - 1 = 9 so x = 3X - 1 = 5 so x = 7 – 2X = 1 so x = 4 - 2X = 0 so x = 2X - 3 = 3 so x = 4X - 3 = 5 so x = 2X + 2 = 6 so x = 8 – 4X = 0 so x = 5X - 2 = 1 3 so x = B

15. In these simple equations, x is either 1, 2, 3, 4 or 5 2X + 1 = 5 so x = 2X - 1 = 9 so x = 3X - 1 = 5 so x = 7 – 2X = 1 so x = 4 - 2X = 0 so x = 2X - 3 = 3 so x = 4X - 3 = 5 so x = 2X + 2 = 6 so x = 8 – 4X = 0 so x = 5X - 2 = 1 3 so x = 2 2 5 3 2 3 2 3 2 2 B

16. Challenge X – 2 = -1 so x = X – 4 = -2 so x = 2x – 4 = -2 so x = X – 3 = -1 so x = 4x -15 = -3 so x = C

17. Challenge X – 2 = -1 so x = X – 4 = -2 so x = 2x – 4 = -2 so x = X – 3 = -1 so x = 4x -15 = -3 so x = 3 1 1 1 2

18. The solutions to these equations are either X = 1, 2, 3, 4 or 5 (1) X + 4 = 9 (2) X – 5 = -2 (3) X + 4 = 8 (4) X – 2 = -1 (5) 2X + 1 = 7 (6) 2X + 4 = 12 (7) 2X – 7 = -1 (8) 3X = 9 (9) 4X = 20 (10) 3X = 8 (11) 4X – 7 = 13 (12) 10 – 3X = 1 (13) 12 – 3X = 0 (14) 2X + 1 = 8 (15) 8 – 3X = 2 (16) 4X – 3 = 12 (17) 6X = 6 (18) 12 = 15X (19) 16 = 4X (20) 7X -1 = 20 There are a few odd ones out. Can you spot them ?

19. Answers ! (1) X = 5 (2) X = 3 (3) X = 4 (4) X = 1 (5) X = 3 (6) X = 4 (7) X = 3 (8) X = 3 (9) X = 5 (10) X = 8/3 (11) X = 5 (12) X = 3 (13) X = 4 (14) X = 3.5 (15) X = 2 (16) X = 9/4 (17) X = 1 (18) X = 12/15 (19) X = 4 (20) X = 3 Did you spot the odd ones out ?

20. Answer first ! x = 2 2x = 4 2x + 3 = 7 Start with the answer add... to both sides.......... both sides Now give the finished equation to your partner to solve. You can help them because you made up the question.

21. Answer first ! x = 3 3x = 9 3x + 4 = 13 Start with the answer add... to both sides.......... both sides Now give the finished equation to your partner to solve. You can help them because you made up the question.