Substitution Game x - 90 10 -3x x - 2 1 - x 4 - x2 10 -2x x - 50 2 - x 100 99 x - 90 98 97 96 10 -3x 95 94 93 x - 2 92 91 1 - x 81 82 83 4 - x2 84 85 86 87 10 -2x 88 89 x - 50 90 80 79 78 77 2 - x 76 75 x+2 74 73 3x 72 71 61 62 2(x-2) 63 38 Miss A Go 65 66 67 x2 - x 68 69 x2 70 60 59 58 2x 57 56 55 54 3(x-2) 53 52 51 41 x+15 42 43 44 45 46 x2 - 10 47 48 49 50 (x-1)2 40 39 37 36 (x-2)2   35 34 x(x-1) 33 32 31 21 22 x2 - 2x 23 24 25 x - 10 26 27 28 29 30 20 19 18 17 4(x-2) 16 15 14 3 - x 13 12 2(x-1) 11 1 2 3 4x - 2 4 5 6 2x + 3 7 8 9 10 START

4x - 2 Substitution Game 4 (3) – 2 = 10 So move forwards 10… The number on the dice is ‘x’. 4x - 2 4 (3) – 2 = 10 So move forwards 10…

2 - x Substitution Game 2 – 3 = -1 How do you think you should move? The number on the dice is ‘x’. 2 - x 2 – 3 = -1 How do you think you should move?

Substitution Game The number on the dice is ‘x’. (x – 2)2 (3 – 2)2 = 1

Substitution Game To finish, you must land exactly on 100. 99 x - 90 98 97 96 10 -3x 95 94 93 x - 2 92 91 1 - x 81 82 83 4 - x2 84 85 86 87 10 -2x 88 89 x - 50 90 80 79 78 77 2 - x 76 75 x+2 74 73 3x 72 71 61 62 2(x-2) 63 38 Miss A Go 65 66 67 x2 - x 68 69 x2 70 60 59 58 2x 57 56 55 54 3(x-2) 53 52 51 41 X+15 42 43 44 45 46 x2 - 10 47 48 49 50 (x-1)2 40 39 37 36 (x-2)2   35 34 x(x-1) 33 32 31 21 22 x2 - 2x 23 24 25 x - 10 26 27 28 29 30 20 19 18 17 4(x-2) 16 15 14 3 - x 13 12 2(x-1) 11 1 2 3 4x - 2 4 5 6 2x + 3 7 8 9 10 To finish, you must land exactly on 100. If you go past it, then ‘bounce back’ START

(x – 2)2 Substitution Game If you threw a 6 and landed on this square, what did you move? (x – 2)2

x + 2 x - 2 Substitution Game If you threw a 4 and landed on this square, what did you move? x + 2 x - 2

x + 2 x - 2 Substitution Game If you threw a 5 and landed on this square, what did you get? How would you move? x + 2 x - 2

4 – x2 Substitution Game If you threw a 3 and landed on this square, what did you move? 4 – x2

Substitution Game Which squares are SNAKES? (Always negative) Which squares are LADDERS? (Always positive) Are any squares sometimes snakes and sometimes ladders? If so, which values make them snakes, and which make them ladders?

Substitution Game Challenges: Can you write some different expressions that would always be positive? Can you write some different expressions that would always be negative? Can you write an expression for square 10 that would take you back to square 1 if you threw a 6? And another? And another?

Substitution Game In your books… Title – Substituting into expressions Going up in order, the first expression you get to is You write: 4x – 2 When x = 10 4(10) – 2 = 38

Substitution Game Write down the first 9 expressions from the board game and find their value when: x = 10 Set them all out in the same way as the first question Challenges: Find their values when x = ½ Find their values when x = -1

Substitution Game Make your own board game. This time you have two dice – one represents the letter a, the other represents the letter b. Rules for making the game: You must have 20 expressions. The expressions must include a’s, b’s or a mixture of both. Some must always be snakes; some must always be ladders. You must have at least one square that takes you back to square 1 when a double 6 is thrown You must have at least one expression that takes you to another expression square when a 3 is thrown on dice a and a 1 is thrown on dice b.