You are going to work in pairs to produce a Maths board game

 Part One  Design a board game base on substitution  Part Two  Use the game to look at sequences

 Design a board game base on substitution Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win Your game must be based on substitution

 Design a board game base on substitution Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win This is a very basic example of a possible game.

 Design a board game base on substitution Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win If you start by rolling a “2”, you will land here.

 Design a board game base on substitution Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win You then need to substitute n = 2 into the expression given in the square

 Design a board game base on substitution Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win If n = 2 then n – 3 will be 2 – 3 which is -1 You would have to move back by 1 space. It is then the other players turn.

 Design a board game base on substitution Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win Notice that not all the squares are substitutions – but most are.

 Design a board game base on substitution Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win Your turn

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win Lets look at all the possible results from the dice

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win It would be sensible to work sequentially

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total2 + 3

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total5

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total54 + 3

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total57

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total579

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total This is a linear sequence

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total It goes (up) by the same amount each time +2

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n total We say the difference is

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n n total This tells us that the basic sequence is 2n in other words, it is based on the 2 times table

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n n total Lets look at the two times table

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n n total So, the first part of our rule is 2n but that’s not the end because our sequence is slightly different – we need a correction factor

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n n total How do we get from here

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n n total How do we get from here To here

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n n total How do we get from here To here We +3

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n n n This gives us our final rule 2n + 3

 Look at the first square Move forwards by 2n + 3 Move forwards by n - 3 Move backwards by 2n + 3 Move forwards by 4 squares Move forwards by -n + 3 Move backwards by n + 7 Move forwards by 2n + 3 Go back to the start. Throw a four to win Start Win n n n This gives us our final rule 2n + 3 Use your game to show that this always works.