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

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 by2n + 3

Move forwards byn - 3

Move backwards by2n + 3

Move forwards by4 squares

Move forwards by-n + 3

Move backwards byn + 7


Go back to the start.

Throw a four to win

Start

Win

Your game must be based on substitution










Throw a four to win

Start

Win

This is a very basic example of a possible game.










Throw a four to win

Start

Win

If you start by rolling a “2”, you will land here.










Throw a four to win

Start

Win

You then need to substitute n = 2 into the expression given in the square










Throw a four to win

Start

Win

If n = 2 then n – 3 will be 2 – 3 which is -1You would have to move back by 1 space. It is then the other players turn .










Throw a four to win

Start

Win

Notice that not all the squares are substitutions – but most are.










Throw a four to win

Start

Win

Your turn

Look at the first square









Throw a four to win

Start

Win

Lets look at all the possible results from the dice










Throw a four to win

Start

Win

It would be sensible to work sequentially










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

2 + 3










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

5










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

5 4 + 3










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

5 7










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

5 7 6 + 3










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

5 7 9










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

5 7 9 11 13 15










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

5 7 9 11 13 15

This is a linear sequence










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

5 7 9 11 13 15

It goes (up) by the same amount each time

+2










Throw a four to win

Start

Win

n 1 2 3 4 5 6

total

5 7 9 11 13 15

We say the difference is + 2

+2

+2

+2










Throw a four to win

Start

Win

n 1 2 3 4 5 6

2n

total

5 7 9 11 13 15

This tells us that the basic sequence is 2n in other words, it is based on the 2 times table










Throw a four to win

Start

Win

n 1 2 3 4 5 6

2n 2 4 6 8 10 12

total

5 7 9 11 13 15

Lets look at the two times table










Throw a four to win

Start

Win

n 1 2 3 4 5 6

2n 2 4 6 8 10 12

total

5 7 9 11 13 15

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










Throw a four to win

Start

Win

n 1 2 3 4 5 6

2n 2 4 6 8 10 12

total

5 7 9 11 13 15

How do we get from here










Throw a four to win

Start

Win

n 1 2 3 4 5 6

2n 2 4 6 8 10 12

total

5 7 9 11 13 15


To here










Throw a four to win

Start

Win

n 1 2 3 4 5 6

2n 2 4 6 8 10 12

total

5 7 9 11 13 15


To here

We +3










Throw a four to win

Start

Win

n 1 2 3 4 5 6

2n 2 4 6 8 10 12

2n+1

5 7 9 11 13 15

This gives us our final rule

2n + 3










Throw a four to win

Start

Win

n 1 2 3 4 5 6

2n 2 4 6 8 10 12

2n+3

5 7 9 11 13 15

This gives us our final rule

2n + 3

Use your game to show that this always works.

Date post:	29-Jan-2016
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You are going to work in pairs to produce a Maths board game.

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