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
Move forwards by2n + 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 by2n + 3
Move forwards byn - 3
Move backwards by2n + 3
Move forwards by4 squares
Move forwards by-n + 3
Move backwards byn + 7
Move forwards by2n + 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 by2n + 3
Move forwards byn - 3
Move backwards by2n + 3
Move forwards by4 squares
Move forwards by-n + 3
Move backwards byn + 7
Move forwards by2n + 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 by2n + 3
Move forwards byn - 3
Move backwards by2n + 3
Move forwards by4 squares
Move forwards by-n + 3
Move backwards byn + 7
Move forwards by2n + 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 by2n + 3
Move forwards byn - 3
Move backwards by2n + 3
Move forwards by4 squares
Move forwards by-n + 3
Move backwards byn + 7
Move forwards by2n + 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 -1You would have to move back by 1 space. It is then the other players turn .
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
Move forwards by2n + 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 by2n + 3
Move forwards byn - 3
Move backwards by2n + 3
Move forwards by4 squares
Move forwards by-n + 3
Move backwards byn + 7
Move forwards by2n + 3
Go back to the start.
Throw a four to win
Start
Win
Your turn
Look at the first square
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
Move forwards by2n + 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 by2n + 3
Move forwards byn - 3
Move backwards by2n + 3
Move forwards by4 squares
Move forwards by-n + 3
Move backwards byn + 7
Move forwards by2n + 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 by2n + 3
Move forwards byn - 3
Move backwards by2n + 3
Move forwards by4 squares
Move forwards by-n + 3
Move backwards byn + 7
Move forwards by2n + 3
Go back to the start.
Throw a four to win
Start
Win
n 1 2 3 4 5 6
total
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
Throw a four to win
Start
Win
n 1 2 3 4 5 6
total
2 + 3
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
Throw a four to win
Start
Win
n 1 2 3 4 5 6
total
5
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
Throw a four to win
Start
Win
n 1 2 3 4 5 6
total
5 4 + 3
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
Throw a four to win
Start
Win
n 1 2 3 4 5 6
total
5 7
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
Throw a four to win
Start
Win
n 1 2 3 4 5 6
total
5 7 6 + 3
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
Throw a four to win
Start
Win
n 1 2 3 4 5 6
total
5 7 9
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
Throw a four to win
Start
Win
n 1 2 3 4 5 6
total
5 7 9 11 13 15
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
To here
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
To here
We +3
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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
Look at the first square
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
Move forwards by2n + 3
Go back to the start.
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.