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
Start
Move
forwards
by
2n + 3
Move
forwards
by
n-3
Move
backwards
by
2n + 3
Your game must be based on substitution
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Design a board game base on substitution
Start
Move
forwards
by
2n + 3
Move
forwards
by
n-3
Move
backwards
by
2n + 3
This is a very basic example of a possible
game.
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Design a board game base on substitution
Start
Move
forwards
by
2n + 3
Move
forwards
by
n-3
Move
backwards
by
2n + 3
If you start by rolling a “2”, you will land
here.
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Design a board game base on substitution
Start
Move
forwards
by
2n + 3
Move
forwards
by
n-3
Move
backwards
by
2n + 3
You then need to substitute n = 2 into the
expression given in the square
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Design a board game base on substitution
Start
Move
forwards
by
2n + 3
Move
forwards
by
n-3
Move
backwards
by
2n + 3
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 .
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Design a board game base on substitution
Start
Move
forwards
by
2n + 3
Move
forwards
by
n-3
Move
backwards
by
2n + 3
Notice that not all the squares are
substitutions – but most are.
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Design a board game base on substitution
Start
Move
forwards
by
2n + 3
Move
forwards
by
n-3
Move
backwards
by
2n + 3
Move
forwards
by
-n + 3
Your turn
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
4 squares
Move
forwards
by
2n + 3
Move
backwards
by
n+7

Look at the first square
Start
Move
forwards
by
2n + 3
Move
forwards
by
n-3
Move
backwards
by
2n + 3
Lets look at all the possible results from
the dice
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Start
Move
forwards
by
2n + 3
Move
forwards
by
n-3
Move
backwards
by
2n + 3
It would be sensible to work sequentially
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Move
forwards
by
2n + 3
Start
n
1
2
Move
forwards
by
n-3
3
4
Move
backwards
by
2n + 3
5
6
total
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Move
forwards
by
2n + 3
Start
n
1
total
Win
2
Move
forwards
by
n-3
3
4
Move
backwards
by
2n + 3
5
6
2+3
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Move
forwards
by
2n + 3
Start
n
1
total
5
Win
2
Move
forwards
by
n-3
3
4
Throw a
Go back to
four to win the start.
Move
backwards
by
2n + 3
5
6
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Move
forwards
by
2n + 3
Start
n
1
2
total
5
4+3
Win
Move
forwards
by
n-3
3
4
Throw a
Go back to
four to win the start.
Move
backwards
by
2n + 3
5
6
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Move
forwards
by
2n + 3
Start
n
1
2
total
5
7
Win
Move
forwards
by
n-3
3
4
Throw a
Go back to
four to win the start.
Move
backwards
by
2n + 3
5
6
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
n
1
2
3
total
5
7
6+3
Win
4
Throw a
Go back to
four to win the start.
Move
backwards
by
2n + 3
5
6
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
n
1
2
3
total
5
7
9
Win
4
Throw a
Go back to
four to win the start.
Move
backwards
by
2n + 3
5
6
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
total
5
7
9
11
13
15
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
total
5
7
9
11
13
15
Win
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
This is a
linear
sequence

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
total
5
7
9
11
13
15
Win
+2
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
It goes (up)
by the
same
amount
each time

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
total
5
7
9
11
13
15
Win
+2
+2
+2
Throw a
Go back to
four to win the start.
Move
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
We say the
difference
is + 2

Look at the first square
Move
forwards
by
2n + 3
Start
n
1
2
Move
forwards
by
n-3
3
4
Move
backwards
by
2n + 3
5
6
2n
total
Win
5
7
9
11
13
15
Throw a
Go back to Move
four to win the start.
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
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
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
2n
2
4
6
8
10
12
total
5
Win
7
9
11
13
15
Throw a
Go back to Move
four to win the start.
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
Lets look at
the two
times table

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
2n
2
4
6
8
10
12
total
5
Win
7
9
11
13
15
Throw a
Go back to Move
four to win the start.
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
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
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
2n
2
4
6
8
10
12
total
5
Win
7
9
11
13
15
Throw a
Go back to Move
four to win the start.
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
How do
we get
from here

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
2n
2
4
6
8
10
12
total
5
Win
7
9
11
13
15
Throw a
Go back to Move
four to win the start.
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
How do
we get
from here
To here

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
2n
2
4
6
8
10
12
total
5
Win
7
9
11
13
15
Throw a
Go back to Move
four to win the start.
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
How do
we get
from here
To here
We +3

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
2n
2
4
6
8
10
12
2n+1
5
Win
7
9
11
13
15
Throw a
Go back to Move
four to win the start.
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
This gives
us our final
rule
2n + 3

Look at the first square
Move
forwards
by
2n + 3
Start
Move
forwards
by
n-3
Move
backwards
by
2n + 3
n
1
2
3
4
5
6
2n
2
4
6
8
10
12
2n+3
5
Win
7
9
11
13
15
Throw a
Go back to Move
four to win the start.
forwards
by
2n + 3
Move
forwards
by
4 squares
Move
forwards
by
-n + 3
Move
backwards
by
n+7
This gives
us our final
rule
2n + 3
Use your
game to
show that
this
always
works.