Linear Relationships

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Linear Relationships
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Matchstick pattern
Pattern 1
Pattern 2
Pattern 3
3
Colour helps
Pattern 1
Pattern 2
Pattern 3
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4 added on each time
Even the first house is one stick with 4 added on
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How many sticks are needed for the 7th pattern?
Click for solution
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29 sticks are needed
1 4 4 4 4 4 4
4
1 ( 7 ? 4)
29
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Table of values
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Points show adding on 4 each time
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The points line are in a line
The points are linear
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Lets look at the mapping
Number of sticks
Pattern number
5 9 13 17 21 25 29
1 2 3 4 5 6 7
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The flow diagram shows the rule
How many sticks in the 10 th pattern?
output
input
40
Multiply by 4
Add 1
41
10
41 sticks
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We use algebra to make a general rule
How many sticks in the n th pattern?
output
input
4n
Multiply by 4
Add 1
n
4n1
Pattern number
Number of sticks
13
s
Now we have the formula
s 4n 1
n
We can label the graph line
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We can work out the formula from the table
4
8
12
16
20
24
28
differences
4
4
4
4
4
4
Formula s 4 x
1
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What do you notice about this sequence?
Pattern 1
Pattern 2
Pattern 3
Answer
It gives the same sequence of numbers as the
matchstick pattern
different example
End
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Investigate this sequence
Pattern 1
Pattern 2
Pattern 3
table of values
Add colour
graph
mapping
End
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Colour highlights the change
Pattern 1
Pattern 2
Pattern 3
Add on 3 each time
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You can find information from the mapping
Number of sticks
Pattern number
5 8 11 14 17
1 2 3 4 5
10
32
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How many sticks in the 50th pattern?
output
input
150
Multiply by 3
Add 2
152
50
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How many sticks in the nth pattern?
The formula is s 3n 2
output
input
3n
Multiply by 3
Add 2
n
3n2
Pattern number
Number of sticks
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The plotted points lie in a straight line
n
The line has equation s 3n 2
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You can easily find the formula from the table
3
6
9
12
15
18
21
differences
3
3
3
3
3
3
Formula s 3 x
2
23
The End