This task is about rules for spatial patterns.
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| Shape 1 | Shape 2 | Shape 3 |
Petra made these shapes out of matches.
The rule for the number of squares can be written as an equation like this:
The rule for the number of squares can be written as an equation like this:
| sn = 2n2 – 2n + 1 |
where n represents the shape number,
and sn represents the number of squares in shape n.
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| a) |
How many squares will there be in |
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i)
ii)
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shape 6? __________
shape 10? ___________
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The rule for the number of matches in a shape can be written in words as:
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| b) |
Use this rule to work out how many matches would be needed to make |
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i)
ii)
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shape 5? __________
shape 20? __________
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| c) |
Write the rule for the number of matches as an equation.
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Use n to represent the shape number, and
Use tn torepresent the number of matches in shape n.
Complete this equation for the number of matches needed for shape n.
tn = ____________________
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