CLASS 6 MATHS · ALGEBRA

Algebra with matchstick patterns

A pattern rule like 3n + 1 tells you how many sticks are needed for n shapes.

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Worked examples

Example 1 · level 1

For a pattern of joined triangles in a row, the rule is 2n + 1 matchsticks for n shapes (because the first triangle needs 3 sticks and each new one adds 2). How many matchsticks are needed for 5 shapes?

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2n + 1 with n = 5: 2 × 5 + 1 = 11.

Answer: 11

Example 2 · level 2

For a pattern of joined squares in a row, the rule is 3n + 1 matchsticks for n shapes (because the first square needs 4 sticks and each new square adds 3). How many matchsticks are needed for 43 shapes?

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3n + 1 with n = 43: 3 × 43 + 1 = 130.

Answer: 130

Example 3 · level 3

A pattern of joined squares in a row uses 3n + 1 matchsticks for n shapes. How many shapes can be made with exactly 88 matchsticks?

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3n + 1 = 88
3n = 87
n = 29.

Answer: 29