Matchstick puzzles If I was to carry this pattern on so that there were 100 squares in a row, how many matchsticks would I need?

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Presentation transcript:

Matchstick puzzles If I was to carry this pattern on so that there were 100 squares in a row, how many matchsticks would I need?

Matchstick puzzles 400? No. Why not?

Matchstick puzzles So how many are there? Discuss in your pairs. Write down how you got your answer on your whiteboards.

Matchstick puzzles 1 +3 +3 +3 + … How many times must I add 3? 1 + 3 x 100

Matchstick puzzles … 3 +3 +3 … + 1 How many times must I add 3? 3 x 100 + 1

Matchstick puzzles 4 +3 +3 + … How many times must I add 3? 4 + 3 x 99

Matchstick puzzles … … 100 100 x 2 100 x 3 + 1 How many matchsticks would be in this row? 100 How many matchsticks do you have now? 100 x 2 How many matchsticks do you have now? 100 x 3 + 1

Matchstick puzzles I’ve changed my mind… I want to find how many matchsticks I need to make 50 squares.

Matchstick puzzles The answer should be 151 matches. How can you show that? Show me on your whiteboards. I shouldn’t see 151 on your whiteboard

Matchstick puzzles I’ve changed my mind… I want to find how many matchsticks I need to make a squares.

Matchstick puzzles 1 +3 +3 +3 + … How many times must I add 3? 1 + 3 x a 1 + 3a

Matchstick puzzles … 3 +3 +3 … + 1 How many times must I add 3? 3 x a + 1 3a + 1

Matchstick puzzles 4 +3 +3 + … How many times must I add 3? 4 + 3 x (a – 1) 4 + 3(a – 1)

Matchstick puzzles … … a a x 2 a x 3 + 1 How many matchsticks would be in this row? a How many matchsticks do you have now? a x 2 How many matchsticks do you have now? a x 3 + 1

How many matchsticks would be needed to make 100 triangles? In your book: Title: Matchstick puzzles How many matchsticks would be needed to make 100 triangles? Show your working out and relate it to the diagram. Can you count them matchsticks in a different way? How many matchsticks would be needed to make t triangles?

Explain your reasoning Matchstick puzzles - challenge How many matchsticks would be needed to make this shape, but with 100 squares across and up? Explain your reasoning How many matchsticks would be needed to make this shape, but with n squares across and up?