Jumping Cricket
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Age
5 to 7
Challenge level
El Crico the cricket has to cross a square patio to get home. He likes to jump along the lines made by the sides of the tiles.
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He can jump the length of one tile. He can jump the length of two tiles. If he tries hard he can even jump the length of three tiles.
Here's one path where he could make four jumps to get home - 1, 2, 2, 1
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Can you find a path that would get El Crico home in three jumps?
Can you find all the paths of three jumps?
What size jump are you going to try next?
Can all his jumps be the same size?
Can you find another way of doing it?
How will you know which ways you've tried?
Using a counter on a grid may help. This sheethas twelve copies of the square patio.
Harry sent us his thoughts on this problem:
My first way was that El Crico jumps along one tile, down three tiles and along one tile.
Then I thought that there are six different ways El Crico starts off his journey. He jumps along one, two or three tiles or he jumps down one, two or three tiles. Then he has two moves to get to the end. One of these jumps takes him to the very right of the board and the other takes him to the very bottom.
I made a table of all the possible moves. There are twelve of them.
| First Move | Second Move | Third Move |
| Along one | Along two | Down three |
| Along one | Down three | Along two |
| Along two | Along one | Down three |
| Along two | Down three | Along one |
| Along three | Down one | Down two |
| Along three | Down two | Down one |
| Down one | Down two | Along three |
| Down one | Along three | Down two |
| Down two | Down one | Along three |
| Down two | Along three | Down one |
| Down three | Along one | Along two |
| Down three | Along two | Along one |
That's great, Harry. Thank you!
Why do this problem?
This problem is a useful context in which to encourage children
to work systematically in pairs or small groups.
This sheet, which
could be photocopied, has twelve copies of the square patio.
Key questions
What size jump are you going to try next?
Can all his jumps be the same size?
Can you find another way of doing it?
How will you know which ways you've tried?