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We worked on this problem today in Year 5.

Firstly, we read the problem and discussed the information given. We then used a table to present this. Using cubes to help us, the children worked in pairs to build a staircase with 3 steps up and 3 steps down. We counted the number of cubes used and added this to our table. We then predicted what we thought our results would be for a staircase with 4 steps up and 4 steps down. Once we had built the model, we added the information to our table and compared the results to our predictions.

Lots of children noticed that if they squared the number of steps up and down, they would get the number of blocks used. We calculated that a staircase with 5 steps up and 5 steps down would need 25 blocks as 5 squared is equal to 25. To check that we were correct and to convince our partners, we each built the 5 up and 5 down staircase and counted the blocks.

To challenge ourselves, we applied the rule to larger staircases. We found that a staircase with 18 steps up and 18 steps down would need 324 blocks to build.