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# That Number Square

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Age 5 to 11

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- Problem
- Getting Started
- Student Solutions
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Thank you to everybody who sent us their strategies for putting the hundred square back together.

Benji and Elizabeth from Trefonen Primary School in England sent in this explanation of their strategy:

We placed the numbers 1-10 first. This helped us to place other numbers below each of these in their columns with the same digits in the ones column. We also placed the numbers which were multiples of ten in the last column as they were easy to replace.

Well done for using this pattern in the hundred square to replace the numbers quickly!

The children in Puffins Class at Trefonen Primary School had a competition to replace the numbers in the hundred square as quickly as possible:

We used multiples of 10 to fill in the end column; then we filled in the rest of the top row; then we could do it randomly really quickly. We worked in small groups and timed which group was the fastest and we thought that this was probably the best strategy because it was the quickest, they were called 'The Number Bonds FC'.

One group had a really good idea to cover the whole 100 square in glue, at the start.

These are some good ideas - I wonder what the winning strategy was?

We also received some solutions from children at Maria L Baldwin School in the USA. Lillian said:

I filled in all the ones then the twos etc.

Thank you all for sharing your strategies with us. I wonder what Lillian means by 'ones' and 'twos'?

D from the UK shared a pattern they found:

I saw a pattern on the 100 square. My dad and I talked about this and he helped me write down my thoughts.

In each column, the 10s of the numbers change by 10 and the 1s stay the same.

E.g. The 8th column from the left side have these numbers in order from 8 to 98 from top to bottom. The tens increase with each number - 8, 18, 28, 38, 48, 58, 68, 78, 88, and 98.

When I pick a number up from the pile, I put it in the right place by looking at the 10s of the number and I know which row it goes in by counting down to the row of this digit plus 1. And I know which column it goes in, by using the 1s of the number, by counting from the left.

E.g. If I pick 78, it goes in the 8th column and the 8th row.

Then my Daddy told me this doesn't work for 30. He asked me to look at this and this is what I saw.

The 10th column is different because all these numbers have a zero on the end. The row that they go into is done by counting down from the top row.

E.g. With 50, it goes in the 10th column and the 5th row because it has 5 10s and a zero on the end.

This is faster because if I tried to find the number 1 first then I might have to check 100 numbers to find the right one.

When I use my method, I only do 2 checks for each number.

Very clearly explained, D. You've thought really carefully about how to find the right place for each number on the grid.

Do you agree with D that the quickest method is to pick up a number from the pile and work out where to place this number on the grid, or have you found another strategy that you think is quicker? We'd love to hear your thoughts - please email us if you'd like to share your ideas.