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# That Number Square!

## That Number Square!

When you arrive in the classroom on Monday morning you discover all the numbers have fallen off the class number square and they are in a heap on the floor. All that is left on the wall is a blank grid!

There's five minutes to go before the lesson starts and you need the number square.

Can you find a quick way of putting the numbers back in their right places on the grid?

Where will you start?

Before you start think - does your class number square start with $0$ or $1$? Or a different number?

Some of your friends may want to have a go too.

What different ideas are there about how to put the number tiles back as quickly as possible?

Let us know what you think is a 'smart' way of putting the number square back together.

How quickly can you achieve this using your 'smart' strategy?

### Why do this problem?

This activity gives children the opportunity to use, reinforce and extend their knowledge of place value, multiples and times tables.  It enables them to use their understanding of pattern and possibly their visualising skills. This activity also offers an opportunity to discuss the strategies the children come up with - what is a good strategy for putting the number tiles back in the correct places as quickly as possible?  What makes one strategy 'smarter' than another?

### Possible approach

Choose the 0-99 set or the 1 -100 set of number tiles provided .docpdf  . Alternatively, you may have your own sets of blocks, tiles or cards that the children could use.  Let the children try getting started with placing the number tiles on the number grid. Watch how they set about it.

After a little while, discuss different approaches together such as:

Did you try and place the first tile in the random pile on the floor on the number grid first? If so, how did you decide where to put it?
Or did you sift through the number tiles to find one that you know exactly where to place on the number grid?
Which one did you choose?
What was significant about that one?
Which do you think are key number tiles to get in place on the number grid that help you place the rest?

See if the children can devise some good strategies between them and then encourage them to experiment with different ones to see which ones help them put the number tiles back as fast as possible. You may find that different children find different strategies useful.  Encourage them to articulate how they know where to put a particular number tile. Encourage explanations that focus on pattern, place value and multiples.

### Key questions

Where will you put that tile?
How do you know that it goes there?
Are you sure it goes there?
(Not to be asked only when a slip-up has occurred as then children often learn that such questions indicate that something is wrong!  Asking it when they are right sometimes too helps for better communication and exploration of reasoning.)

### Possible extension

What happens if it is a 50 - 149 number square, for example?
Can you use the same strategies?
What happens if the number square is not $10$ x$10$ but only $6$ squares wide, for example?
How do you know where to place the number tiles now?
Which widths of number square are harder/easier than the $10$ x $10$?

The children may like to try a related problem: Hundred Square.

### For the highest-attaining

Have a go at Exploring Squares and Others.

### Possible support

You may like to give some children a number grid where some numbers remain.  Some children could work with the number grid up to $50$ or up to $30$.  Some children will benefit from having an adult alongside to help them talk about where they want to place particular number tiles.