### Stairs

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

### Month Mania

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

### Taking a Die for a Walk

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

# Sorting Numbers

## Sorting Numbers

Numbers can be sorted in many different ways. We are just going to be using the numbers from 0 to 50.

In this box there is a set of numbers:

They are the odd numbers between 20 and 40.

In this box there is a set of numbers:

They are multiples of five.

Now you can make your own sets. Think of a good title for each of your sets.

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### Why do this problem?

This problem provides an opportunity for children to sort and categorise, both of which are important mathematical processes. This open activity challenges children to find their own categories and then name them, which might mean it is a good way to introduce specific vocabulary.

### Possible approach

You could begin by using the interactivity with the whole class, putting some numbers into the box yourself and asking the children to describe the set. Encourage learners to find different ways of naming a particular group of numbers or introduce them to new vocabulary as appropriate. Pairs of children could come to the board to create their own set in a similar way.

If you have access to a computer suite, children could work in pairs on a computer to create sets of numbers which they record elsewhere. Alternatively, they could easily work with pencil and paper. As they work, it is a great opportunity for you to listen to their justifications and how well they are able to use mathematical language.

As a plenary you could drag several numbers into the box and ask pupils to say which is the odd one out and why. Encourage creative responses to this - in fact any could be the odd one if we give an appropriate reason.

The interactivity could also be used as a starter activity on subsequent occasions. You could also use this interactivity where you drag numbers you "like" (i.e. are part of a set) to one side and numbers you "don't like" (i.e. are not in your set) to the other. The children then have to ask questions with yes/no answers to determine the name of your set.

### Key questions

What is the same about these two numbers?
Can we find others that could go with them?
What could we call this set?
Is there another way we could describe the set?

### Possible extension

The range of numbers could be extended to include, for example, up to 100.

### Possible support

Some children might want to use just the numbers up to 20, for example, to start with. You could get them started by suggesting categories to make. Digit cards would be useful for many children as well.