### Homes

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

### 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.

### Train Carriages

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

# Unit Differences

## Unit Differences

This challenge is about finding the difference between numbers which have the same tens digit.

Here are two examples where I’ve decided to use numbers which have two tens:

The number above is always the difference between the two beneath it.

Can you find different pairs of numbers with a difference of 1 or 2 or 3 or 4 ... and so on?

Can you find more than one way of doing it?

#### Why do this activity?

This activity provides a context for practising finding a small difference between two two-digit numbers. It encourages children to record their results, notice patterns and make predictions.

#### Possible approach

The children may need reminding about what it means to find the difference between numbers, and some strategies for doing this.

A possible starting point for the activity is using the same idea but with single digit numbers, perhaps starting with 7 and 9 on the bottom first. This is an opportunity to model how to find the difference and also how to write this difference into the circle on top.

As a class, you could explore other possibilities for having a difference of 2 starting with just single-digit numbers (1 and 3, 2 and 4 …) and as you collect the results in, they could be organised to enable the children to notice the patterns.

As children attempt the main task, they may explore different ways of having a difference of 5 (for example) within the twenties (21 and 26, 22 and 27 …) or across different tens (21 and 26, 31 and 36, 43 and 48). Encourage the children to record their work and spot patterns as in the introduction.  This sheet of blank pyramids may be useful.

Some children may move onto the extension task (below).

#### Key questions

What is the difference between the numbers?
Do any other pairs of numbers have the same difference?
Can you spot a pattern?

#### Possible extensions

Extension 1: This time there are three numbers at the bottom of the pyramid (all with the same number of tens) but otherwise the pyramid is constructed in exactly the same way.
3 is the difference between 24 and 21.
5 is the difference between 21 and 26.
2 is the difference between 3 and 5.

Children could make some pyramids of their own.  Here is a sheet of blank 'three tiered' pyramids.

Extension 2:  Can learners find different pyramids with the same number at the top?

#### Possible support

A 100 square or number line/track.
Blank pyramids.