### A City of Towers

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

### The Tall Tower

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

### Lots of Biscuits!

Help share out the biscuits the children have made.

# What Could It Be?

## What Could It Be?

In the calculation below, the box represents a missing digit:

What could go in the box? What would the total be each time?

Which is the highest/lowest total?

Which totals are odd/even?

#### Why do this activity?

This activity provides an opportunity for children to practise their addition skills through a meaningful open-ended task. It encourages children to record their results, notice patterns and make predictions.

#### Possible approach

A possible starting point is to begin with a question such as 3+□= and ask the class to come up with what it could be. The box represents one missing digit. The children should be encouraged to come up with as many answers as possible. How will you know when you’ve found them all? As the possibilities are collated, these could be organised systematically so that the children notice the pattern:
3 + 0 = 3
3 + 1 = 4
3 + 2 = 5
3 + 3 = 6 and so on …
It is possible to draw out which totals are odd/even, which is the highest/lowest total, which totals are single digit numbers and so on.

Children can then be set a similar challenge working within 20 or could move on to the original problem. Some children may start with or move onto the extension tasks (below).

#### Key questions

What totals were possible?
Which is the highest/lowest total?
Which totals are odd/even? Could you have predicted this?
Are there different ways of getting to the same total?

#### Possible extensions

Extension 1:
13 + 1□ =     The box represents a missing digit.
What could go in the box? What would the total be each time?
Make predictions and then check, which is the highest/lowest total possible? Which totals are odd/even?

Extension 2:
1□ + 1□ =     This time there are two boxes and each represents a missing digit.
What could go in the box? What if the missing digits are the same, what if they are different? What would the total be each time? Which is the highest/lowest total?
Can you find two different ways of getting the same total but using different digits?

Extension 3:
Make up your own similar problem.

#### Possible support

Whatever resources are being used to support the development of addition skills are appropriate to use for this challenge. For example: a 100 square, a number line or track, a bead string, Diennes (base 10) apparatus ….