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### Number and algebra

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# Ladybird Box

## Ladybird Box

Some toy ladybirds are kept in this box which has 9 little square compartments.

Printable NRICH Roadshow Resource.
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Age 5 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Can you place six ladybirds into the box so that there are just two ladybirds in every column and every row?

You could try this interactivity.

Printable NRICH Roadshow Resource.

This problem requires both spatial and number understanding. It fits well with work on pairs and counting by twos. To understand the problem, the children will need to be comfortable with the idea that the $3$ by $3$ grid represents a top view of the nine-hole box. They will also need to be familiar with the meaning of rows and columns. The problem provides a good opportunity for developing positional language and utilising ordinal numbers. For example: "I put a ladybird in the middle of the second row" or "Go across three then down one". It is also a good context in which to discuss what makes one solution different from another.

You could place some ladybirds in the box in some way using the interactivity and invite children to describe the positions of the ladybirds. This will give an opportunity for the class to come to an agreement about good ways to describe each 'cell' and to check the meaning of words such as 'row' and 'column'. You could then introduce the problem and encourage the children to work on it
individually or in pairs. They could use a prepared $3$ by $3$ grid and six counters or the grid and ladybirds from this sheet.

When someone finds a solution quietly ask him/her to explain why it is correct, then have him/her draw the solution onto a grid. Invite him/her to find another way to do it. This could lead to a plenary discussion comparing the different solutions. You can encourage learners to decide what makes a solution different from another one - how about rotating the grid and mirror reversals of
solutions?

To extend the opportunity for developing positional language, the $3$ by $3$ grid could be marked out with chalk on the floor or playground, and children used as the ladybirds. Children could take turns in giving instructions for the movement of the ladybirds until a solution has been formed.

How many counters/ladybirds have you in this row? In this column?

Which row and which column can still have a second counter/ladybird?

Children could be encouraged to find all possible solutions and explain why they are sure they have found them all.

You could encourage children to start by placing just four counters then seeing which row and which column have less than two counters in them.