Children will need a large supply of shapes, cubes or other manipulatives for this problem. As they build each 'garden plan' they should explain to an adult or a partner the following;

• the number of tiles along the width of the lawn
• he number of tiles along the breadth of the lawn
• the number of tiles in total to make the lawn
• the number of tiles along the width of the border
• he number of tiles along the breadth of the border
• the number of tiles in total that will be needed to make the border around the lawn.

With some prompting about how the numbers increase, the children might identify the relationship between the two answers. They should be encouraged to sketch the various arrangements they make, these can be cut out and arranged by lawn size or border tiles used, to help them identify the relationship and extend the pattern. More able or older pupils might record there results in a table to help them identify the relationship and to reason their method of extending the pattern.

In words the pupils might be able to explain the formula;

"You need the length of the lawn plus two tiles across the top and bottom. You need the width of the lawn plus two tiles on each side".