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;
  <br />

  <div style="margin-left: 40px;">
    the number of tiles along the width of the lawn
  </div>

  <div style="margin-left: 40px;">
    the number of tiles along the breadth of the lawn
  </div>

  <div style="margin-left: 40px;">
    the number of tiles in total to make the lawn
  </div>

  <div style="margin-left: 40px;">
    the number of tiles along the width of the border
  </div>

  <div style="margin-left: 40px;">
    the number of tiles along the breadth of the border
  </div>

  <div style="margin-left: 40px;">
    the number of tiles in total that will be needed to make the
    border around the lawn.
  </div>

  <div>
    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.
  </div><br />

  <div>
    In words the pupils might be able to explain the formula;
  </div><br />

  <div>
    2(L+2) + 2W = B
  </div><br />
  "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".<br />