Worksheet 1 Area as a function

1. Use the box to write down the height and length of all the rectangles that have an area of 12 units.
2. Draw the rectangles on a grid with horizontal and vertical axes with one corner always starting at (0,0). Mark the corner of each rectangle which is opposite the (0,0) corner. Using a coloured pen join up the marked corners to form a smooth curve.

Think about these questions:

• What does the coloured line that you have just drawn actually mean?
• Was the apprentice correct in thinking that there were only 6 possible rectangles of area 12? Can you think of any more pairs of numbers that will also give an area of 12?
• Where do you think that the coloured line starts and finishes?

• Where will the coloured line for area 24 go? When you feel sure about it draw it on the grid.
• Think carefully about this to decide what the coloured line means. What have you noticed or realised?

How are you going to put your ideas into words?