1. London joint ATM and MA branch meeting Task design 20th May 2017 Mike Ollerton

2. A B H G F E D C

3. a c b

4. On squared paper draw a rectangle so both dimensions are greater than 2 and less than 15

5. Calculate the perimeter and the area of your rectangle so you have four pieces of information about your rectangle: length (l) width (w) Perimeter (P) Area (A)

7. Using a piece of square grid paper cut out all possible rectangles, with whole number dimensions, so each rectangle has the same area of 24cm2

8. Paste each of your rectangles onto another piece of squared grid paper, so the bottom left-hand corners sit on the origin What happens? What do you notice?

9. Turn the pairs of dimensions of your rectangles into coordinate pairs and plot these coordinates. What do you notice about the ‘shape’ this set of points make?

10. When are we ‘allowed’ to join all these points together to form a graph?

11. Suppose we allow the use of non-whole number dimensions (so the area is still 24cm2) For example if one dimension is 16cm, what will the other dimension be?

12. Try to find a few more pairs of coordinates which contain non-integer values.

13. Explore the dimensions of a rectangle (so the area is still 24cm2) whose dimensions are the same.

14. What kind of graph do we gain when we plot (l, w) For example, (1, 24), (2, 12) etc What is the equation of this graph?

15. What are the perimeters of the rectangles with a common area of 24
What are the perimeters of the rectangles with a common area of 24? What kind of graph do we gain when we plot (l, P) For example, (1, 50), (2, 28) etc What is the equation of this graph?

16. Repeat similarly to explore the dimensions and areas of rectangles with a common perimeter. For example if P = 20 we can generate graphs of (l, w) and (l, A)

17. What would the general equations be for each of the different graphs formed by beginning with: a) rectangles with constant Area, b) rectangles with constant Perimeter?

18. Explore rectangles which have perimeters (in cm1) equal to their areas (in cm2)...

19. And finally... Explore cuboids which have a surface area of exactly 100 cm2 and whose dimensions are whole numbers...