London joint ATM and MA
branch meeting
Task design
20th May 2017
Mike Ollerton
A
B
C
D
E
F
G
H
a
c
b
On squared paper draw a rectangle
so both dimensions
are greater than 2 and less than 15
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)
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
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?
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?
When are we ‘allowed’ to join all
these points together to form a
graph?
Suppose we allow the use of nonwhole number dimensions (so the
area is still 24cm2)
For example if one dimension is
16cm, what will the other
dimension be?
Try to find a few more pairs of
coordinates which contain noninteger values.
Explore the dimensions of a
rectangle (so the area is still 24cm2)
whose dimensions are the same.
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?
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?
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)
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?
Explore rectangles which have
perimeters (in cm1) equal to their
areas (in cm2)...
And finally...
Explore cuboids which have a
surface area of exactly 100 cm2 and
whose dimensions are whole
numbers...