Understanding and Connecting
Area and Perimeter - Designing Gardens
This progression continuum outlines a sample learning trajectory
f
The learner
Identifies base units for length [metre], and area [square metre].
g
The learner
Explores how to read a simple scale and use conventional measuring instruments.
h
The learner
Explores, estimates and then measures the perimeter and area of regular 2-D shapes.
i
The learner
Explores, estimates and measures the perimeter and area of regular and irregular 2-D shapes.
J
The learner
Uses knowledge of existing attributes to find the measure of unknown attributes.
k
The learner
Determines the relevant features and
finds the perimeter and area of circles
and composite
shapes.
Thinking about Area and Perimeter
Max has been drawing rectangles in his mathematics copy. This is what he has done so far.
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Looking at these rectangles, Max starts to think.
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‘I can see that the area is always a smaller number than the perimeter number in these rectangles’ he thinks ‘And I notice that as the area value increases then the perimeter number increases as well. I bet this is true for every rectangle.’
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Is Max correct?
Can you investigate with lots of rectangles and see if you can say if Max’s idea is:
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Always
Sometimes or
Never true?
Can you convince somebody who is not sure?
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Have you found any rectangles where the area is the same, but perimeters are different?
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How about any rectangles where perimeters are the same, but areas are different?
Designing Gardens
In the grid each cm represents a metre (that is the scale is 1cm: Im). So each cm represents a m.
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Some designers at ‘Lovely Gardens” are using the grid to make drawings of gardens that have an area of 12m (but, of course, 12cm in their drawings). How many different garden designs can you make that have an area of 12cm ?
Hint: the gardens do not have to be rectangular.
Look at all the designs. If each garden has to have a fence around its perimeter, would the same amount of fencing be needed for each of them?
One of the designers, Poppy, likes to design gardens that have at least one curved wall.
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What might her designs look like, do you think?
Suppose, later in the day, the manager issues an order that the gardens have to be shrunk in area by a half. Draw the new designs. Remember that the shapes have to remain the same. So if you shrink a rectangle in area by a half, the ‘new’ shape should be a rectangle with an area of 6 cm . Does the fencing for each also reduce by half?
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