Perimeter and Area
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Perimeter and AreaYr 7
QCA, HBS, Ri
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Pin-board shapesWrite down the following information for the shape:
1.Count the dots around the perimeter (D.P.)
Draw shapes on the pin-board by joining dots.
2. Count the dots inside the shape (D.I.)3. Calculate the area of the shape (A.)
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Pin-board shapes
Shape
A D.I. D.P. Comments
No.1 1 0 4
No.2 5 1 10
No.3 5 2 8
... ... ... ... ...
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At home...Conduct your investigation and write
down any patterns relating the three variables that you find.
Find a formula for the area of a shape using the dots in the perimeter and number of dots in the middle.
Give reasons for why your formula works.
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Pick’s Theorem
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Does the number of dots in the perimeter give us the length of the perimeter of the shape?
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Who was Pick?
Georg Alexander Pick
August 10, 1859 – July 26, 1942
Born in Austria, died in Bohemia, now Czech Republic
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Teac
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nlyPick’s Theorem...
… is not a relationship about perimeter and area!
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Pick’s Theorem
What did you discover?
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What’s the longest perimeter you can
make?
Perimeter and area
Is there always a relationship
between perimeter and
area?
Draw a shape with area 24, what’s the
perimeter of your shape?
What’s the smallest area
you can make?
Draw a shape with perimeter 24, what’s the area of your
shape?
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Teac
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nlyActivity
Ask pupils to investigate rectangles with the perimeter and area in the previous slide using their maths books (squared paper)
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Perimeter, area, shapes and
designing clothes
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...
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Which shapes match?
?
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Make your own match
In pairs, cut the sleeve of the old t-shirt.
In the body of the t-shirt draw a shape that you can ‘sew’ the sleeve into – you cannot chose a circle.
What is your guess of how it will look like?
If you have time repeat with the other sleeve, with a different shape
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Plan your design, draw the shape.
Cut out the shape to make a hole.
Create your design by stapling the sleeve into your hole.
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Perimeter, area, shapes and designing
clothesCan you explain
your design process?
How did you know you would be able to sew the sleeve
into the hole?
What shape was your
hole?
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Teac
her o
nly