Perimeter and AreaYr 7
QCA, HBS, Ri
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.)
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
... ... ... ... ...
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.
Pick’s Theorem
Does the number of dots in the perimeter give us the length of the perimeter of the shape?
Who was Pick?
Georg Alexander Pick
August 10, 1859 – July 26, 1942
Born in Austria, died in Bohemia, now Czech Republic
Teac
her o
nlyPick’s Theorem...
… is not a relationship about perimeter and area!
Pick’s Theorem
What did you discover?
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?
Teac
her o
nlyActivity
Ask pupils to investigate rectangles with the perimeter and area in the previous slide using their maths books (squared paper)
Perimeter, area, shapes and
designing clothes
...
Which shapes match?
?
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
Plan your design, draw the shape.
Cut out the shape to make a hole.
Create your design by stapling the sleeve into your hole.
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?
Teac
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