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

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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

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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)

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?

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