# Perimeter and Area Yr 7 QCA, HBS, Ri

## Presentation on theme: "Perimeter and Area Yr 7 QCA, HBS, Ri"— Presentation transcript:

Perimeter and Area Yr 7 QCA, HBS, Ri
The Royal Institution of Great Britain

Pin-board shapes Draw shapes on the pin-board by joining dots.
Write down the following information for the shape: Count the dots around the perimeter (D.P.) Count the dots inside the shape (D.I.) Calculate the area of the shape (A.) The Royal Institution of Great Britain

Pin-board shapes Shape A D.I. D.P. Comments No.1 1 4 No.2 5 10 No.3 2
4 No.2 5 10 No.3 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. The Royal Institution of Great Britain

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

Teacher only Pick’s Theorem...
… is not a relationship about perimeter and area! Teacher only

Pick’s Theorem What did you discover?

Perimeter and area Is there always a relationship between perimeter and area? Draw a shape with perimeter 24, what’s the area of your shape? What’s the smallest area you can make? Draw a shape with area 24, what’s the perimeter of your shape? What’s the longest perimeter you can make? The Royal Institution of Great Britain

Activity Ask pupils to investigate rectangles with the perimeter and area in the previous slide using their maths books (squared paper) Teacher only

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 use the sleeve from their old t-shirt. They will detach the sleeve. In the body of the t-shirt they will draw a suitable shape to match with the sleeve -- any shape but a circle. Pupils work on the activity, in groups. Pupils are encouraged to conjecture what the sleeve will look like, how it will drape as a result of their choice of shape The Royal Institution of Great Britain

Plan your design, draw the shape. Cut out the shape to make a hole
Plan your design, draw the shape. Cut out the shape to make a hole. Create your design by stapling the sleeve into your hole. use the sleeve from their old t-shirt. They will detach the sleeve. In the body of the t-shirt they will draw a suitable shape to match with the sleeve -- any shape but a circle. Pupils work on the activity, in groups. Pupils are encouraged to conjecture what the sleeve will look like, how it will drape as a result of their choice of shape The Royal Institution of Great Britain

Perimeter, area, shapes and designing clothes
Can 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? The Royal Institution of Great Britain

Teacher only