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Perimeter and Area. Yr 7. QCA, HBS, Ri. 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.).
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Perimeter and Area Yr 7 QCA, HBS, Ri
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.)
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.
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
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?
Activity Ask pupils to investigate rectangles with the perimeter and area in the previous slide using their maths books (squared paper) Teacher only
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 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?