FUNDAMENTALS GCSEKS 3 Area Perimeter by Counting jamiedrfrostmaths

FUNDAMENTALS GCSE/KS 3 : : Area & Perimeter by Counting jamie@drfrostmaths. com @Dr. Frost. Maths Objectives: Be able to find the area and perimeter of 2 D shapes by counting squares. (This resource is intended for Foundation Tier students only) Last modified: 23 rd January 2020

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The need for area and perimeter Suppose you’re making a new rectangular enclosure for some sheep. You need to plant some grass seed to cover the space, but also need to put fencing around the enclosure to stop the sheep getting out! ! Area is the amount of space something takes up in 2 D. This will affect the amount of seed we need, as the more ‘space’, the more grass needed. ! Perimeter is the total length around the outside of the shape. In this example, it will be the total length of fencing that we need to buy.

Perimeter 1 cm 1 2 We saw earlier that the perimeter of a shape is the total length around the edge. 4 3 5 12 Count the parts of the edge one square at a time. You may want to leave a mark to remember what edges you have counted. 6 11 10 7 8 9 Perimeter = 12 cm 2 1 14 12 3 13 4 11 7 10 8 9 6 5 What about units? For any ‘measure’, e. g. length, volume, mass, height, we need to say what each ‘ 1’ is worth. For example, if someone says they are “ 175 tall”, then we’d need to know 175 of what! At the top of this slide, we’ve indicated that each square length is 1 cm. Perimeter = 14 cm

Spot The Error 1 2 3 4 5 6 16 7 15 8 14 13 12 11 10 9 To get the perimeter, I can just add the number of squares around the shape! I get 16 cm. Misguided Mike The problem is that we overcounted, because the corner squares don’t count towards the perimeter. You must count on the edges, and not the squares around the shape. 1 2 3 4 12 5 11 6 10 9 8 7

Test Your Understanding Determine the perimeter of these shapes on the centimetre grid. 12? cm 14? cm

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. (All questions ©Edexcel) 1 Solution: ? 16 cm

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. 2 Solution: ? 20 cm

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. 3 ? 16 cm Solution:

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. 4 ? 14 cm Solution:

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. 5 Solution: ? 14 cm

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. 6 ? 26 cm Solution:

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. 7 Solution: ? 14 cm

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. 8 ? 14 cm Solution:

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. 9 Solution: ? 10 cm

Exercise 1 (on printed worksheet) Find the perimeter of these shapes. All grids are grids of centimetre squares. 10 Solution: ? 14 cm

Finding the area by counting We said that area is the amount of space something takes up in 2 D. 1 2 3 4 5 6 7 8 Can you think of a good way we could give a good measure of how much space this rectangle takes up? We could count squares! The more squares, the more space it takes up. So the area of the rectangle would be 8. What about units? 1 cm Suppose that we say that each square is worth 1 cm (“a unit cm”)… …then we say that one square is “a cm squared”, written cm 2 1 cm

Finding the area by counting Each shape is drawn on a centimetre grid. Find the area of each. 1 2 3 4 5 6 7 8 9 3 10 11 12 7 4 1 2 5 6 7 cm ? 2 12? cm 2 1 4 2 3 5 7 1 Two triangles combined make up a square. 6 2 7 ? cm 2

Test Your Understanding Each shape is drawn on a centimetre grid. Find the area of each. 10 ? cm 2 8 cm ? 2

Exercise 2 (on printed worksheet) Find the area of these shapes. All grids are grids of centimetre squares. Ensure you put the correct unit! (All questions ©Edexcel) 1 Solution: ? 4 cm 2

Exercise 2 (on printed worksheet) Find the area of these shapes. All grids are grids of centimetre squares. Ensure you put the correct unit! 2 Solution: ? 8 cm 2

Exercise 2 (on printed worksheet) Find the area of these shapes. All grids are grids of centimetre squares. Ensure you put the correct unit! 3 ? Solution: 28 cm 2

Exercise 2 (on printed worksheet) Find the area of these shapes. All grids are grids of centimetre squares. Ensure you put the correct unit! 4 Solution: ? 6 cm 2

Exercise 2 (on printed worksheet) Find the area of these shapes. All grids are grids of centimetre squares. Ensure you put the correct unit! 5 Solution: ? 6 cm 2

Exercise 2 (on printed worksheet) Find the area of these shapes. All grids are grids of centimetre squares. Ensure you put the correct unit! 6 ? 14 cm 2 Solution:

Exercise 2 (on printed worksheet) Find the area of these shapes. All grids are grids of centimetre squares. Ensure you put the correct unit! 7 Solution: ? 22 cm 2

Exercise 2 (on printed worksheet) Find the area of these shapes. All grids are grids of centimetre squares. Ensure you put the correct unit! 8 Solution: ? 16 cm 2

Exercise 2 (on printed worksheet) Find the area of these shapes. All grids are grids of centimetre squares. Ensure you put the correct unit! 9 ? 15 cm 2 Solution:

Summary Perimeter is the total length around the outside of the shape. (You can think of it as the distance you’d have to walk around the shape) Area is the amount of space a shape takes up. (You can think of it as the amount of space you’d have to colour) ? Perimeter = 12 cm 2 Area = 5 cm? Perimeter = 14 cm? Area = 6 cm 2?