187 Unit 5. Perimeter and area. To calculate the perimeter of this rectangle… Perimeter is the distance all the way around the outside of a 2-D shape. Activity 1. Perimeter of 2-D shapes. 1. Chumani was asked to calculate the perimeter of the soccer field to make sure that the markings were correct. This is how he did it. Calculate the perimeter of the soccer field. 2. Calculate the perimeter of the rectangle.

start 3,5 cm

3,5 cm

2,5 cm 2,5 cm P = ℓ + ℓ + ℓ + ℓ = 3,5 cm + 2,5 cm +3,5 cm + 2,5 cm = 12 cm

start

2,3

cm 16,4 cm 2,3 cm

16,4 cm

188 3. Write down the measurement of each side in mm. Add up the measurements to calculate the perimeter of the triangle. Example:

4. 5. Calculate the perimeter of each square. 6. You are given the perimeter of 6 squares. Calculate the length of a single side in each square. a. 68 m d. 36 mm b. 8,8 cm e. 28,6 cm c.24,5 cm f. 40 km

Remember that these lines show that the sides are of = length.

18,2 cm 76,7 cm

189 7. Measure the length of the sides and diagonal of these squares and record your answers. a. b. c. Activity 2. Area of 2-D shapes.

1. Calculate the area of each 2-D shape by counting the number of squares.

What would we do if there are half blocks? 2. Find the area of each shape.

We can calculate the area of this rectangle by counting the number of squares.

Area is the size of the surface of a shape and is measured in squares. The area of this rectangle is 8 squares.

190 How do I calculate the area of this shape?

3. Count the squares to calculate the area of the shape below. Unit 6. Perimeter, Area, Volume and the History of Measurement. Activity 1. Calculate the area of squares and rectangles.

Count all the squares that are half or more as full squares. Don’t count squares that are less than half. I have put a on each square that I have counted I get an area of 8 squares.

Brenda’s method.

I counted all the squares and I got a total of 36 squares.

Siya’s method.

I multiplied the length of the rectangle (9 squares) by the breadth (4 squares) and got 36 squares. Length x breadth = 36 squares.

What method would you use?

191 1. Use your favourite method to calculate the area of these 2-D shapes.

Activity 2. Perimeter and Area. Each of these rectangles below has a perimeter of 16 cm but they have different area. 1.a. Draw 4 different rectangles each with a perimeter of 20 cm. Write the area of each rectangle. b. Draw 4 different rectangles with a perimeter of 18 cm. Write the area of each rectangle. Activity 3. Doubling and halving 2-D shapes. Doubling a 2-D shape means making the area twice as big…

area = 12 squares area = 7 squares area = 15 squares

Challenge! Draw 1 rectangle with a perimeter of 22 cm and an area of 30 cm.

3 cm

3 cm

2 cm

2 cm

area = 6 squares.

Double the length of 1 pair of opposite sides.

6 cm

6 cm

2 cm 2

cm

192 The length of the rectangle has doubled. What has happened to the area of the rectangle? 1. Double the area of each of these rectangles and squares. 2. Draw the same 2-D shapes as above. Halve the length of 1 pair of opposite sides. What do you notice about the area of the shape? Activity 4. Volume. Volume is the amount of space an object occupies. It is measured in cubes. 1. Count cubes.

Example:

Homework.

Make 2 cubes from the net. Bring them to school tomorrow.

• Trace this net onto paper.

• Write your name on 1 of the outward faces.

• Cut, fold and paste the net to form a cube.

193

a. Estimate how many containers will fit into the container on the teacher’s desk. b. Take turns to pack the cubes into a shoebox. Keep count as you pack the cubes. c. The volume of the shoebox is ____ cubes. d. Repeat this activity using other containers, for example ice-cream boxes. 2.a. Take turns to make stacks with your cube:

• Estimate the number of cubes in the stack. • Count the cubes in each stack.

3. Write the volume of each stack.

• The first layer has 10 cubes. • The second layer has 6 cubes. • The third layer has 6 cubes. • The fourth layer has 2 cubes.

I counted the cubes in layers. The volume of the stack is 24 cubes.

194 4. How many matchboxes in each stack? Activity 5. The History of Measurement.

The Egyptians were skilled builders. They did not have measuring instruments like rulers or builders’ tapes. The Egyptians used body parts as units of measurement. These measurements were copied onto wood, metal or stone so that everyone used the same measure. These are some of the non-standard units of measurement that people used long ago…

195 1. Use your handspan as the unit of measurement. Follow these steps to work out how many times your handspan fits into your height. Step 1: Make your handspan: take a strip of paper and stretch your hand along it. Make a mark where your thumb starts and your little finger ends. Step 2: Cut the paper on the mark on each end. You now have a strip of paper the same length as your handspan. Measure your handspan. Step 3: Measure your height against a wall. See how many times your handspan fits into your height. Calculate your height. Assessment. Properties of 3-D objects. 1. Copy and complete the table. 3-D object

Name of 3-D object.

Number of faces.

Shape of each face.

Number of edges.

Number of vertices.

Perimeter and Area. 2. Find the perimeter and area of each shape.

196 3. Find the area of each shape. Volume. 4. Write the volume of each stack of cubes.

5. Name the non-standard units of measurement.

Checked GM 2016