Review of Shapes OK, so we are going to try and name the following shapes: No calling out, I want you to write down the name of the shapes We will take these up when we are done

Handout 4.1.1 Sort the shapes into 2-D and 3-D (#1) Match the shape to its definition (#2) Now for #2 choose one of the shapes, sketch it and write two more properties that the shape has

Handout 4.1.2 Complete the table for the shapes A – E (#1) Write the formula that matches the area of the shape (#2) Using the cm2 paper (on the back of the first handout) try to draw the three shapes from #3

Calculate Areas of Rectangles,Triangles and Parallelograms We are Learning to…… Calculate Areas of Rectangles,Triangles and Parallelograms

What is the perimeter of this shape? To find the perimeter of a shape we add together the length of all the sides. What is the perimeter of this shape? Starting point 1 cm 3 Perimeter = 3 + 3 + 2 + 1 + 1 + 2 = 12 cm 2 3 Ask pupils if they know how many dimensions measurements of perimeter have. Establish that they only have one dimension, length, even though the measurement is used for two-dimensional shapes. Tell pupils that when finding the perimeter of a shape with many sides it is a good idea to mark on a starting point and then work from there adding up the lengths of all the sides. 1 1 2

Perimeter of a rectangle To calculate the perimeter of a rectangle we can use a formula. length, l width, w Using l for length and w for width, Explain the difference between the two forms of the formula. The first formula means double the length, double the width and add the two together. The second formula means add the length and the width and double the answer. Perimeter of a rectangle = l + w + l + w = 2l + 2w or = 2(l + w)

Perimeter Sometime we are not given the lengths of all the sides. We have to work them out from the information we are given. 9 cm 5 cm 12 cm 4 cm For example, what is the perimeter of this shape? The lengths of two of the sides are not given so we have to work them out before we can find the perimeter. Stress that to work out the perimeter we need to add together the lengths of every side. If we are not given some of the lengths, then we have to work them out before we can find the perimeter. a cm Let’s call the lengths a and b. b cm

Perimeter Sometime we are not given the lengths of all the sides. We have to work them out from the information we are given. 9 cm 12 – 5 a = = 7 cm 5 cm b = 9 – 4 = 5 cm 12 cm 4 cm Discuss how to work out the missing sides of this shape. The side marked a cm plus the 5 cm side must be equal to 12 cm, a is therefore 7 cm. The side marked b cm plus the 4 cm side must be equal to 9 cm, b is therefore 5 cm. a cm 7 cm P = 9 + 5 + 4 + 7 + 5 + 12 = 42 cm 5 cm b cm

Calculate the lengths of the missing sides to find the perimeter. 5 cm p = 2 cm p 2 cm q = r = 1.5 cm q r s = 6 cm t = 2 cm s 6 cm u = 10 cm Discuss how to find each missing length. 4 cm 4 cm P = 5 + 2 + 1.5 + 6 + 4 + 2 + 10 + 2 + 4 + 6 + 1.5 + 2 2 cm t 2 cm u = 46 cm

What is the perimeter of this shape? Remember, the dashes indicate the sides that are the same length. 5 cm 4 cm P = 5 + 4 + 4 + 5 + 4 + 4 = 26 cm

Area The area of a shape is a measure of how much surface the shape takes up. For example, which of these rugs covers a larger surface? Rug B Rug A Rug C Discuss how we can compare the area of the rugs by counting the squares that make up each pattern. Conclude that Rug B covers the largest surface.

Area of a rectangle Area is measured in square units. For example, we can use mm2, cm2, m2 or km2. The 2 tells us that there are two dimensions, length and width. We can find the area of a rectangle by multiplying the length and the width of the rectangle together. length, l width, w This formula should be revision from key stage 2 work. Area of a rectangle = length × width = lw

Area of a rectangle What is the area of this rectangle? 4 cm 8 cm The length and the width of the rectangle can be modified to make the arithmetic more challenging. Different units could also be used to stress that units must be the same before they are substituted into a formula. Area of a rectangle = lw = 8 cm × 4 cm = 32 cm2

Area of a triangle What proportion of this rectangle has been shaded? 4 cm 8 cm Drawing a line here might help. A line is drawn on the diagram to split the shape into two rectangles each with one half shaded. Pupils should conclude from this that one half of the whole rectangle is shaded. Establish that the area of the whole rectangle is equal to the base of the shaded triangle times the height of the shaded triangle. Conclude that the area of the shaded triangle is equal to half the base times the height. What is the area of this triangle? 1 2 Area of the triangle = × 8 × 4 = 4 × 4 = 16 cm2

Area of a triangle The area of any triangle can be found using the formula: Area of a triangle = × base × perpendicular height 1 2 base perpendicular height Ask pupils to learn this formula. Or using letter symbols, Area of a triangle = bh 1 2

Area of a triangle What is the area of this triangle? 6 cm 7 cm Area of a triangle = bh 1 2 Tell pupils that to work out the area of the triangle they must start by writing the formula. They can then substitute the correct values into the formula provided that they are in the same units. Stress that it is important to always write down the correct units at the end of the calculation. The numbers and units in the example may be modified to make the problem more challenging. = 1 2 × 7 × 6 = 21 cm2

Area of a parallelogram The area of any parallelogram can be found using the formula: Area of a parallelogram = base × perpendicular height base perpendicular height Ask pupils to learn this formula. Or using letter symbols, Area of a parallelogram = bh

Area of a parallelogram What is the area of this parallelogram? We can ignore this length 8 cm 7 cm 12 cm Area of a parallelogram = bh Tell pupils that to work out the area of the parallelogram they must start by writing the formula. They can then substitute the correct values into the formula provided that they are in the same units. Point out that the length of the diagonal can be ignored. Stress that it is important to always write down the correct units at the end of the calculation. The numbers and units in the example may be modified to make the problem more challenging. = 7 × 12 = 84 cm2

Area formulae of 2-D shapes You should know the following formulae: b h Area of a triangle = bh 1 2 b h Area of a parallelogram = bh l w Use this slide to summarize or review key formulae. Area of a rectangle = lw

Homework Complete the two handouts from class

Homework Draw a sketch of the following shapes and write a sentence explaining what they are… Parallelogram Trapezoid Equilateral triangle Rhombus Rectangular prism Triangular prism