3
Review: shapes, coordinates, volume and pie charts
Discover Mathematics P5: Term 2, Units 7–12, Review
GoalReview areas of shapes, the coordinate plane, volume of boxes and pie charts.
New words
ordered pair · two numbers (x, y) that give the position of a pointvolume · the space inside a solid, measured in cubic unitssector · a slice of a circle in a pie chart
Explanation
Here are the main tools of Term 2. Area of a rectangle = length × width. Area of a square = side × side. A point on the plane is written as an ordered pair (x, y): go x across, then y up. Volume of a box = length × width × height, in cubic units. The whole circle of a pie chart is 100% and 360°, so a sector of 1/4 is 25% and 90°. Example: a rectangle 10 cm long and 6 cm wide has area 10 × 6 = 60 square centimetres. A box 5 cm by 4 cm by 3 cm has volume 5 × 4 × 3 = 60 cubic centimetres.
| Idea | Rule |
|---|---|
| Rectangle area | length × width |
| Square area | side × side |
| Box volume | length × width × height |
| Pie chart | 100% = 360° |
Worked examples
The rectangle ABCD has corners (1, 1), (5, 1), (5, 3) and (1, 3). Its length is 5 − 1 = 4 and its width is 3 − 1 = 2, so its area is 4 × 2 = 8 square units.
A swimming-pool model is 8 cm long, 5 cm wide and 3 cm high. V = 8 × 5 × 3 = 120 cubic centimetres.
In a survey of 40 children, 25% walk to school. That is 1/4 of 40 = 10 children, and the sector has an angle of 90°.
Class activity
Review stations. Set up four tables: draw a rectangle and find its area; plot four points and join them; build a box from cubes and find its volume; make a pie chart of 12 answers. Spend three minutes at each table, then swap.
Practice
1
Find the area of a square with sides of 9 cm.
9 × 9 = 81 square centimetres.
2
The points (2, 5) and (7, 5) are on the same horizontal line. How far apart are they?
They have the same y-number, so the distance is 7 − 2 = 5 units.
3
A water tank is 6 m long, 4 m wide and 2 m high. Find its volume.
6 × 4 × 2 = 48 cubic metres.
4
A solid is a 4 × 3 × 2 block joined to a 2 × 3 × 2 block. Find its volume.
4 × 3 × 2 = 24 and 2 × 3 × 2 = 12, so 24 + 12 = 36 cubic units.
5
In a survey of 60 children one sector has an angle of 90°. How many children does it show?
90/360 = 1/4 and 1/4 of 60 = 15 children.