Mathematics notes, unit 8
Data Handling and Likelihood
Textbook Mathematics Year 6 SK (DLP, Semakan 2017), pages 207–224
What this chapter covers
- You can complete a pie chart and read data from it when the angles are 45°, 90° and 180° (8.1.1)
- You can link each angle to a fraction of the whole circle and to a number of items (8.1.1)
- You can write facts about a pie chart: largest part, most and least data, differences and fractions (8.1.1)
- You can describe how likely an event is as impossible, less likely, equally likely, more likely or certain (8.2.1)
- You can give a sensible reason for the likelihood of an event (8.2.2)
- You can solve problems about pie charts and likelihood (8.3.1)
8.1Pie charts
A pie chart shows data as slices of a circle. The whole circle stands for all the data, and each slice shows one part of it. In Year 6 we use pie charts where the slices are 180°, 90° or 45°.
A full circle is 360°. 180° is 1/2 of the circle, 90° is 1/4 and 45° is 1/8. The bigger the angle, the more data in that slice.
| Angle | Fraction of the circle | How to find it |
|---|---|---|
| 180° | 1/2 | 360° ÷ 2 |
| 90° | 1/4 | 180° ÷ 2 |
| 45° | 1/8 | 90° ÷ 2 |
Reading a pie chart
Insect stamps take half the circle, so 20 stamps are half of all the stamps. The whole collection is 40 stamps. Bird stamps are a quarter of the circle: 40 ÷ 4 = 10. Flower stamps are 45°, which is half of 90°, so there are 5 flower stamps. Plant stamps are also 45°, so they are also 5.
Worked example: from an angle to a number
Step 1. Find one slice you know both ways. Here 180° = 20 stamps.Step 2. Halve both together: 90° = 10 stamps and 45° = 5 stamps.
Step 3. Add the parts to check the total: 20 + 10 + 5 + 5 = 40 stamps.
The slice with the largest angle stands for the most data. Equal numbers have equal angles.
Completing a pie chart from a table
Sixteen marbles are put in a pie chart. The marbles are red (8), green (4), blue (2) and yellow (2).
Worked example: find the angles
Step 1. Write each count as a fraction of the total 16: red 8/16 = 1/2, green 4/16 = 1/4, blue 2/16 = 1/8, yellow 2/16 = 1/8.Step 2. Change the fractions to angles: 1/2 = 180°, 1/4 = 90°, 1/8 = 45°.
Step 3. Check: 180° + 90° + 45° + 45° = 360°.
The angle shows the share of the circle, not the number. 90° does not mean 90 items. Two pie charts can have the same angles but different totals.
A pie chart of the pupils in a class has 90° for cats and 45° for rabbits. 6 pupils chose rabbits. How many chose cats?
Show answerHide answer
45° = 6 pupils, so 90° = 2 × 6 = 12 pupils.
8.2Likelihood
Likelihood tells us how possible it is that an event happens. There are five words, from the least to the most possible.
| Word | Meaning | Example |
|---|---|---|
| impossible | can never happen | A sea turtle climbs a tree. |
| less likely | may happen, but not often | Picking a yellow ball from a bag with 1 yellow and 5 blue. |
| equally likely | same chance either way | A tossed coin shows a head. |
| more likely | will probably happen | Picking a blue ball from a bag with 1 yellow and 5 blue. |
| certain | always happens | The day after Monday is Tuesday. |
An event is likely to occur if it will probably happen and unlikely to occur if it will probably not. Always give a reason when you state a likelihood.
Counting to decide
Worked example
A ball is picked without looking.Step 1. Count each colour: 7 white, 3 orange.
Step 2. Compare: 7 is more than 3.
Step 3. Picking a white ball is more likely, because there are more white balls than orange balls. Picking an orange ball is less likely.
To make two events equally likely, make the numbers equal. For 7 white and 3 orange, take out 2 white and add 2 orange: 5 white and 5 orange.
A prediction is not a promise. "More likely" does not mean "certain". An orange ball can still be picked.
A bag has 1 red pen and 7 black pens. State the likelihood of picking a red pen, with a reason.
Show answerHide answer
Less likely, because there is only 1 red pen but 7 black pens.
8.3Solving problems
Worked example: mass from angles
The mass of rambutan sold is 30 kg and its angle is 90°. Langsat and mangosteen have equal masses and each has 45°. Find all the masses.Step 1. 45° is half of 90°, so langsat and mangosteen are each half of 30 kg = 15 kg.
Step 2. The rest of the circle is 360° − 90° − 45° − 45° = 180°, which is twice 90°, so mango is 2 × 30 kg = 60 kg.
Step 3. Check: 30 + 15 + 15 + 60 = 120 kg.
Plan: (1) find a slice with both an angle and a number; (2) find what 45° is worth; (3) multiply or add to answer; (4) check that the angles total 360°.
Player A won 4 of 5 matches against player B. What is the likelihood that B wins the sixth match? Give a reason.
Show answerHide answer
Less likely, because B won only 1 of the 5 matches. It is not impossible, because B can still win.
Ideas follow the Mathematics Year 6 (DLP) textbook, Unit 8, pp. 207-223. Figures redrawn.