Discover Mathematics P5: Term 2, Unit 12, Lessons 1–3
GoalSay what a pie chart shows: the whole circle, the sectors, and how they are linked to a frequency table.
New words
pie chart · a circle cut into sectors to show how a whole is sharedsector · a slice of the circle between two radiifrequency table · a table that shows how many times each answer occurswhole · all the data together, shown by the full circle
Explanation
A pie chart shows how a whole is shared into parts. The whole circle stands for all of the data. Each sector stands for one group, and the bigger the sector, the bigger the share. The sectors fit together with no gaps and no overlaps, so they always add up to the whole circle. A pie chart is made from a frequency table. Twenty children were asked for their favourite fruit: mango 8, guava 6, banana 4 and orange 2. The total is 8 + 6 + 4 + 2 = 20. Each count is a fraction of the total: mango is 8/20 = 2/5 of the circle, guava is 6/20 = 3/10, banana is 4/20 = 1/5 and orange is 2/20 = 1/10. Check that the fractions add up to 1: 2/5 + 3/10 + 1/5 + 1/10 = 4/10 + 3/10 + 2/10 + 1/10 = 10/10 = 1.
Worked examples
In the fruit survey the mango sector is the biggest because mango has the biggest count (8 of 20). The orange sector is the smallest (2 of 20). The four sectors fill the whole circle.
Hana has 40 LE pocket money. She spends 20 LE on snacks, 10 LE on books and saves 10 LE. Snacks are 20/40 = 1/2 of the circle, books 10/40 = 1/4 and saving 10/40 = 1/4. The halves and quarters add up: 1/2 + 1/4 + 1/4 = 1.
A pie chart is made for 25 children: football 10, swimming 5, running 5, volleyball 5. The total is 25, so football is 10/25 = 2/5 and each of the others is 5/25 = 1/5. The sum is 2/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1.
Class activity
Class survey. Ask 20 children or family members to choose a favourite (a colour, a fruit, a sport). Record the answers in a frequency table with tally marks, find the total, and write each count as a fraction of the total in simplest form. Check that the fractions add up to 1.
Practice
1
In a survey of 25 children, 10 chose football. What fraction of the circle is the football sector?
10/25 = 2/5.
2
The swimming sector is half of the circle. 40 children were asked. How many chose swimming?
1/2 of 40 = 20 children.
3
Which sector is bigger: one that is 3/8 of the circle or one that is 1/4?
1/4 = 2/8, and 3/8 is more than 2/8, so 3/8 is bigger.
4
Marwan makes sectors of 1/2, 1/4 and 1/8 of a circle. Do they fill the whole circle? What is missing?
