eduKatePunggol · Secondary 1 Mathematics
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Comparing Pie Charts: Check the Totals. Choose the reading route closest to your question.
Route 1 · Chapters 1–2
Route 2 · Chapters 3–4
Route 3 · Chapters 5–6
Route 4 · Chapters 7–8
Full chapter index · Independent practice · Secondary 1 Mathematics support
If your child says the larger pie-chart sector must represent more people, check the total behind each chart. A quarter of a group of forty is ten people. A fifth of a group of one hundred is twenty. The smaller share can represent the larger count when the groups have different sizes.
Secondary 1 Mathematics tuition in Punggol can help students separate fraction, angle and frequency. A Punggol Secondary 1 Maths tutor should ask whether the task compares proportions or actual numbers. A 90° sector is a larger share than a 72° sector, but those angles alone do not compare counts across different totals.
This guide uses invented survey groups and ordinary pie charts, not area-scaled population diagrams. It explains how to recover frequencies, compare like quantities and identify missing information. Small-group 3-pax support should make the total visible before students draw conclusions from the size of a slice.
Full chapter index
Name the whole and the share · Chapters 1–2
Recover the frequency · Chapters 3–4
Check the comparison · Chapters 5–6
Practise and continue · Chapters 7–8
An ordinary pie chart divides one whole into category shares. A sector angle of ninety degrees represents 90/360 = 1/4 of that chart’s total. Its meaning depends on both the category and the whole being described. The angle gives a proportion rather than a person count by itself.
Before reading a chart, identify the group, the total and the category labels. If two charts refer to different populations, their circles each still represent their own whole. Equal-looking circles do not imply equal population sizes unless the diagram explicitly defines such a relationship.
Chapter 2 of 8 · Name the whole and the share
2. How does the smaller sector contain more people?
In Group A, total forty and share 1/4 give frequency 40 × 1/4 = 10. In Group B, total one hundred and share 1/5 give frequency 100 × 1/5 = 20. The corresponding angles are ninety and seventy-two degrees. Group B has a smaller proportion but twice the count.
Neither conclusion contradicts the other. ‘A has the larger share’ compares fractions. ‘B has more people in the category’ compares frequencies. A complete answer should name the requested measure. Replacing one statement with the other silently changes what is being compared.
| Invented group | Total | Sector share | Angle | Category count |
|---|---|---|---|---|
| A | 40 | 1/4 | 90° | 10 |
| B | 100 | 1/5 | 72° | 20 |
Chapter 3 of 8 · Recover the frequency
3. How are angle, percentage and frequency connected?
For an ordinary pie chart, share = angle/360°, percentage = share × 100%, and frequency = share × total. Thus a 120° sector in a group of ninety represents one third, approximately 33⅓%, and exactly thirty observations under the given exact model.
Keep the total attached to the frequency calculation. The same 120° sector would represent sixty observations in a group of 180. The fraction stays one third while the count doubles. If an angle has been rounded for display, a count recovered from it may only be approximate rather than an exact integer.
Multiply each percentage by its own total. Twenty per cent of sixty is twelve, while fifteen per cent of one hundred is fifteen. The second category has more observations despite its smaller percentage. Comparing twenty and fifteen alone answers only the proportion question.
If totals are missing, do not invent them from the radius of an ordinary pie chart. You can compare the percentages, but generally cannot determine which category has more observations. Stating that limitation is a valid mathematical conclusion when the data do not support a count comparison.
In an ordinary single pie chart, a sector’s share is determined by its angle relative to the full circle. Making the entire chart larger on a page does not change its percentages. Printing one chart bigger for readability therefore does not automatically communicate a larger population.
Some specially designed diagrams scale whole-circle area to totals. That requires an explicit convention or legend. If such a convention is supplied, follow it; do not assume it for every pair of pie charts. This guide’s examples use ordinary charts whose totals are provided as numbers.
Chapter 6 of 8 · Check the comparison
6. What conditions should be checked before comparing categories?
Check that the category means the same thing in both charts and that the totals refer to comparable units. A chart of individual people and a chart of households cannot be compared as person counts without further information. Different dates or survey questions may also change what a category represents.
Do not turn a numerical comparison into an unsupported explanation of why groups differ. The chart can show that one stated count or share is larger. It does not by itself establish a cause, the quality of sampling or a trend beyond the observations supplied.
Question 1: compare counts for 20% of sixty and 15% of one hundred. Question 2: a 120° sector belongs to a total of ninety; find its frequency. Question 3: two charts show 40% and 25%, with no totals; can the larger category count be identified? Question 4: a quarter of eighty and a fifth of one hundred represent how many each?
Answers: 1) Twelve versus fifteen; the second count is larger. 2) Thirty. 3) No, not from those percentages alone. 4) Twenty in each. Ask your child to state separately which share is larger and which count is larger. Equal counts do not require equal shares.
Chapter 8 of 8 · Practise and continue
8. What should parents and tutors check next?
Bring both charts, their titles and the exact comparison question. A useful diagnostic note is ‘compares sector angles when the task asks for people’. In a small-group 3-pax lesson, students can keep percentages fixed while changing totals, then predict when the frequency ordering will reverse.
For parents considering Secondary 1 Mathematics tuition in Punggol, the next-question routine is to identify the total, name the measure requested, convert to that measure and compare. A short explanation of the whole behind the slice is more useful than immediately practising more angle calculations.
