T

Side-by-Side Column Graphs and Pie Graphs

Maths · Stage 3
Year 5
Lesson Guide
Explanation
A side-by-side column graph puts two sets of bars next to each other, and the key says which colour is which. Read the key first, because the bars mean nothing without it. Year four borrowed sixty books in the first year and eighty in the second, an increase of twenty; year three went from forty down to thirty, a fall of ten, and was the only group to fall. A question about which group changed most compares the differences, not the heights.
Your Turn
Year 5 went from 50 to 70. How much did it increase by? Check: 20.
Watch Out
Comparing bar heights answers "who borrowed most". Comparing the gaps answers "who changed most".
Explanation
A pie graph divides one whole, so the size of each sector is its share of the total. With six hundred children, a sector that is half the circle is three hundred, and each quarter is a hundred and fifty. The check is that the sectors add back to the total and the fractions add to one. That check catches most errors in these questions.
Your Turn
A quarter of 600 children walk. How many is that? Check: 150.
Watch Out
A pie graph shows shares, not counts. Without the total you cannot say how many.
Explanation
Name the fraction before doing any arithmetic. A sector that is an eighth of the circle is the total divided by eight, so an eighth of eight hundred is a hundred, and three eighths would be three hundred. When a sector is not exactly a neat fraction the question will say about, and you estimate to the nearest easy one — a bit less than a quarter, say. Then check that all the sectors add back to the total.
Your Turn
An eighth of 800 people cycle. How many is that? Check: 100.
Watch Out
Divide by the bottom of the fraction. An eighth of 800 is 100, not 8.
Explanation
For a comparison, turn both sectors into numbers first and only then answer. Bus is three hundred and walking is a hundred and fifty, so a hundred and fifty more come by bus, and the bus figure is exactly twice the walking one. That last distinction matters for claim questions: exactly twice means the claim more than twice as many is false, even though it feels close.
Your Turn
Bus 300, walk 150. Is "more than twice as many come by bus" true? Check: no — it is exactly twice.
Watch Out
"Exactly twice" makes "more than twice" false. Check the wording against the numbers.
Explanation
Three steps, always: name the fraction the sector takes up, take that fraction of the total, and only then compare or subtract. Half of six hundred is three hundred, a quarter is a hundred and fifty, and the difference is a hundred and fifty. Check the sectors add back to the total before you move on. Quiz and exercises now.
Your Turn
A pie graph of 800 has a half, a quarter and two eighths. Do they add to 800? Check: 400 + 200 + 100 + 100 = 800 ✓.
Watch Out
Use the total given in the question. The same pie graph with a different total gives different answers.
📌 Key Points — this lesson in a nutshell
  • A side-by-side column graph puts two sets of bars together. Read the key before any bar.
  • A pie graph shows shares of one whole. Half the circle is half the total, a quarter is a quarter.
  • To read a sector: work out its fraction of the circle, then take that fraction of the total.
  • A pie graph alone never tells you how many — you need the total as well.
Step 1: Introduction
Step 1 of 5
Books borrowed in 2025 and 2026 020406080100Y3Y4Y520252026 The key says which colour is which year. Read it first — the bars mean nothing without it. Year 4 borrowed 60 in 2025 and 80 in 2026: an increase of 20. Year 3 went from 40 down to 30, a fall of 10. Only Year 3 fell. "Which year changed the most?" compares the differences, not the heights: 20, 20 and 20 would be a tie.
How 600 children travel to school buswalkcar bus: half the circlehalf of 600300 children walk: a quarter600 ÷ 4150 children A pie graph divides ONE whole. The size of a sector is its share of the total. Bus is half of 600 = 300; walking is a quarter = 150; car is a quarter = 150. They add back to 600 ✓. Check by adding: the sectors must come to the total, and the fractions must come to 1.
A sector of 800 ABCD C is an eighth800 ÷ 8100 A 400 · B 200 · C 100 · D 100 400 + 200 + 100 + 100 = 800 ✓ a half, a quarter and two eighths Name the fraction first — a half, a quarter, an eighth — then take it of the total. An eighth of 800 is 800 ÷ 8 = 100. Three eighths would be 3 × 100 = 300. If a sector is not exactly a neat fraction, the question will say "about" — estimate to the nearest easy one.
How many more come by bus than walk? buswalkcar bus 300− walk 150150 more work out BOTH sectors first then subtract, or add, as asked "twice as many" → is 300 = 2 × 150? yes Turn both sectors into numbers, then answer the question with those numbers. Bus 300, walk 150: 150 more by bus, and bus is exactly twice walking. A claim like "more than twice as many" needs the numbers: 300 is exactly twice 150, so "more than twice" is false.
Reading the question Half of 600 travel by bus. How many?300 A quarter walk. How many?150 How many more by bus than walking?150 An eighth of 800 cycle. How many?100 Name the fraction · take it of the total · then compare. And check the sectors add back to the total every time. Quiz and exercises now.
Was this lesson helpful? Rate this Course
Discussion
Loading comments...