Here are two circles cut into slices. One is a birthday pizza cut into four slices that are all the same size. The other is a survey of our favourite fruit, drawn as a circle where the slices are all different sizes.
The pizza has equal slices. The fruit survey does not. What is the difference between them?
Take two or three hands-up answers, not open call-out. Steer toward the word size: the pizza slices are equal because we chose to cut them fairly; the survey slices are different because they show different amounts of data.
Do not name the term "pie chart" yet — let the noticing land first.
On the left is a pizza cut into four equal slices — a quarter each. On the right is a pie chart of a favourite-fruit survey: 12 apples, 6 bananas, 4 oranges, 2 pears. Look at how the slices are different sizes.
Notice which slice fills exactly half the circle, and read each slice as a percentage.
Point to the equal-slice pizza first: these are equal because we cut them fairly, not because the data made them that way.
Now the fruit pie. The apple slice got 12 of the 24 votes — point out that it fills exactly half the circle. Ask the class to predict the banana slice size before you point to it; 6 of 24 is a quarter, so 90°.
Hold out for the class to notice that a bigger count makes a bigger slice. Do not tell them the rule — let the half-slice and quarter-slice do the work.
Two slices give awkward percentages, so do not chase exact decimals with the class. The orange slice is 4 of 24, so call it about a sixth. The pear slice is 2 of 24, so call it a small slice, less than a tenth. Keep the friendly half and quarter as the numbers pupils read exactly.
Revoice a strong answer: so the slice size follows the number of votes.
Now we build our own pie chart and watch the slices reshape. Our survey asks how the class gets to school: 8 walk, 4 cycle, 6 take the bus and 4 come by car.
A pie chart is proportional. That means the slice size always matches how many votes it got — more votes, a bigger slice.
First, predict which slice will be biggest. Then read each slice as a percentage. After that, we change the walk count and watch every other slice move to make room.
Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.
Start with the how-do-you-get-to-school survey: 8 walk, 4 cycle, 6 bus, 4 car (total 22). Before a pupil enters each count, ask the class to predict whether walking or bus will win.
The teaching move is the reshape: change the walk count from 8 up to 14 and ask the class to predict what happens to every other slice before the pie redraws. This is where "proportional" lands — one slice growing squeezes the others.
Watch for the common slip: pupils expecting the other slices to stay the same size when one count rises. Revoice: the whole circle is always full, so if one slice grows the rest must shrink to fit.
In your maths copy, sketch the favourite-fruit pie chart with the four slices drawn to different sizes: 12 apples, 6 bananas, 4 oranges, 2 pears.
Before you label the percentages, we turn one count into a percentage together. Add the votes to get the total: 12 + 6 + 4 + 2 = 24. Apples got 12 of those 24. Divide the count by the total, then multiply by 100: 12 ÷ 24 = 0.5, and 0.5 × 100 = 50. So the apple slice is labelled 12, 50%.
Now label each of your four slices with both its data count and its percentage. Shade the biggest slice.
Board the worked example before anyone starts sketching. Total = 24. Apples: 12 ÷ 24 = 0.5, then × 100 = 50%. Write the two steps once, revoice once (count ÷ total, then × 100), then release the class to copybook.
Expected labels: apples 12 (50%), bananas 6 (25%), oranges 4 (about 17%), pears 2 (about 8%). Accept nearest whole percent on the two awkward slices.
Walk the room glancing at whether the apple slice is drawn as a genuine half of the circle, this is whole-class copybook practice, not marking. A rough freehand circle is fine; the point is that the biggest count gets the biggest slice. Watch for the slip of writing the count as if it were already the percentage, or dividing total ÷ count instead of count ÷ total.
Now we work through four targets together. First, build a pie for 10 red and 10 blue counters. Next, 15 red and 5 blue counters. After that, a sweet survey with 8 fizzy, 4 chews, 6 chocolate and 2 mints. Last, the break-time drinks survey: 11 water, 4 juice, 3 milk and 2 none.
Each time, predict the shape first. Then press the Check button to confirm.
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
The 10:10 target lands on two equal halves — a good confidence-builder to open with. The 15:5 target makes the red slice three-quarters, so the class sees a familiar friendly fraction. The four-way sweet survey is the real work. The break-time drinks survey has one slice (water, 11 of 20) just over half, so the class must decide which slice "wins" the circle.
Before each Check, ask the class to predict the biggest slice. The Check button confirms each count by label; use the ✓ as part of your narration — yes, that's it.
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