L4 · Constructing circle graphs

Learning goal

“I can build a circle graph: turn counts into percents, turn each percent into a central angle by taking that percent of 360°, and label every sector - and I check that my percents add to 100% and my angles add to 360°.”

Circle graph — a graph that shows data as parts of one whole, drawn as sectors of a circle. Also called a pie chart.

Sector — one slice of the circle, standing for one category of the data.

Central angle — the angle at the centre of the circle that opens up a sector. It decides how big the slice is.

Percent of 360° — how a category's share becomes its angle: central angle = percent x 360°. For example, 25% of 360° = 90°.

Worked example

A survey asked students their favourite season. Results: Spring 25%, Summer 50%, Fall 15%, Winter 10%. Step 1: Check the shares: 25 + 50 + 15 + 10 = 100%. Good - the parts make the whole. Step 2: The whole circle is 360°, so each category gets its percent OF 360°: Spring: 25% x 360° = 90°. Summer: 50% x 360° = 180°. Fall: 15% x 360° = 54°. Winter: 10% x 360° = 36°. Step 3: Check the angles: 90 + 180 + 54 + 36 = 360°. Good. Step 4: Draw each sector with a protractor and label it with the category name AND its percent. A sector without a label is just a slice. Model both ways: the percent table with an angle column added step by step, AND the circle itself, sectors drawn one at a time. Say it plainly: the angle is NOT the percent with a degree sign stuck on. 10% of the circle is 36°, because the angle is 10% of the whole 360°.

Check yourself — explain it

Why do we multiply the percent by 360°?

Paired problem — example still visible

Favourite pets: Dogs 40%, Cats 30%, Fish 20%, Birds 10%. Find the four central angles. -> Dogs 144°, Cats 108°, Fish 72°, Birds 36° (sum 360°)

Faded completion — last step is yours

"Snacks: Chips 35%, Fruit 30%, Cookies 20%, Other 15%. The Chips sector: 35% x 360° = ___." -> 126°

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