L5 · Interpreting circle graphs

Learning goal

“I can read a circle graph to solve problems: turn a percent into a number of people or items, turn a central angle back into a percent, compare sectors, and combine sectors - all from the labels given in the graph.”

Interpret — to read a graph and answer questions from it: what it shows, how big each part is, and what the numbers mean.

Sector label — the text on or beside a sector giving its category and its percent or angle. The label is where every answer starts.

Estimate — to judge a value that is close to exact, like seeing that a sector is a little more than a quarter of the circle, so a little more than 25%.

Combine sectors — to add the percents of two or more sectors when a question asks about them together.

Worked example

A circle graph shows how 200 students chose their lunch: Pizza 40%, Sandwich 25%, Salad 20%, Pasta 15%. Step 1: Every answer starts at the label and the total. The total is 200 students. Step 2: Pizza: 40% of 200 = 80 students. Sandwich: 25% of 200 = 50. Salad: 20% of 200 = 40. Pasta: 15% of 200 = 30. Step 3: Check: 80 + 50 + 40 + 30 = 200. Every student is counted exactly once. Model both ways: the circle with its four labelled sectors, AND a table with columns category / percent / count, filled in from the graph. Say it plainly: a percent on a graph is not an answer until you apply it to the total. 40% means nothing countable until you know "40% of how many?"

Check yourself — explain it

Why do you need the total number of students before you can say how many chose pizza?

Paired problem — example still visible

A circle graph shows how 120 students get to school: Bus 50%, Walk 30%, Car 20%. How many students use each? -> Bus 60, Walk 36, Car 24 (sum 120)

Faded completion — last step is yours

"A sector has central angle 90°. As a percent that is 90 / 360 = 25%. Out of 80 students, that sector stands for 25% x 80 = ___ students." -> 20 students

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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