Depth · one concept from first principles · step 2 of 4
An item's angle out of 360° gives its percent
The circle graph at the right shows the favorite snacks of the students in Jia's class. How many students like pizza?
Data & probabilityRatios
Your answer
How to solve
Strategy Analyze the Units — The right-angle mark is the given that is easy to miss -- it is a percentage written in a different language. Translate it, and the last slice falls out of the fact that the four shares add to 100%.
1STEP 1
Read the right angle as a share
A full circle is 360 degrees, and a right angle is 90 of them, so the tteokbokki slice is a quarter of the circle.
90 ÷ 360 × 100 = 25
Tteokbokki is 25%.
4.MD.C.5Analyze The UnitsA right angle at the centre marks off a quarter of the circle.
Why?
A full turn round the centre is degrees, and four right angles laid side by side make exactly that turn.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Those four right angles cut the circle into four pieces with no gap and no overlap, so each piece is one of four equal shares.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
2STEP 2
Use the whole circle to find pizza
The four slices add to 100%, and three of them are now known.
100 - 35 - 10 - 25 = 30
Pizza is 30%.
6.SP.B.4Identify Subproblems3STEP 3
Turn the share into a count
Take 30% of the 40 students in the class.
40 × 0.3 = 12
12 students like pizza.
6.RP.A.3Organize Information In More WaysAnswer
12 students
Count all four: chicken 14, tteokbokki 10, pizza 12 and other 4 add back to 40 students.
Takeaway
An angle on a circle graph is a percentage in disguise -- 360 degrees is the whole 100%.
- Read the right angle as a share
- Use the whole circle to find pizza
- Turn the share into a count
Where next?
Level upsuggested
Another one like thissuggested
Same look, different logicsuggested
Step back and solidifysuggested
A parent dashboard for the family lives at sensimlab.com.
The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Coordinate Plane Figure Computation. Why the shapes repeat →