Competition · AMC preparation · step 4 of 4
AMC 8 · 2002 · #7
Grade 6 rate-ratio
Pick an answer.
AMC 8 2002 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The work splits cleanly into Tool #7 subproblems: (1) read the five bar heights, (2) add them to get the class total, (3) form the fraction E/total and convert to a percent. Tool #5 (Look for a Pattern) finishes the last step quickly — 5 out of 25 is the familiar 1/5 = 20% pattern, so no long division is needed.
Read the five bar heights
Read the five bar heights off the graph; candy E's bar reaches 5 students.
Reading values off a scaled bar graph is the Grade 3 "draw and interpret a scaled bar graph" skill.
3.MD.B.3Identify SubproblemsAdd for the class total
Add the five bar heights, counting each student once — the class totals 25 students.
Combining several known quantities to get a total is the Grade 4 multi-step word-problem move.
4.OA.A.3Identify SubproblemsWrite E as a fraction
Write E's share as a fraction over the class total: × 100%.
Choosing the class total as the base of the percent (the "whole") is the key Grade 6 ratio move.
The share of the class that chose candy E is found by taking E's student count over the class total and measuring that fraction against a whole of one hundred: 5/25 × 100%.
▸ Why?
The "whole" to compare E against is the entire class, and that class total is exactly the five candy counts added together with no student left out.
▸ Why?
Each student chose exactly one candy, so the five candy groups cover the class with no gaps and no overlaps, and adding them back rebuilds the full total of 25.
▸ Why?
E's share is the fraction 5/25 because the class breaks into 25 equal one-student parts and E holds 5 of them.
▸ Why?
The class of 25 is 25 equal groups of one student each, so every student is an identical unit, and comparing E's 5 units against all 25 is a fair part-to-whole reading.
▸ Why?
Reporting E's share as a percent means restating the fraction 5/25 as the matching number of parts out of one hundred, and multiplying by 100 is exactly the step that finds that matching count.
▸ Why?
A percent is by definition parts per hundred — "p percent" means p out of every hundred — so a share written as a percent is the very same share measured against a whole of one hundred instead of against 25.
Simplify into a percent
Simplify to , the well-known 20% pattern → (E).
Recognizing 1/5 = 20% without long division is the Grade 6 percent-pattern shortcut.
6.RP.A.3Look For A PatternRead each bar, add them for the class total, then write the E-share as a fraction and turn it into a percent — a Grade 6 part-to-whole move that turns an AMC 8 problem into one step of arithmetic.
- Read the five bar heights
- Add for the class total
- Write E as a fraction
- Simplify into a percent
A parent dashboard for the family lives at sensimlab.com.