Data & Graphs

Depth · one concept from first principles · step 2 of 4

Find the value of one grid interval

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 1818 students in all, find how many students live in Town C.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has 22 circles, Town B has 22 circles, Town C has 44 circles, and Town D has 11 circle. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are □\square circles in all and 1818 students, how many students does one circle represent?

(3) Town C has 44 circles, so the number of students living in Town C is □×4=□\square\times4=\square students.

Number of students by town Number Town A B C D
Measurement & data
Your answer
students
How to solve
Strategy Analyze the Units — One circle is a unit standing for some students. Counting all circles and matching them to the 18 students gives the value of one circle; then I scale Town C's circles by that unit. This is unit reasoning broken into small steps.
1STEP 1

Count all the circles

Add the circles in every column: 2 + 2 + 4 + 1 = 9 circles in all.

2 + 2 + 4 + 1 = 9
2STEP 2

Find what one circle is worth

9 circles stand for 18 students, so one circle stands for 18 ÷ 9 = 2 students.

18 ÷ 9 = 2
3STEP 3

Scale Town C

Town C has 4 circles and each circle is 2 students, so Town C has 2 × 4 = 8 students.

2 × 4 = 8
Answer
8 students
2 × 4 = 8
Check the whole graph with 2 per circle: A=4, B=4, C=8, D=2, totaling 4+4+8+2 = 18, which matches the given total. So Town C = 8 is consistent.
Takeaway

This only needs the Grade 3 idea that one picture stands for a set number — find that, then multiply!

  • Count all the circles
  • Find what one circle is worth
  • Scale Town C
Where next?
Level upsuggested
Determine the value each picture symbol stands forConvert a pictograph into a frequency table
Another one like thissuggested
10 practice problems
Step back and solidifysuggested
Count sticks needed via multiplication
4 reasoning problems grow out of this type — the bridge toward competition →

A parent dashboard for the family lives at sensimlab.com.

▶ Practice — 10 problems

The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Coordinate Plane Figure Computation. Why the shapes repeat →