Find the value of one grid interval

3.MD.B.3 · take · grade 3

Archetype: Read and Scale a Data Graph · step in a 21-type progression

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $18$ 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 $2$ circles, Town B has $2$ circles, Town C has $4$ circles, and Town D has $1$ 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 $18$ students, how many students does one circle represent?

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

Show solution

Understand

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 18 students all together. I need to find how many students live in Town C.

Givens

Circle counts: Town A = 2, Town B = 2, Town C = 4, Town D = 1.
The four towns have 18 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town C.

Constraints

Total circles times students-per-circle equals the total students.

Plan

#8 Analyze the Units · also uses: #7 Identify Subproblems

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.

Execute

#7 Identify Subproblems 3.MD.B.3

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

2 + 2 + 4 + 1 = 9

Reading and totaling the symbols is how you interpret a scaled picture graph.

#8 Analyze the Units 3.MD.B.3

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

18 \div 9 = 2

Sharing 18 students equally among 9 circles tells the value of each circle (the scale).

#8 Analyze the Units 3.MD.B.3

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

2 \times 4 = 8

Multiplying circles by students-per-circle gives the town's real value.

Answer: 8 students

Review

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.

Since C has the most circles (4 of the 9), it should hold the most students; 8 of 18 is the largest share, which fits.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town C's value from the scaled graph.

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