Read and compare multiple bars

3.MD.B.3 · take · grade 3

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

The bar graph shows the population of three towns. Town A has $30$ people, Town B has $40$ people, and Town C has $60$ people.

Write, as a fraction, the part of the total population that lives in Town B.

The vertical axis shows population (number of people), with gridlines drawn every $50$ people. The horizontal axis lists Towns A, B, and C in order. The bar heights are $30$ for Town A, $40$ for Town B, and $60$ for Town C.

Show solution

Understand

A bar graph gives the populations of three towns: Town A = 30, Town B = 40, Town C = 60. We must write, as a fraction, the part of the total population that lives in Town B.

Givens

Town A has 30 people.
Town B has 40 people.
Town C has 60 people.
The bars read 30, 40, and 60 against gridlines every 50 people.

Unknowns

The fraction of the total population that lives in Town B.

Constraints

The 'total' is the sum of all three towns.
The answer must be expressed as a fraction.

Plan

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

This breaks into two small steps: first find the total population (a sum), then write Town B's count over that total as a fraction and simplify. Checking the units (people over people) confirms the fraction is a pure part-of-whole ratio.

Execute

#7 Identify Subproblems 3.MD.B.3

From the bar graph the populations are 30, 40, and 60 people for Towns A, B, and C.

Each bar's height against the scaled axis gives that town's number of people.

#7 Identify Subproblems 3.MD.B.3

Add the three town populations to get the whole.

30 + 40 + 60 = 130

The total is just all the people in the three towns added together.

#8 Analyze the Units 3.NF.A.1

Town B has 40 of the 130 total people, so the fraction is 40/130.

\dfrac{40}{130}

The part (Town B) over the whole (all towns) is the fraction that lives in B.

#8 Analyze the Units 3.NF.A.1

Both 40 and 130 are divisible by 10, so divide top and bottom by 10.

\dfrac{40}{130} = \dfrac{40 \div 10}{130 \div 10} = \dfrac{4}{13}

Dividing numerator and denominator by the same number keeps the fraction equal but simpler.

Answer: 4/13

Review

Town B (40) is a bit less than a third of the total 130, and 4/13 is a little under 1/3 (since 4 is a bit under 13/3 = about 4.3), so the fraction is the right size.

Organize the information differently (tool 15): list the parts as 30 : 40 : 60 = 3 : 4 : 6, total 13 parts, so Town B is 4 of the 13 parts = 4/13.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the town populations from the bar graph and summing them.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Expressing Town B's population as a part of the whole total and simplifying.

💡 Add up all the bars for the whole, then put one bar over that total - it's just part-over-whole fractions you learned in Grade 3!