Use total and clues to fill missing bars

3.MD.B.34.OA.A.3 · adapt · grade 4

Archetype: Solve a Table or Graph Step by Step from Clues · step in a 5-type progression

The populations of two towns are being shown in a bar graph. Town A has a population of $100$ people. Town B's population is $3$ more than half of Town A's population.

Find Town B's population, then draw the bar for Town B to complete the graph.

The vertical axis shows population (number of people), with gridlines marked at $0$ , $50$ , and $100$ . The horizontal axis lists Town A and Town B. Town A's bar is drawn up to $100$ , and Town B's bar is still empty.

Show solution

Understand

A bar graph compares two towns' populations. Town A is 100 people. Town B is 3 more than half of Town A. Find Town B's population so its bar can be drawn.

Givens

Town A population = 100 people
Town B = 3 more than half of Town A's population
Gridlines are marked at 0, 50, and 100

Unknowns

Town B's population
The height of Town B's bar

Constraints

Half of Town A must be computed before adding 3
The bar height matches the population on the same scale as Town A

Plan

#7 Identify Subproblems · also uses: #11 Work Backwards

The phrase '3 more than half of Town A' breaks into two ordered subproblems: first halve 100, then add 3. Order matters, so we build the value step by step.

Execute

#7 Identify Subproblems 4.OA.A.3

Town A has 100 people, so first find half of 100.

100 \div 2 = 50

Half of a number is just dividing it into two equal parts.

#7 Identify Subproblems 4.OA.A.3

Town B is 3 more than that half, so add 3 to 50.

50 + 3 = 53

'3 more than' means we increase the previous result by 3.

#7 Identify Subproblems 3.MD.B.3

Town B's bar reaches 53, a little above the halfway gridline (50) and well below the 100 gridline, matching Town A's scale.

50 < 53 < 100

On the same scale, a value of 53 sits just past the 50 line.

Answer: Town B has 53 people

Review

53 is just over half of 100, which fits 'a bit more than half', and it stays between the 50 and 100 gridlines, so the bar height is sensible.

Work backwards (tool 11): if Town B were exactly half it would be 50; the extra '3 more' nudges it to 53, confirming the answer.

Standards · min grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Halving Town A and then adding 3 to find Town B
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Placing Town B's bar at the correct height on the population scale

💡 This only needs Grade 4 'do it in order' thinking: halve first, then add 3!