Problem
Use total and clues to fill missing bars
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.
Measurement & dataOperations
Your answer
people
Watch out A common mistake is to add 3 before halving (giving 51.5) instead of halving Town A first and then adding 3.
How to solve
Strategy Identify Subproblems — 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.
1STEP 1
Half of Town A
Town A has 100 people, so first find half of 100.
100 ÷ 2 = 50
Half of a number is just dividing it into two equal parts.
4.OA.A.3Identify SubproblemsHalf of Town A's population of 100 is 50.
Why?
Halving 100 asks for the one number that fits into 100 exactly twice.
Why?
The two equal halves must join back to the full 100 with nothing missing and nothing extra.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Asking what number doubled makes 100 is undoing the doubling, and dividing by 2 is the move that undoes multiplying by 2.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
That number is 50, because 50 is five tens and two sets of five tens make the ten tens that are 100.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
2STEP 2
Add 3 more
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.
4.OA.A.3Identify Subproblems3STEP 3
Draw the bar
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 less than 53 less than 100
On the same scale, a value of 53 sits just past the 50 line.
3.MD.B.3Identify SubproblemsAnswer
53 people
50 + 3 = 53
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.
Takeaway
This only needs Grade 4 'do it in order' thinking: halve first, then add 3!
- Half of Town A
- Add 3 more
- Draw the bar
Where next?
Level upsuggested
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Step back and solidifysuggested