Problem
Set up the correct add/subtract equation
At a school performance the audience has 53 boys, and the number of girls is 14 fewer than the number of boys. We need the total number of students in the audience.
Reasoning · Grade 2-1 Addition and Subtraction Word Problems
Your answer
students
Watch out It is easy to work out 39 girls and stop there. The question asks for the two groups combined.
How to solve
Strategy Identify Subproblems — This is a two-step word problem, so split it into subproblems: first find how many girls there are (a subtraction because girls are fewer), then add boys and girls for the total. A bar model showing the boys' bar and a shorter girls' bar keeps us from accidentally adding 14 instead of subtracting it.
1STEP 1
Find the number of girls (subproblem 1)
'Fewer' means subtract, so the girls number 39.
53 - 14 = 39
'Fewer than' is a take-away comparison, so we subtract to land on the smaller amount.
2.OA.A.1Identify Subproblems"14 fewer girls than boys" means the girls' count is the boys' count with 14 taken away, so you subtract rather than add.
Why?
Drawn as two bars, the girls' bar is the boys' bar with a 14-long piece cut off the end, so the boys' bar is the whole and the girls' bar is a part of it.
🧱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?
Finding a part when the whole and the other part are known is exactly what subtraction does, because taking away undoes putting together.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Add boys and girls for the total (subproblem 2)
The question wants the total, so add both groups: 92.
53 + 39 = 92
'In all' means combine the two groups, which is addition of the two two-digit numbers.
2.NBT.B.5Identify Subproblems3STEP 3
Picture it as two bars to confirm the setup
As bars, the girls' bar is 14 shorter, and joining both gives 53 + 39 = 92.
53 + (53 - 14) = 92
Seeing the girls' bar shorter than the boys' bar makes it obvious the 14 is taken away, the common trap in this problem.
2.OA.A.1Draw A DiagramAnswer
92 students
53 + 39 = 92
Girls (39) are fewer than boys (53), exactly 14 fewer, which matches the story. The total 92 is more than the boys alone (53) and is a sensible audience size, so it is reasonable.
Takeaway
'Fewer than' tells you to subtract first, then add the groups - two careful steps and the trap disappears!
- Find the number of girls (subproblem 1)
- Add boys and girls for the total (subproblem 2)
- Picture it as two bars to confirm the setup