Competition · AMC preparation · step 4 of 4
AMC 10 · 2021A · #2
Grade 4 arithmeticPick an answer.
AMC 10 2021 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
"3 times as many" begs for a tape diagram (tool #1): draw one box for Lara and three identical boxes for Portia. That makes the four boxes together equal to 2600, so one box is 2600 ÷ 4 = 650 and Portia gets 3 boxes. Tool #6 (Guess and Check) and tool #3 (Eliminate) confirm: the answer must be more than half of 2600, knocking out (A), (B); and the matching small box value 650 shows up as choice (B) for Lara — confirming Portia's 1950.
Picture the schools as boxes
Draw each school as identical boxes: Lara is one box, Portia is three — so together they make four equal boxes.
"3 times as many" is a Grade 4 multiplicative comparison — the bar model turns the comparison into countable boxes.
4.OA.A.2Draw A DiagramDivide 2600 by 4
Four equal boxes total 2600, so each box is 2600 ÷ 4 = 650 students — that is Lara's school.
Splitting a four-digit total evenly among 4 groups is Grade 4 long division.
Splitting the total evenly among the equal boxes gives the size of one box.
▸ Why?
Each box is one of the equal shares the whole is cut into.
▸ Why?
The whole is those equal boxes repeated, which is exactly what multiplying counts.
Triple one box
Portia's school is 3 boxes: 3 × 650 = 1950 students.
Multiplying a three-digit number by a one-digit number is Grade 4 "multi-digit by one-digit".
4.NBT.B.5Draw A DiagramCheck against the choices
Check: 1950 is choice (C), and it beats half of 2600, matching that Portia's share is the larger one.
Plugging the candidate back into the two given relationships and seeing them both hold is Grade 4 "multi-step word problem with reasonableness check".
4.OA.A.3Eliminate PossibilitiesThis AMC 10 problem only needs Grade 4 "3 times as many" tape diagrams you already know — split 2600 into 4 equal boxes, give Portia 3 of them, and the answer is 1950.
- Picture the schools as boxes
- Divide 2600 by 4
- Triple one box
- Check against the choices
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