Competition · AMC preparation · step 4 of 4
AMC 8 · 2010 · #1
Grade 2 arithmeticPick an answer.
AMC 8 2010 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The total is naturally split into three disjoint pieces — one per teacher — so Tool #7 (Identify Subproblems) just means counting each class separately and then adding. Because there is no overlap between classes, the total is simply the sum 11 + 8 + 9. Tool #14 (Sanity Check) is used at the end to confirm the sum lands in the choice range and to double-check by re-grouping the addends.
List each class count
Read each class size straight from the problem: 11, 8, and 9.
Pulling the three numbers out of the word problem is exactly the Grade 2 "represent a word problem with numbers" skill.
2.OA.A.1Identify SubproblemsAdd the first two classes
Add the first two classes: 11 + 8 gives 19.
Adding two two-digit numbers within 100 is the Grade 2 fluency standard.
2.NBT.B.5Identify SubproblemsAdd the third class
Add the last class: 19 + 9 makes 28 (make a ten: 19 + 1 = 20, then + 8).
Decomposing 9 as 1 + 8 to make a friendly 20 is a standard Grade 2 mental-math move.
Adding the third class's 9 students onto the 19 already counted from the first two classes gives the whole school's contest total.
▸ Why?
The three teachers' classes together are exactly the students taking the contest, and no student sits in two of them at once.
▸ Why?
When one group is cut into pieces that never overlap and leave no one out, adding the pieces back returns the size of the whole group.
▸ Why?
The running total 19 already stands for the first two classes counted together, so adding the third class's 9 is just combining the three class sizes in the order first-two-then-last.
▸ Why?
Adding three amounts lands on the same total no matter which two you push together first.
▸ Why?
To add the 9, you can slide 1 of it over to fill 19 up to a whole 20, then add the leftover 8.
▸ Why?
Ten ones bundle into exactly one ten, so topping 19 up to 20 makes a clean count to continue from.
Match against the choices
The total 28 matches answer choice (C).
Confirming the computed total is one of the listed options is the final "does this answer the question?" check.
2.OA.A.1Extreme PrincipleThis AMC 8 problem only needs Grade 2 addition within 100 — just add the three class sizes!
- List each class count
- Add the first two classes
- Add the third class
- Match against the choices
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