Competition · AMC preparation · step 4 of 4
AMC 8 · 2006 · #2
Grade 3 arithmeticPick an answer.
AMC 8 2006 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The unit on every question is "points". Each correct answer is worth 1 point and each non-correct answer (wrong or blank) is worth 0 points. Tool #8 (Analyze the Units) frames the question as a points-per-answer rate, which collapses everything to a single multiplication. Tool #7 (Identify Subproblems) splits the 25 questions into three buckets — correct, incorrect, blank — so the points from each bucket can be counted separately and then added. Two buckets contribute zero, so the score is just the count of correct answers.
Sort the answers into buckets
Sort the 25 answers into three buckets — correct, wrong, blank — where correct is worth 1 point and wrong and blank are worth 0.
Sorting answers by their points-rate is a Grade 3 "multiplication word problem" setup — same rate within a group.
3.OA.A.3Identify SubproblemsScore each bucket and add
Multiply each bucket by its rate and add: wrong and blank give 0, so the total is 13.
Anything times 0 is 0, so the wrong and blank buckets vanish and the score equals the count of correct answers.
Billy's total score equals the number of questions he answered correctly.
▸ Why?
The total score is the sum of the points from the three answer groups — correct, wrong, and blank — and only the correct group adds any points.
▸ Why?
Every one of the 25 answers falls into exactly one of the three groups, with none left out and none counted twice, so the three group point-totals add back to the whole score.
▸ Why?
The 7 wrong answers and the 5 blank answers each carry a rate of 0 points, and any count of answers at 0 points apiece totals 0 points.
▸ Why?
A count of answers times 0 points each means that many equal groups of 0, which is just 0 added over and over.
▸ Why?
Adding 0 again and again never builds up any points, so the running total stays at 0.
▸ Why?
The 13 correct answers each carry a rate of 1 point, and a count of answers at 1 point apiece totals exactly that count.
On the AMC 8, only correct answers add points — wrong and blank both score zero. So the total score is just the count of correct answers: 13.
- Sort the answers into buckets
- Score each bucket and add
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