Problem
If all 50 answers were correct, Ava would earn 4 points each.
Pretending everything is right gives a simple multiplication to anchor the count.
3.OA.A.3Solve An Easier Related ProblemTurning one right answer into a wrong one loses the +4 it would have earned and adds a -1 penalty, so the score drops by 5 for each wrong answer.
Each mistake costs the missed 4 points plus a 1-point penalty, a steady 5 each time.
3.OA.B.5Guess And CheckTurning one right answer into a wrong answer always lowers the score by exactly 5 points.
The drop of 5 is made of two parts: the 4 points the right answer would have earned but now never come, and the 1-point penalty a wrong answer adds.
When a right answer becomes wrong, the score never gains the 4 points it would have, so the total lands 4 lower than before.
The full score is every question's points added together, so leaving one question's 4 points out of the pile makes the whole total 4 smaller.
A drop of 4 and a separate drop of 1 join into one bigger drop of 4 + 1 = 5.
Two amounts taken away from the same total combine into a single amount equal to their sum.
Her actual score is 155, which is 45 below the perfect 200.
The gap from a perfect score is the total damage all the wrong answers caused.
3.OA.D.8Work BackwardsEach wrong answer costs 5 points, and the total loss is 45, so divide to get the number of wrong answers.
Sharing the 45 lost points into groups of 5 tells how many mistakes there were.
3.OA.A.3Guess And CheckPretend every answer was right, then count how far the score fell; each mistake costs the same amount, so just divide!