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Solves Problems and Reasons Logically
Lesson 26		 Construct Solutions and Verify
  Objectives/Vocab/Tips > Examples 1 | 2 > Practice: 1 | 2 > Reflection

Practice 1:

A multiple-choice test contains 40 items. A correct response earns 5 points, but 2 points are deducted for every incorrect response. Nothing is given nor deducted if the question is unanswered. Michelle scored 96.

  • How might she have gotten this score?
  • Find two solutions as to how Michelle received her score.

Explain how there can be more than one correct answer.

Look at the following three possible responses to this 4 point problem. Click on the score you would give this student response and then write why you would give the score you did. Remember the requirements for 4 point responses.

Response #1

Michelle could have gotten 20 correct and 2 incorrect with 18 questions not answered. This is how Michelle would have gotten a score of a 96.

20 x 5 = 100
2 x 2 = 4

100 - 4 = 96

Michelle could have received her 96 in another way too as long as when you add the number of points for the correct answers and subtracted the total points for the ones she missed.

Reason for score:

Response #2
Michelle got a 96 by getting 22 right, 7 wrong, and then not doing 11 of the problems. This was the only solution I could find.

Reason for score:

Response #3
She could have gotten 20 right, 2 wrong, and didn't do 18 of the problems. I also found out that once I found one solution I quickly found another solution worked as well. She could have also had 24 correct with 12 wrong and then didn't do 4 problems. There can be more than one solution for this problem because I did the math and found the two ways to work. They worked like this.

20x5 = 100 points right
2x2 = 4 points wrong

100 - 4 = 96 total points received

The other way is:

24x5 = 120 points right
12x2 = 24 points wrong

120 - 24 = 96 total points received

Reason for score:

Click here to see the three possible correct answers to this problem.

 

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