7. Ervin and some friends were going to eat a pizza. Ervin wasn't very hungry so he said he only wanted half of a half of a half of the pizza. He took the napkin and wrote:
1/2 + 1/2 + 1/2 = 3/6 = 1/2
When the pizza came, Ervin took half of it. Ellen said he made a mistake. Was she right? If so, describe the mistake(s) Ervin made.
| 0 | Answer is unresponsive, unrelated, or inappropriate. Answer contains nothing correct. Or, says Ellen was right but description in no way supports this choice. |
| 1 | Answer correctly recognizes one of the two mistakes. Description of the mistake reveals a significant lack of detail/lack of clarity, or is only partly correct. |
| 2 | Answer correctly recognizes that 1/2 + 1/2 + 1/2 does not equal 3/6, and description of this mistake is clear and complete. |
| 3 | Answer correctly recognizes the mistake of adding instead of multiplying, and description of this mistake is clear and complete. Or, answer recognizes both mistakes, but with minor error, omission, or lack of clarity in the description. |
| 4 | Answer correctly recognizes both mistakes, with clear and complete description. |
7. Ervin and some friends were going to eat a pizza. Ervin wasn't very hungry so he said he only wanted half of a half of a half of the pizza. He took the napkin and wrote:
1/2 + 1/2 + 1/2 = 3/6 = 1/2
When the pizza came, Ervin took half of it. Ellen said he made a mistake. Was she right? If so, describe the mistake(s) Ervin made.
Ellen was right, Ervin said he wanted have of a 1/2 of a 1/2 of the pizza so Ervin should have got 3/6 of the pizza.
0 --Answer says Ellen was right but description in no way suports this choice.
Yes, Ervin made a mistake because he said he was only going to take half of a half of a half but instead he took one half of the hole thing.
1 -- Answer recognizes that the amount asked for and the amount taken are not the same. However, there is a lack of numerical detail in explaining how the amounts differ.
He had the part right about the halfs but he couldn't have got a half again this is how it should be done 1/2 + 1/2 + 1/2 = 3/2 reduce it will equal to 3/4.
1 -- Recognizes that 1/2 + 1/2 + 1/2 = 3/2; then goes on to make mistake (3/2 does not "reduce" to 3/4).
Ellen was right in sayint that Ervin made a mistake. Ervin's calculations were incorrect.
| 1/2 + 1/2 + 1/2 = 3/2 |
1 -- The mistake in addition is described. However, the last statement is incorrect.
Ellen was right. The mistakes Ervin made was he said that 1/2 + 1/2 + 1/2 = 3/6. But it doesn't. 1/2 + 1/2 + 1/2 = 3/2 = 1 1/2. So Ervin was wrong. Ellen was right.
2 -- Answer correctly recognizes mistake made within the addition. Description is clear and complete. Did ;not address the other mistake (1/2 X 1/2 X 1/2 = 1/8).
1 -- The mistake in addition is described. However, the last statement is incorrect.
Ellen was right because half of a half of a half of the pizza is not 1/2. I'll explane this. Half of the pizza is . Half of a h alf pizza is
. Half of a half of a half is
. So Ervin will only take this much of pizza
(according to the circles I have drawn.) Ervin shouldn't add the three one half together cause the problem said half of a half of a half of the pizza ("of" means multiply.) So I take 1/2 X 1/2 X 1/2 = 1/8. This is how much Ervin should eat.
3 -- Answer recognizes the error of adding instead of multiplying, with a clear and complete description.
1 -- The mistake in addition is described. However, the last statement is incorrect.
First of all Ervin didn't add right. The answer to that equation would've been 3/2. But that is beside the point because he set up the problem wrong anyhow. He was supposed to start of with 1 which represented the pizza, then he should've multiplied that by 1/2, which would've given him 1/2. Then he needed to take tha 1/2 and multiply that by 1/2 which would've gotten him 1/4. Lastly he should've mul;tiplied that by 1/2 which would've gotten him the answer 1/8. So Ervin needed to take 1/8 of the pizza.
4 -- Answer recognizes both errors, with clear and complete description.