POTW #16 Grade 7 Question
POTW #16 Grade 8 Question
POTW #15 Grade 7 Answer
If you follow the question carefully you will be left with the formula.
V = 8 * 3 * 10 cm3 - x * x * 3 cm3 = 165 cm3
And when you isolate and solve for x you will find that side length x is equal to 5cm. Do you see why the answer involves algebraic sense?
POTW # 15 Grade 8 Answer
So it would be two of these cones, therefore 575.67 x 2 = 1151.34 cubic cm
Grade 7 POTW:
ReplyDeleteHe found 4 questions hard. Math was done in my math book.
~Michelleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Grade 7 POTW:
ReplyDelete-20 questions
-6 minutes per question (est)
-2 hours
-7/20 questions took 6 minutes
-some took 15 minutes
-some took 2 minutes
-2 hours= 120 minutes.
First, I find the total time of how many minutes the 6 minutes question took:
7*6= 42 minutes
120-42= 78 minutes
So Stu Deus has to finish 13 questions in 78 minutes, I next use the process of elimination to find: 4 questions took 15 minutes, 9 questions took 2 minutes and 7 questions took 6 minutes. To check I:
15*4= 60 minutes
6*7= 42 minutes
2*9= 18 minutes
60+42+18=120 minutes=2 hours
4+7+9= 20 questions
So, Stu Deus found 4 questions difficult.
Stu Dues found 4 questions difficult. I did this by first finding out hoe much time the 6 minute questions took. 7*6=42 min and 120-42=78. That means 13 questions took 78 min. Then by guessing, I said there were 4 difficult questions and then there were 9 easy questions. 4*15+2*9= 60+18=78.
ReplyDeleteAleks and Yoav. In order to figure this out we started with 120 since that's how many minutes are in 2 hours. Then we multiplied 7x6 because there were 7 moderate questions which took 6 minutes each to complete. This gave us 42 and so we subtracted that from 120, and got 78. Now all this really came up to, was finding different ways that 15 and 2 could add up to 78. There could either be 4 hard question (60 minutes) and 9 easy questions (18 minutes). But we could also do 2 hard questions (30 minutes) and 24 easy questions (48 minutes). This means that the exam had either 4 or 2 hard questions.
ReplyDeleteThis is how I figured out the Grade 7 POTW:
ReplyDeleteFirst of all, I know that there are 2 hours in total, so that is 2*60 =120 minutes. There were 7 questions that took 6 minutes, which is in total 42 minutes. That means that the rest of the questions would take a total of 120-42=78 minutes.
In 78 minutes, there are both 15 minute questions and 2 minute questions. I also have to make sure the number of questions add up to 13, since there are 20 questions and 7 of them took 6 minutes, which means that 20-7=13 other questions.
Now, I use guess and check to figure out the number of hard questions. I used a benchmark of 60, which is 4 hard questions. 13-4=9, so there were 9 easy questions that took 2 minutes each, in total 18 minutes. Since 18+60=78 minutes, I know that my answer is correct.
Therefore, Stu Deus found 4 questions hard.
-Alan
Stu Deus found 4 difficult questions. The work was done in my math booooook. yay
ReplyDeleteGrade 8 POTW:
ReplyDeleteHow I did it was to see what was a possible way to figure out the sum of 1 sphere and 1 cube, but it wouldn't be possible to figure out what the weight of the sphere and cube actually is. There is a trick to figure this out though!
Because I know the weight of 3 cubes and 4 spheres, and 4 spheres and 3 cubes, I can add them up to get the total weight of 7 spheres and 7 cubes! This is equal to 33+37=70 grams. Dividing by 7, I would be able to make the weight of a cube and sphere by itself. However, doing that I would have to divide 7 by both sides.
Therefore, the weight of 1 sphere and 1 cube is the weight of 70/7=10g.
The weight of 1 sphere and 1 cube is 10 grams.
-Alan
Grade 7 POTW:
ReplyDeleteAfter taking all the information, we knew that all the 20 question needed to be completed under 2 hours. We knew that there were hard questions that took 15 minutes to complete and easy question that took 2 minutes. We also knew that seven of the 20 questions took 6 minutes to complete. That means he spent 42 minutes completing 7 questions. That means he needed to complete 13 more questions.
Next, we needed to figure out the questions that were difficult and the questions that were easier. After guessing and checking, we found that there were 4 difficult and 9 easy questions, adding up to 78 minutes for the 13 questions.
Therefore, there were 4 questions he found difficult.
Stu Dues found 4 questions difficult because there were 7 6-minute questions, which took 43 minutes, and he has 120 minutes in total. So 120-42=78. Through trial and error, I found that there were 4 questions difficult and 9 easy questions because 1, 9+7+4=20. Then, 4*15+2*9=60+18=78.
ReplyDeleteHere is how I went about solving the Grade 7 POTW:
ReplyDeleteThere were 20 questions on the exam and two hours were given to complete it. Stu solved seven questions while each of them took six minutes to solve. So we do (7*6) to get 42. That means it took him 42 minutes to solve seven of the questions. So there are 13 questions left (20-7) with 78 minutes left (120-42). I wanted to get the total down to 60, so I used the two minute question and multiplied them by 9. This gave me 18 minutes and nine questions. So (78-18 = 60) and (18/2=9). Now there are 60 minutes left to solve 4 more questions. And luckily, they are the 15 minutes ones so it works our perfectly. We do (60/15) and get a quotient of 4. Therefore, there were four examination questions that he found difficult.
Stu Deus found 4 questions difficult. This is because he spent 42 minutes on the 6 minute questions (7 minutes each, 7*6=42). So, he had 78 minutes to finish the 13 easy and hard questions. 4 hard questions=60 minutes, and 9 easy questions=18 minutes, 18+60=78, and 4+9=13. So, he found 4 questions hard.
ReplyDeleteMy work is hard copy, but I came to the conclusion that he found 4 questions hard
ReplyDeleteThey have a combined weight of 10 grams.
ReplyDeleteGrade 7 POTW:
ReplyDeleteI know that there were 20 questions on the exam and 7 questions took 6 minutes while the rest took either 15 or 2 minutes. 6 * 7 is equal to 42 so I know he took 42 minutes to answer the 6 minute questions. That leaves him with 1 hour and 18 minutes (2:00 - 0:48) left for the other 13 questions (20 - 7). I used the guess and check method for this question and after multiple tries, I ended up with 4 question that he found hard and 9 he found easy.
To make sure it works,
4 + 9 + 7 = 20 questions
60 + 18 + 42 = 120 = 2 hours
It works.
Stu Deus found 4 questions hard.
Since there were 20 questions on the test and 7 of them took 6 minutes, we do 7*6 and get 42. Since 120 (2 hours) - 42 is 78, I knew that he had 1 hour and 18 minutes to answer 13 more questions (20 - 7 = 13). I started to try all of the possibilities until I found the answer of 9 easy questions (2*9 = 18) and 4 hard questions (15*4 = 60).
ReplyDelete42+18+60 = 200
Both problems involved guess and check and estimations.
ReplyDeleteGrade 7: With 4 difficult questions taking 1 hour and a set in stone normal question time of 42 minutes and the leftover easy 18, there were 4 difficult questions.
Grade 8: I concluded based on weights that a sphere weighed four grams more than a cube (C+4=S) and you have to reverse engineer and estimate to the total to find that a sphere weighs 7 grams and a cube weighs 3. Thus, they have a combined mass of 10 grams.
Grade 7 POTW:
ReplyDeleteIn order to solve this question, I first found out how long it took Stu Deus to complete the questions of which the time was accurately estimated. Since there were 7 questions that took 6 minutes each to complete, and 7x6 is 42, it took him 42 minutes to complete 7 of the questions. Next, I calculated which of the questions were hard and easy, by using the guess and check method to find a combination of time limits that would add up to 78 (minutes). Using this method, I found that Stu Dent found 9 questions easy and 4 hard. Therefore, Stu found four of the 20 exam questions difficult.
Grade 8 POTW:
ReplyDeleteI did this on my book. And the weight of the sphere and cube combined is 10 grams.