Welcome back all returning Cranny Intermediates,
and hello to all of you new Intermediates! (i.e. Grade 7s and newcomers to our
school).
As most of you know, this website is a space
where Mr. Milette seeks to challenge you with the Math Problem of the Week!
(A.K.A. POTW). In a bit of a different twist this year, two questions will be
posted most weeks. One question is geared toward the Grade 7s and a second
question is more for the Grade 8s. You are challenged to answer both questions
each week, but only your specific-grade question is mandatory. Also, the Grade
8 question will be similar to math questions found in the Grade 9 & 10 curriculum
so it’s a great way to see what’s ahead for you young mathematicians!
The most important
requirement of this website is YOUR participation. This may come in the form
of:
- sharing your POTW answer
- posting your comments, questions, and replies to others
- seeking out the answers to POTWs (answers are posted a week after the question has been posted)
- reading and following new posts
With that being said, it is absolutely pivotal that you remind yourself about online netiquette. You must always consider the feelings of others when posting comments. Before you press 'submit' or 'send' or 'publish' please ask yourself two questions: "Would I say this in-person to someone's face?" and "Is my comment helpful?" If the answer to either of those questions is "No" then consider revising your comment.
- sharing your POTW answer
- posting your comments, questions, and replies to others
- seeking out the answers to POTWs (answers are posted a week after the question has been posted)
- reading and following new posts
With that being said, it is absolutely pivotal that you remind yourself about online netiquette. You must always consider the feelings of others when posting comments. Before you press 'submit' or 'send' or 'publish' please ask yourself two questions: "Would I say this in-person to someone's face?" and "Is my comment helpful?" If the answer to either of those questions is "No" then consider revising your comment.
Without further ado,
below is your first POTW for the year! Please submit any and all
responses regardless if you think someone else has the same answer. Both Grade
7 and Grade 8 students can submit answers in the same reply section, please
just state which question you’ll be answering at the beginning of your post
(although it should be pretty obvious to the audience anyway). You can always
show your work in different ways! And be sure to comment on other students'
work, provide feedback, and ask clarifying questions.
Always remember to be
signed-in to your gapps account before submitting a response. Enjoy the POTW!
Grade 7 POTW #1
Grade 8 POTW #1
Here is How I solved the Grade 8 POTW:
ReplyDeleteSO to figure out the score Mark needs to get to boost his average to 180, I had to figure out what is the total of all his scores was and the amount of scores he got in total. So I began with figuring out the amount of scores he got in total, by taking 177 ( his old average score) multiplying it by an unknown, adding 199 ( His score he added) and dividing the total by another unknown 1 bigger that the last that will equal 178:
( 177 * x + 199) / y = 178
x + 1 = y
So I began plugging in numbers in after countless of tries I soon found what x and y equaled:
x = 21
y = 22
( 177 * 21 + 199) / 22 = 178
( 3717 + 199) / 22 = 178
3916 / 22 = 178
178 = 178
Now that I knew the amount of scores he added up to get the average, I took 180 ( The desired average score) and multiplied by one more than y, because we are adding one more score. Then I subtracted that number by 177 * 21 + 199 ( The total of all the scores so far) to get the answer:
180 * 23 - 3916 =
4140 - 3916 = 224
Mark need would need to bowl 224 to accomplish his goal.
Thanks for the thorough post Vivian. You were always strong with the POTW last year, keep it up! Can I share this tomorrow?
DeleteHere is how I solved the GRADE 7 POTW XD:
ReplyDeleteSo I first wrote down what you would do to get the average ( 75%):
y / 6 = 75
Because the total of all his marks added up is unknown, and then dividing that by the total number of marks ( 6) would have to equal 75. I then worked backwards from that point and decided to figure out the total of all of Stu Dent's marks:
75 * 6 = 450
y = 450
So the total of all Stu Dent's marks added up is 450, I then took away 39 from that because one mark was wrong, then added the correct mark to the difference.
450 - 39 = 441
441 + 93 = 504
So Stu Dent's new current total of all his marks is 504, I now divided it by 6 ( The total number of marks)
504 / 6 = 84
Stu Dent's new average is 84% Good job Stu dent! A- Average!
* note*
To find the average you take all the numbers and added them up to get the total, then divide that total by the amount of numbers you added up to get the average
I solved the Grade Seven POTW by the following steps:
ReplyDeleteI knew that there were six marks that he had.
If his average was 75%, that means that the total of each mark would be 450 because
75*6=450
Now, I subtract his incorrect score of 39, which leaves us with 411 because
450-39=411.
Now, I add his correct score of 93 to 411 which gives us 504.
411+93=504
So, then I divided 504 by 6, which is the number of marks he got.
504/6=84.
So, his correct report card average is 84%
Grade 6 POTW
ReplyDeleteTo get the total amount of marks Stu got, we would have to multiply the average by 6. When we calculate average, we divide the total marks by the number of subjects so we are doing the opposite to get the total number of marks.
His total score (75x6) is 450.
Stu's correct math mark was 93% and his wrong one was 39% so we have to replace the 39% with the 93%. 450-39+93= 504. So this real total amount of marks is 504. If I divide that by 6, I would get 84%.
Stu's correct report card average is 84%.
Grade 6 POTW
ReplyDeleteTo get the total amount of marks Stu got, we would have to multiply the average by 6. When we calculate average, we divide the total marks by the number of subjects so we are doing the opposite to get the total number of marks.
His total score (75x6) is 450.
Stu's correct math mark was 93% and his wrong one was 39% so we have to replace the 39% with the 93%. 450-39+93= 504. So this real total amount of marks is 504. If I divide that by 6, I would get 84%.
Stu's correct report card average is 84%.
Well, I also think the answer is 84%.
DeleteThis is a test
DeleteThis is a test
DeleteI figured out the Grade 7 POTW in a different way (I think).
ReplyDeleteHis old average was a 75%.
As we know, to calculate an average you take all the numbers, add them together, and divide them by the number of numbers you added.
If we reverse the order, we get: 75*6 (because there are 6 numbers)=450
He had thought he had 39% in math, which means (5x+39)/6=75
X would equal 82.2, as 82.2*5 is 411, and 411 + 39 is 450. 450/6 is 75.
Now if instead of 39 it is 93, then you dont change the equation other than the 39.
82.2*5+93=504. 504/6 is 84.
Therefore Stu's correct average is an 84%
Grade 7 POTW:
ReplyDeleteThe way solved it was i first had to figure out all 6 marks he got on his report card. So i did 75*6 to give me a total of 450. I knew to find the average, I would have to divide the sum of numbers by the number of marks. So, I reversed it by multiplying the amount of marks by the average.
Next, the question stated that one of his scores was written incorrectly. 39% was supposed to be 93%. This means I would have to subtract that score to the total amount because i have to change replace with another mark, due to the mark being incorrect. Instead, the correct mark that was supposed to be given was 93.
This left us with: 450-39+93
This gives us the answer of 504
This last step is to now find the new average. Taking this sum of marks, we would have to divide it by the number of marks, which was 6. This gives us the answer to this problem.
504 divided by 6 would equal 84.
Stu new and real report card average is 84%
Well, I must say the very first day (and not even "officially" assigned and there is some wonderful work here on the POTW! Great job kids. Don't forget you can also comment on others' posts and ask questions of your peers.
ReplyDeleteFor the grade 7 problem
ReplyDelete600 divided by 6=100
Therefore 6 grade points= 1 average point
75 ap + 54 gp= 84 ap
Therefore Stu Dent's new average is 84%
For the grade 8 problem
22 game points= 1 average point
2ap=44gp
178ap+44gp=180ap or 222gp
Therefore Mark would need a score of 222 points.
Grade 7 POTW:
ReplyDeleteFirst I need to find out the sum of all of Stu Dent's marks. I can do that by multiplying the average, 75%, by the number of marks, 6. That will give me 450 in total.
Now, I need to find out his actual total. His mark was mistaken for 39% so I can subtract 39 from 450. that gives me 411. Now, I need to add the actual mark, 93%, so I can add 93 to 411. That gives me 504 as the sum of all his marks.
To find out Stu's actual average, I need to divide 504 into 6. That gives 84%. So this determines that Stu Dent's average is 84%
G8: To solve this question I did the following:
ReplyDelete178*2=356
180*3=540
540-356=184
Mark will need to score 184 to have the average of 180.
Basically I worked backwards to solve the question. First I see the current total of points which is 356. Then I find out the total score if his average was 180 which is 540. Then I subtract 356 from 540 to find out how much Mark needs to score. So I ended up with a total of 184.
G7: To solve this question I did the following:
(75*6-39+93)/6
=(450+54)/6
=84%
Stu's average should actually be 84%.
This comment has been removed by the author.
ReplyDeleteI think my other answer was wrong, as we don't know how many times he bowled.
ReplyDeleteHis old average was 177, and since we don't know how many games he played, we will use the variable x for the number of games. I will use z for the total number games which we divide the total by:
177x + 199/z = 178 (average)
I then figured that we need to find the correct values for z and x that would work for 178.
After some tries, I found this (I started at 20)
x= 21
z=22
(177 x 21 + 199)/22 = 178
(3717 + 199)/22 = 178
3916/22 = 178
178= 178
Now, we can multiply 180 by the 23rd time and subtract by the previous sum.
180 x 23 - 3916 = score he needs.
4140 - 3916 = 224
He needs a score of 224 to make his average 180.
Good luck with that!
This comment has been removed by the author.
ReplyDeleteGrade 7 POTW:
ReplyDeleteSo we know that the "Wrong" average is a 75% (Out of 6 subject grades). Original to get the average you add all of the grades together then divide it by the number of grades. What i did was i reversed it or something like that. Multiplying 75 by 6 to get the "Added together average" which is 450. Now we take away the 39 and replace that with the correct mark of 93 so:
450-39=411 (Mark not including the math mark)
411+93=504 (Total points)
Now we divide that by 6 marks. Leaving us with 84%. Therefore his new average would be 84% <:
~Michelle
Grade 7 POTW:
ReplyDeleteIn order to solve this problem, we must multiply his incorrect average by his 6 report card marks, add the difference of the correct and incorrect marks from his multiplied average, and divide his new multiplied average by his 6 marks.
Step 1: First, I multiplied Stu's average (75%) between his 6 marks
75x6=450
Step 2: Then I figured out the difference between Stu's correct and incorrect marks..
93-39=54
...and added that to his multiplied average.
450+54=504
Step 3: Finally, I divided Stu's new multiplied average by his 6 report card marks to get his correct average.
504/6=84
Therefore, Stu's correct average is 84%
GRADE 7 POTW:
ReplyDeleteFirst: 75*6=450
Second: 93-39=54
Third: 450+54=504
Last: 504/6=84
Therefore his correct average should be 84%
Grade 7 POTW:
ReplyDeleteI think that the best and most simple way to do this was to get the total amount of marks that Stu got, and add the amount of marks that were supposed to be added from the math mark. Finally, I would divide the total by 6 to figure out his correct average.
Since the question already states the fact that there are six marks and the average is 75%, You can multiply these to numbers to get the total amount of marks that he got on his report card. But, since there are still the marks that I need to add because of the incorrect marking of math. So, I subtract the incorrect mark, which is 39%, from the correct mark, which is 93%. Therefore, I can now figure out the two numbers, add them together, and get Stu Dent's correct average.
Calculations:
The two numbers that I needed to multiply are 75 and 6.
75*6=450
The total amount of marks that Stu Dent received on his report card was 450.
The two math scores I need to find the difference of are 93 and 39.
Therefore,
93 - 39 = 54
The marks that were not given was an amount of 54.
Now, I can add the two numbers together, and divide it by 6, since 6 was the amount of different marks there were to figure out the average.
450 + 54 = 504
Stu Dent got a total of 504 marks.
504 / 6 = 84
84% is the correct average of Stu Dent's Report Card.
-Alan
This is how I went about solving the Grade 7 POTW #1:
ReplyDeleteSo since it is said that his overall average was 75%, we would have to multiply 75 by 6 because he was assessed on six things. After multiplying, we found that the product is 450. But the reason as to why his final mark was incorrect was because the teacher mixed up his mathematics mark. She wrote 39% when it was actually 93% which brought down is overall mark/average. So to correct his mark, we would need to subtract 39 from the 450 that we got earlier. This gives us a difference of 411. But to get his total marks, we would also need to add 93 to 411 which gives us 504. And our last step would be to divide 504 by 6 (the number of subjects), and that equals 84. Therefore, his mark is 84%.
Grade 7 POTW:
ReplyDeleteFirst we take the average (75) and multiply it by 6 to get 450. Then we subtract the incorrect 39 to get 411. Next the add the correct score 93 into 411 to get 504. Finally we divide it into 6 to get 84 which is the answer.
Stu Dent's correct average is 84%
Troubleshoot
ReplyDeletetesting
ReplyDeleteTroubleshoot.
ReplyDeleteTesting
ReplyDeleteThe answer is 84%
ReplyDeleteThe answer is 84%
ReplyDeletetroubleshoot
ReplyDeleteThe new average is 84%. What you do is multiply 75 by 6 to get 450. Then add the difference between 39 and 93 (54) and add that to 450 (504). Then divide that by 6 to get the new average (84%).
ReplyDeleteGrade 7 POTW:
ReplyDeleteI think that the best and most simple way to do this was to get the total amount of marks that Stu got, and add the amount of marks that were supposed to be added from the math mark. Finally, I would divide the total by 6 to figure out his correct average.
Since the question already states the fact that there are six marks and the average is 75%, You can multiply these to numbers to get the total amount of marks that he got on his report card. But, since there are still the marks that I need to add because of the incorrect marking of math. So, I subtract the incorrect mark, which is 39%, from the correct mark, which is 93%. Therefore, I can now figure out the two numbers, add them together, and get Stu Dent's correct average.
Calculations:
The two numbers that I needed to multiply are 75 and 6.
75*6=450
The total amount of marks that Stu Dent received on his report card was 450.
The two math scores I need to find the difference of are 93 and 39.
Therefore,
93 - 39 = 54
The marks that were not given was an amount of 54.
Now, I can add the two numbers together, and divide it by 6, since 6 was the amount of different marks there were to figure out the average.
450 + 54 = 504
Stu Dent got a total of 504 marks.
504 / 6 = 84
84% is the correct average of Stu Dent's Report Card.
-Alan
Stu Dent's correct average is 84
ReplyDeleteThe answer to the gr.8 potw is that mark needs to bowl 224 score an average. To get this you first need to find out how much other numbers there are. So what you need to do is subtract 178 from 199. This is 21. Then with the extra bowled score he has bowled 22 times. Then what to do is multiply 178 by 22 (3916). Then multiply 180 by 23 which would be his total score with 23 bowls (because of next bowl to get average(4140)). Subtract 3916 by 4140 (224) to get what he needs to bowl to average at 180.
ReplyDeleteThis is how I did the grade 8 POTW:
ReplyDeleteSince the average goes from 177 to 178, each time it increases by one. Since the number was 199, the extra that the number has to give away to the other numbers to make the correct average is 199 - 178 = 21.
This means that there are 21 other numbers, since the margin of the average was increasing by 1.
There will be 22 numbers in total.
The average is 178, so I multiply 178 by 22.
178 x 22 = 3916.
I also need the right total, which is 22 multiplied by 180.
180 x 22 = 3960.
Now, I figure out the difference between the two numbers.
3960 - 3916 = 44.
This is the extra amount of points I would need for an average of 180.
But, since this new number has to be 180 itself, so I add 180 with 44.
180 + 44 = 224.
The amount that Mark Striker would need to bowl is 224.
GRADE 7 POTW:
ReplyDeleteFirst what I did was multiply 75 by 6 and got 450. I did this because Stu dent got 6 marks and a supposed average of 75%. Normally to find an average we would get the sum of all the numbers (6) and then divide it by the amount of numbers we added. But since we already know the average and need to figure out the sum. So if we reverse the equation into 75x6 then we would get the sum.
Now since we have the sum we can work with the incorrect mark. As we know, Stu dent's previous mark was 39% but he realized it was actually 93%. In order to change that, we would first take away his mistaken mark. Meaning in, 450-39=411.Now since we took away that mark, we have to add in the correct mark(93). This means we would have to do 411=93=504.
The final step is to find the average with the new mark. So, we would simply divide 504 by 6 (504 is the sum, 6 is the amount of numbers added). If we do all these steps correctly then we should get 84% as his final average.
find the difference between the 2 marks
ReplyDelete- 93%
39%
= 54%
since its only 1 of the 6 marks for the average, divide by 6.
_9_
6/54
The average mark should have been 9% higher so add to the average
75%+9%=84%
Grade 7 POTW #1:
ReplyDeleteFirst you multiply his averages, 75 x 6 = 450. Then since his mathematics mark was 39% instead of 93%, we subtract 39 from 450, so 450 - 36 = 411. Now that we have done that, we have to add the correct mark which is 93. 411 + 93 = 504.
Now that we know what his new total is, now we have to find the new average. To find the average, you add all the numbers together which we have already done, followed by dividing that number by how many there are. So, 504 / 6 = 84.
Therefore, Stu Dent's correct report card average is 84%.
Grade 8 POTW:
ReplyDeleteLet x be the number of games bowled
177 * x = Total points
His last game = 199
His new average 178
So now we have x + 1 game and 177x + 199
So the new average is equal to the total points divided by x + 1
so...
(177x + 199)/(x+1) = 178
So now I just had to try plugging different numbers into the equation to find the answer, (I started at 15).
And eventually I came up with 21
(177 * 21 + 199)/(21+1) = 178
(3717 + 199)/(21+1) = 178
3916/(21+1) = 178
3916/22 = 178
178 = 178
Then...
180 * (22 + 1) - 3916
180 * 23 - 3916
4140 - 3916 = 224
So in order for Mark Striker to increase his average to 180 he needs to earn a 224 in the next round.
In order to find out the correct average, we have to backtrack on what Stu did to get the average then we can take out the mark that he inserted wrong and add the correct one in, after all that we can find out the average after the correct mark is in.
ReplyDeleteSo the first step is to multiply the average by 6 which is the number of marks Stu received.
75*6=450
Next we have to take out the wrong mark which is 39 and add the correct one in.
(450-39)+93=x
I simplified the equation and got this :)
411+93=x
Now, if I add the 93 we can get our x.
504=x
We aren't done yet! We have to finish what we started so just divide 504 by 6 and we will get the correct average.
504/6=y
84%=y
The average of Stu's six marks is 84%!
To solve the Grade 8 POTW I first looked at the question, to solve it I had to find out how many games he has played and his total scores, so I can find out what his total scores needs to be so he can reach an average of 180. To do this I need to take 177 and multiply it by GP (Games Played) then add 199, his newest score, and then dividing it by games played plus one, to include 199, and the output needs to be 178 for it to be correct. After several tries I found that 21 fits in for the number of games played,
ReplyDelete((177 x 21)+21)/22=178
Then I had to take 180 and and multiply it by 23 as this would be his 23rd game, then subtract it by, his old score total which would be (177x 21)+199 as this will give the points he needs to get in his next game to get an average of 180.
(177x 21)+199=3916
180x23=4140
4140-3916=224, He will need a score of 224 to get an average of 180
Wow, great work students. Make sure you show all your steps, and be sure to comment and ask your peers questions on this thread.
ReplyDeleteThe answer for POTW #1 Gr. 7 was in fact 84%. And for the Grade 8 POTW #1 it was a bowling score of 224.