Last week, as many students discovered, the correct answer was 2.6cm^2. There were a few ways to solve it. The most common method was to subtract the area of the triangle from the area of the circle. If you did not get the same answer, can you see or think of why? Take a minute to try and solve the problem again, in a different way.
Your intermediate teachers also want to thank you sincerely for a WONDERFUL field trip to LEEF on Monday. We had a wonderful time seeing you all participate and challenge yourselves.
Now, please post your comments to this week's POTW below:
Calista Zeng wrote:
ReplyDeleteFirst, I added all of the marbles together ( minus the white).
3 + 5 + 2 + 6 = 16
Next, I added the amount of black marbles to gold marbles. I also divided this number by 2 to get
the number in which the numerator and denominator were divided by to simplify the fraction.
3 + 5 = 8 8 ÷ 2 = 4
Next, I multiplied 4 by 7 to get the new denominator. I also subtracted the total of the marbles (
minus the white) from the new number.
4 x 7 = 28 28 – 16 = 12
Therefore there are 12 white marbles.
First, I found out how many black and gold marbles there are in total, so 3+5, therefore there are 8 black and gold marbles (our numerator). Now, I add all the marbles together to get a denominator. 8+2+6=16 marbles in total. 8/16=4/8=2/4=1/2. So before, half the marbles were black and gold. Now, I need to know how much would be 1/7, so I divide 8 by 2, getting 4. There, I multiply 4 by 7 to see the new denominator, 28, the new amount of marbles. Lastly, I subtract 28 by 16 to find out the amount of white marbles, 12. Therefore, Raynor Schein added 12 white marbles to the bag.
ReplyDeleteTo get my answer I calculated the possibility of getting a black or gold marble which is (5 + 3) / (5 + 3 + 6 + 2) = 8/16. I made a chart to see how the possibility of getting a black or gold marble changes when added a certain amount of white marble.
ReplyDeleteAdded White Marbles | Possibility for Black or Gold
__________________________________________
0 8/16=1/2
1 8/17
2 8/18=4/9
3 8/19
6 8/22=4/11
8 8/24=1/3
10 8/26=4/13
12 8/28= --> 2/7 <--
I made this chart by adding the amount of white marbles added to the denominator of the 8/16 which was the possibility in the beginning. In the end, I came to a conclusion that 12 white marbles was added so that the possibility of getting a gold or black marble is 2/7
To answer this question, I first found out how many marbles there were in total originally. 3+5+2+6=16. To find the amount of gold and black marbles together, I added 3=5 to get 8. I divided this number by 2 to get 4, and then multiplied 7x4 to get 28. So there were 28 marbles after the white marbles were added. To find how many white marbles were added, I subtracted 16 from 28. 28-16=12. Therefore, 12 white marbles were added to the bag.
ReplyDeletetest
ReplyDelete3 black marbles + 5 gold marbles + 2 purple + 6 red = 16 marbles in total
ReplyDeleteBlack + Gold marbles = 8 marbles
8 ÷ 4 = 2 so if the chance is 2/7, the other number must be 28 (7x4)
28 (new amount) - 16 (old amount) = 12 new marbles (new meaning white marbles)
Raynor added 12 white marbles
The first thing I did to make the question easier, was write out all the date in a table (which I cant post here) I then re read the question and quickly figured out the process I had to follow:
ReplyDeleteTo start of the question, I first added up all the known marbles like so: 3 black marbles + 5 gold marbles + 2 purple + 6 red = 16 marbles in total. I also, added up the black and gold marbles together seperatley, receiving an amount of 8 (golden and black together) marbles in total. I now knew that if the numerator were to be 2, I would have to make the denominator 28. To do this I would need to take 7 and multiplie it by 4. I then took the total amount of marbles and took it away from 24 giving me 12. This means that he found 12 white marbles
Daniel K wrote:
ReplyDelete"Work
3 black marbles + 5 gold marbles + 2 purple marbles + 6 red marbles= 16 marbles
black marbles and gold marbles= 8/16=½
8 divided by 2 = 4
4x7= 28
8/28=2/7
28-12=16
He added 16 marbles to the bag"
Aparna wrote:
ReplyDeleteHe added 12 white marbles to the bag. To solve this I first found the total number of marbles he had before he added the white ones. 3+5+6+2= 16.Then I found out how many black and gold marbles were there. 3+5=8 black and gold marbles. Because the probability of getting a black or gold marble is 2/7, I divided 8 by 2 (numerator) and got 4. I multiplied 4 by 7 (denominator) which equals 28 so now I know there were 28 marbles in the bag after he added the white marbles. finally, I subtracted 16 from 28 to get 12. therefore he found 12 white marbles.
There are 12 white marbles. I got this by, first finding the total amount of marbles before white was added, so that was 3+5+2+6=16, then i found black+gold(3+5)=8, so the fraction was 8/16 or 1/2(but i only worked with 8/16), now what i had to do was find the common numerator between before(8/16) and after(2/7), this was because no matter how many times u changed the total of the marbles, the amount for black+gold would always be the same, so to do that, i cross multiplied 2 by 4 to 8 and multiplied the denominator by 4 as well, this gave me 8/28 versus 8/16, because 8 was the numerator for both fractions, i just cut it out and subtracted the totals, or denominators, 28-16=12, so there were 12 white marbles
ReplyDeleteDaniel P wrote:
ReplyDelete"3+5+2+6=16
Gold and black=8(2/7 probability of getting gold or black after adding white marbles)
8 divided by 2=4(1/7)
4x7=28(total amount of marbles after adding white)
28-16=12(amount of white marbles added to the bag)"
3+5+2+6=16
ReplyDelete3+5=8 8/2=4
4x7=28 28-16=12
12 white marbles were added to the collection