Post a response explaining how you solved the problem and justify why your problem-solving strategy is the best one to use. The winner of the "Math Champ" title will be the student who can explain his or her strategy with the greatest clarity and detail. (Although you may prepare your answer at home you will not post your answers until Friday, in class.)
David's Response
A:
- Well, Ivan would sell the greatest amount of chocolate bars. Ivan already has double the chocolate bars of Sonia, and 5 days isn’t much to make progress, she would only have $28 in total (12+(4 x 4)=28), while Ivan would have $32 ($24+(4 x 2)=$32).The difference would be four, 32-28=4
- They would have the same same value of chocolate bars on the 7th day. For Ivan, it would be (24 + (2 x 6)=36) and for Sonia, it would be (12 + (4 x 6)= 36)
- Sonia’s total would be 10 more than Ivan’s total on the 12th day. Sonia’s total would be (12 + (4 x 11)=56) while Ivan’s would be (24 + (2 x 11)= 46). 56 is 10 more than 46. An easier way to do that would be when they both were at 36, on the 7th day, then Sonia would be (36 + (5 x 4)=56) and Ivan would be (36 + (5 x 2)=46) since Sonia had double the production capability, and since there were 5 days and Sonia produced $4 dollars every day (in five days she would make 4 x 5=$20) and Ivan made $2 (in five days he would make 2 x 5=$10).
Day
|
Sonia’s Money made for that day
|
Ivan’s Money made for that day
|
Sonia’s Total
|
Ivan’s Total
|
1
|
$12
|
$24
|
$12
|
$24
|
2
|
$4
|
$2
|
$16
|
$26
|
3
|
$4
|
$2
|
$20
|
$28
|
4
|
$4
|
$2
|
$24
|
$30
|
5
|
$4
|
$2
|
$28
|
$32
|
6
|
$4
|
$2
|
$32
|
$34
|
7
|
$4
|
$2
|
$36
|
$36
|
8
|
$4
|
$2
|
$40
|
$38
|
9
|
$4
|
$2
|
$44
|
$40
|
10
|
$4
|
$2
|
$48
|
$42
|
11
|
$4
|
$2
|
$52
|
$44
|
12
|
$4
|
$2
|
$56
|
$46
|
My strategy:
My strategy was to make a table of what Ivan and Sonia made every day, and I listed all the days that needed for my calculations, and I also listed the amount of money that each person made each day, as well as their total with it. I calculated this doing it with multiplication, then checking it with the chart. I then used the information I had and confirmed it with 2 references, my list of days and the amount of money, as well as the multiplication. I could have used the multiplication, then the list as a reference, but I found that sometimes when you list things out, you can avoid some tiny calculations that you might not think out clearly when you don’t write it down.It was the best because it was efficient, didn't take much time but it was really detailed. I showed everything I did, and I showed the math clearly. That is why my strategy was the best. (It says to explain why yours is the "best", I wouldn't say mine was the "best" if I didn't need to)
What is an iMuse?
ReplyDeleteIMUSE (Interactive Music Streaming Engine) is an interactive music system used in a number of LucasArts video games. The idea behind iMUSE is to synchronize music with the visual action in a video game so that the audio continuously matches the on-screen events and transitions from one musical theme to another are done seamlessly.
ReplyDeletewow thats really cool!
ReplyDeleteIt sounds like a new apple product. Lol.
ReplyDeleteI thought that they were just make believe things that sounded like a apple product...
ReplyDelete2014.10.28.
ReplyDeleteMath P.O.W.
Chock Full o’ Chocolates
By: Eileen
For their school’s recent fundraiser, Ivan sold $24 worth of white chocolate almond bars on the first day, and $2 worth each day thereafter. Sonia sold $12 worth of caramel crunchies on the first day, and $4 worth each day thereafter. The person who sells the most wins an iMuse.
a) If the campaign ran for 5 days, who sold the greater value of chocolate, and how much greater was the total?
Ivan sold the greater value of chocolates. He sold $32, and Sonia sold $28 worth of chocolate. I figured that out this way: I added the amount that they sold on the first day with the amount that they sold on the other days. To figure that out, I multiplied the number of remaining days (4) times 2 for Ivan, and 4 for Sonia.
b) Suppose the campaign is extended, and each person continues to sell at the same rate. On which day would they both have sold the same value of chocolate bars?
On the seventh day they will both have sold the same value of chocolate bars. I know that because after I knew that the fifth day would be $32 for Ivan, and $28 for Sonia, I added the sixth day, which was $34 for Ivan, and $32 for Sonia (see strategy above). On the seventh day, Ivan would have $36, and Sonia would too.
c) On what day will Sonia’s total be $10 greater than Ivan’s?
Sonia would have $10 more than Ivan on the twelfth day of sales.
I know because, as I figured out in question b), on the seventh day, Sonia and Ivan’s totals will be equal. So from then on Sonia will sell 2 dollars more per day than Ivan. To get $10 dollars, you would therefore divide 10 by 2, and get 5 more days to add on to the seven days that we have already.
Why my strategy is the best:
I think that I used the least amount of steps I could, in order to show how I got the answers. I still think that I showed a lot of detail, and explained my thinking well. I think that my strategy is short, and easy to figure out, and do, and that when I showed how I get my answer I was thorough. I also think that my answers were easy to read, and comprehend. Overall, I feel that I did the best that I could.
Bibliography:
http://mathamaniapi.blogspot.ca/
That is all.
Thank you, thank you very much.
~Eileen
I think that the way I figured out the problem was the easiest and fastest way to figure it out. What you can do is make a table that has rows for each day you will need. each day add 2 dollars to Ivan’s total profit, and 4 to Sonia’s. You will get the answer to question a), b), and c). This is pretty much the clearest way to explain it without just saying “make a chart”. For people that can’t do mental math it works. It also shows the way I did it. finally this strategy is organized and there is really no way to go wrong on it. It is not trial and error. So that is why I think that the strategy that I used is the fastest, easiest and over all BEST way to do the math pow! Now the real question is: who one the Imuse? DUN DUN DUN!!!
ReplyDeleteHappy Halloween! ☻( I wrote this earlier)
-Ronan
Ivan sold 24$ worth of chocolate on the first day, 2$ worth on every other day (4. if the campaign ran for 5 days), so 2 x 4 + 24 = 32$ Ivan sold 32$ worth of chocolate in the week. Sonia sold 12$ worth of chocolate on the first day, and 4$ worth of chocolate on every other day (4, if the campaign ran for 5 days), so 4 x 4 + 12 = 28$
ReplyDeleteIf the campaign for 5 days, Ivan sold the greater value of chocolate by 4, with him having sold 32$ worth of candy, and Sonia having sold 28$ worth of candy.
The amounts increase like this (days in order):
Ivan: 24, 26, 28, 30, 32, 34, 36
Sonia: 12, 16, 20, 24, 28, 32, 36
Day: 1 2 3 4 5 6 7
on day 7 they would have sold the same value of chocolate bars (32$)
The amounts increase like this (days in order)
Ivan: 36, 38, 40, 42, 44, 46
Sonia: 36, 40, 44, 48, 52, 56
Day: 7 8 9 10 11 12
on day 12 Sonia’s total would have been 10$ more than Ivan’s (Sonia:56 Ivan:46)
My problem-solving strategy is the best (my opinion) because it is the simplest, only having to add numbers 2 and 3 (which is basic kindergarten knowledge) only about 7 times! That’s really simple! Its really short, simple, and I don’t understand why anyone would make it more complicated than this. That, is why I think that my problem-solving strategy is the best!
Below Ivan: and Sonia: It says day, the numbers go with the amount of money
Deletea.) Ivan: To figure this Question out quickly multiply 2 by 5 giving you 10 dollars add ten to 24 and you get 34.
ReplyDeleteSonia: Same with this question you simply multiply 4 by 5 which is 20, 20 plus 12 is 32 dollars, which means the difference money wise between Sonia and Ivan's sales are 2 dollars
b.) On the sixth day Ivan and Sonia will get the same value: Day six Ivan: 34+2=36.
Day six Sonia: 32+4=36. therefore they will reach the same value on day six
c.) Day seven Sonia: 36+4=40 Ivan: 36+2=38
Day eight Sonia: 40+4=44 Ivan: 38+2=40
Day nine Sonia: 44+4=48 Ivan: 40+2=42
Day ten Sonia: 48+4=52 now it is ten dollars greater but we need to count Ivan: 42+2=44
Day eleven Sonia: 52+4=56 Ivan: 44+2=46 There! therefore Sonia’s total will be 10 dollars greater on day eleven.~~~~Daniel Poradzisz
I used a bit of algebra for this question. As it says in the question, Ivan sells $24 dollars worth of chocolate on the first day and $2 worth each day afterwards. So that means that each day the worth of chocolate increases by $2 each day. So to find out the worth of chocolate sold the next day you do $24 + $2= $26. But it keeps increasing by 2 each day so you can not keep doing $24 + $2. You can add 2 to 26 and then add 2 to that but I want to find out the worth of chocolate in 5 days and I don’t want to keep adding 2 to that number because it takes a long time.
ReplyDeleteI put d for day. And I remembered the 2n -1 formula for patterns that we learned with the David’s B-day question. I replaced the n with d and then replaced that with 2 for the second day. 2x2-1= 3 and that doesn’t really work. I thought that it doesn’t work because the pattern starts at 24, not 1 or 0. I keep trying other rules that are similar to that one until I come up with something like d - 1 then multiply by 2 and add that to 24. I knew that 24 was the 1st term and you always add 2. Like the input output, I was trying to find out how to go from d to the dollars worth of chocolate. For example: how to go from 1 to 24. the rule that I came up was -1 x2 +24. It was a 3 step one!
I tried that with 2 to 26 and it worked! My new rule/formula was (d-1) x 2+24. So I (Ivan) = (d-1) x 2+24. Then I made a similar rule for Sonia: (d-1) x 4+12. The pattern started with 12 and increased by 4 each time. So I thought that I might have a similar input, output rule: -1 x4 +12.
I used those rules to help me with many of my questions. For a) I did I= (5-1)x 2+24= $32 and S= (5-1) x 4+12= $28. Ivan sold the most by $4 (32-28=4).
For b) I got that on the 7th day they would of sold the same value of chocolate bars. I started from the 6th day since they said if the campaign extended; and kept using that rule until I got the same result from both of them.
6th day: I= (6-1)x 2+24= $34 and S= (6-1)x 4+12= $32. NOPE
7th day: I= (7-1)x 2+24= $36 and S= (7-1)x S= 4+12= $36 YESSS!
For c) I used trial and error like the last question. I tried from the 8th day since as I found out in the last question: that`s when Sonia caught up with Ivan with value. The other times Sonia was lower than Ivan. Anyway my answer for this question is that on the 12th day Sonia`s total will be greater by $10 than Ivan`s.
8th day= I= (8-1)x 2+24= $38 and S= (8-1)x 4+12= $40. $40-$38= $2
9th day= I= (9-1)x 2+24= $40 and S= (9-1)x 4+12= $44. $44-$40= $4
10th day= I= (10-1)x 2+24= $42 and S= (10-1)x 4+12= $48. $48-$42= $6
11th day= I= (11-1)x 2+24= $44 and S= (11-1)x 4+12= $52. $52-$44= $8
12th day= I= (12-1)x 2+24= $46 and S= (12-1)x 4+12= $56. $56-$46= $10! YAY!
My strategy might not the easiest but I think that in some ways it was one of the best strategies. I think that my strategy is the best because it helps you with algebra, with a bit of input, output machines, order of operations and patterning. It also helps because one day you might get harder problems and you can`t keep adding or multiplying and this way would be the fastest way. Also for me, this way is actually less confusing and more organized since you don't keep having to add and you might get the numbers mixed up which happens to me a lot. For me this one is the best, but everybody thinks differently and have different opinions and for some people, keeping adding 2 or another strategy might be easier.
I handed in the acual POW in class. This is how I got the answers:
ReplyDeleteThis is how I solved the Math Problem of the week:
First of all, in order to answer part A, I made two charts; one for Ivan, and one for Sonia, with the sub-title “Day,” under which I listed the days on which they had sold the chocolate bars (in numbers, eg. 1,2,3,4,5). The other sub-title was “Money Made,” under which I listed how much money Ivan or Sonia had made on the given day. To answer the question, I added up the numbers under the “Money Made” column (separately) for Ivan and Sonia. In the end, I found out that Ivan had more money than Sonia. Ivan had $32, while Sonia had $28. To find out how much more money Ivan had I subtracted Sonia’s total from Ivan’s total. The money left over was $4. That answered how much more money Ivan had made, because $28 + $4 = $32. So, Ivan had four more dollars than Sonia.
To answer part B, I extended the chart that I had made earlier by adding two more rows (well, actually, I had accidently put two more rows when I first drew it, and I had decided not to erase them). I filled out the rows, and then added the money from those two rows to the previous total. I figured out that, on the seventh day, Ivan had $36 and Sonia had $36. So, that was the day when they both had the same amount of money.
To answer part C, I added five more rows to both of the charts (it turns out I didn’t need the fifth). I then filled them out. Next, I added the money from these rows to the previous totals, one row at a time. Eventually, I got to the eleventh row, and once I had added up the totals, I realized that, on the eleventh day, Sonia had $52 dollars, and Ivan had $42. This meant that it was on that day that Sonia had ten more dollars than Ivan, because $42 + $10 = $52. Therefore, Sonia had $10 more than Ivan on that day.
I think that my strategy is the best one to use because the concept of the T-chart is very straight forward, and also, once you have your numbers laid out in a neat, organized fashion, it is very easy to think the problem through in a methodical way, and you only need to make a few small and basic calculations. No calculators are required.
-Sara
a ) Ivan: $2 x 4 days = $8 in four days, and $8 + $24 on the first day = $32 for his 5 days he sold chocolate.
ReplyDeleteSonia: $4 x 4 days = $16 in four days, and $16 + $12 on the first day = $28 for her 5 days she sold chocolate.
Ivan- $32 for the five days.
Sonia- $28 for the 5 days.
Ivan had sold 4 more dollars worth of chocolate, because $32 - $28 = $4, and Ivan got the iMuse
b ) Ivan- 32, 34, 36
Sonia- 28, 32, 36
Ivan and Sonia would both earn $36 dollars on the seventh day if they both sold the same amount every day.
c ) Sonia- 36, 40, 44, 48, 52, 56
Ivan- 36, 38, 40, 42, 44, 46
Sonia will have raised $10 more on the 12th day, also if they they sold the same amount every day.
Strategy: To figure out this math P.O.W., I used patterning (like start at 24 and add 2 four more times), we did a test on Tuesday, so I wanted to include it in my math P.O.W. and because I saw it.
I figured out a) by adding 4 and 2 to 12 and 24. I used addition because I thought it would be faster.
ReplyDeleteI figured out b) by putting the number of days and how much each person raised in that day. I used that strategy because I thought it was the best way to figure out the question.
For c) I used the same strategy as b) because I thought that it was a good strategy for both of the questions.
My strategy to solve this week’s math P.O.W, was to make a 3-column chart. Mt chart had the number of days selling chocolates, Sonia’s money and Ivan’s money. I think my strategy was the best because, when I need to find out for example, how much Ivan got on day 8, well I can quickly look at the day, (which I know is on the left hand side) and go across the column to his money, and see that it is 38$. Also since I made the chart at the beginning, it was easy to see the answers to A, B, and C on the math P.O.W. So that is why I think my strategy is the best, it gives me all the information I need, gives the information clearly, and gives me the answers quickly for my math P.O.W.
ReplyDeleteFor question a), the best way to figure out the answer is to multiply $2 (“$2 worth thereafter”) by 4 days. (“the campaign ran for five days” minus the first day.) Then, add the $24 from the first day.
ReplyDelete2 x 4 = 8 8 + 24 = 32
That means that Ivan sold $32 worth of chocolate bars.
Now for Sonia, multiply $4 (“$4 worth each day thereafter”) by 4 days. Then, add the $12 from the first day.
4 x 4 = 16 16 + 12 = 28
That means that Sonia sold $28 worth of chocolate bars.
Since 32 minus 28 equals 4, that means that Ivan sold 4 more chocolate bars than Sonia.
For question b), you would take 28 and add 4, and take 32 and add 2, and count how many times you have to do that until both the numbers are the same.
28 + 4 = 32 32 + 4 = 36
(1) (2)
32 + 2 = 34 34 + 2 = 36
On the second day of the extension they both will have sold the same value of chocolate bars.
For question c), you have to do the same thing as in b), accept you don’t stop until Sonia’s total is $10 more than Ivan’s.
36 + 4 = 40 40 + 4 = 44 44 + 4 = 48 48 + 4 = 52 52 + 4 = 56
(3) (4) (5) (6) (7)
36 + 2 = 38 38 + 2 = 40 40 + 2 = 42 42 + 2 = 44 44 + 2 = 46
On the second day of the extension Sonia’s total will be $10 greater than Ivan’s.
If the campaign ran for 5 days, who sold the greater total value of chocolate bars, and how much greater was the total?
ReplyDeleteI think the best way to solve a) is to just multiply. For Ivan, you add 24 + 2 but multiply 2 by the number of days. But subtract 1 from the number of days, because we have already counted the first day. So it is Day 5, but subtracting 1 we know now to multiply 2 by 4. So 24 + 2 x 4 = 32. Ivan sold a $32 value of chocolate bars. For Sonia, you add 12 + 4 and do the same with 4. Multiply by 4, because we already counted the first day. 12 + 4 x 4 = 28. Sonia sold a $28 value of chocolate bars. Ivan sold the greater total value of chocolate bars, and sold it $4 greater than Sonia. We have done something similar in class with one of our math questions, something to do with planes...
Suppose the campaign is extended, and each person continues to sell at the same rate. On which day would they both have sold the same value of chocolate bars?
I think the best day to solve b) is to just continue counting along. From a), we can just start from Day 5. And the total value of chocolate bars are not far apart so I don’t think you have to count for long. On Day 6, Ivan had the value of $34 (32 + 2) and Sonia had the value of $32 (28 + 4). And on Day 7, Ivan had the value of $36 (34 + 2) and Sonia had the value of $36 (32 + 4). So the seventh day is the day they would both have sold the same value of chocolate bars.
On what day will Sonia’s total be $10 greater than Ivan`s?
I think the best way to probably figure out this is just to add 5 more days to Ivan’s and Sonia’s value. And $10 more, equals 5 days more ($2 x 5 days = $10). Add 5 more days from 7 days for Sonia, she her value of chocolate bars will raise $20 more ($4 x 5 days = $20). After 5 days have passed, it will be Day 12. Ivan will have a $46 value, earning $10 more to his value from Day 7 ($36). Sonia will have a $56 value, earning $20 more to his value from Day 7 ($36). In conclusion, Day 12 is the day that Sonia's value will $10 more than Ivan's.
This comment has been removed by the author.
ReplyDeleteMath P.O.W. - Chock full o' Chocolates
ReplyDeleteBy: Natalie Nusca Due: 2014.10.31.
If the campaign ran for 5 days, who sold the greater value of chocolate bars, and how much greater was the total?
If the campaign ran for 5 days, Ivan sold the greater value of chocolate bars.
Ivan sold $32 total, worth of chocolate bars, and Sonia sold $28 total, worth of
chocolate bars.
Ivan raised $4 more than Sonia.
I got this answer by starting at $24 (which is Ivan’s total on the first day) then added $8 (which is $2 each day thereafter x 4 because the campaign runs for 5 days total) which then = $32 total.
Then I did the same with Sonia. I started with $12 (which is Sonia’s total on the first day) then added $16 (which is $4 each day thereafter x 4 because they campaign runs for 5 days) which then = $28 total.
Suppose they campaign is extended, and each person continues to sell at the same rate. On which day would they both have sold the same value of chocolate bars?
If they campaign is extended, and each person continues to sell at the same
rate, on the 7th day, Ivan and Sonia would have sold the same value of chocolate bars, which is $36.
I got this answer by starting on the 5th day, (which is the actual end of the campaign) and adding $2 onto Ivan’s total each day, and $4 onto Sonia’s total each day, until Ivan and Sonia had the same value of chocolate bars which is 36$.
On what day will Sonia’s total be $10 greater than Ivan’s?
On the 12th day, Sonia’s total will be $10 greater than Ivan’s.
Sonia’s total would be $56, and Ivan’s total would be $46.
I got this answer by starting on the 7th day, (which is the day when they both had
the same value of chocolate bars) then adding $2 onto Ivan’s total each day, and
$4 onto Sonia’s total each day, until Sonia’s total was $10 greater than Ivan’s
total.
For all my answers I also used a chart to help me:
Day Ivan Sonia
1st Day - $24 $12
2nd Day - $26 $16
3rd Day - $28 $20
4th Day - $30 $24
5th Day - $32 $28
6th Day - $34 $32
7th Day - $36 $36
8th Day - $38 $40
9th Day - $40 $44
10th Day - $42 $48
11th Day - $44 $52
12th Day - $46 $56
NOTE! IMPORTANT TO ADD ON FOR MY MATH POW!
ReplyDeletea)Also, the difference between the two values of chocolate was $4, Ivan had $32 and Sonia had $28, which would make the difference be 4 (32-28=4). Sorry I forgot to include that in my actual post.
Also sorry for cap locks.
DeleteAlso, forgot to post this, I explained my strategy but didn't say why it was the best, it was the best because it was efficient, didn't take much time but it was really detailed. I showed everything I did, and I showed the math clearly. That is why my strategy was the best. (It says to explain why yours is the "best", I wouldn't say mine was the "best" if I didn't need to)
ReplyDeleteAnswer:
ReplyDeleteKaren’s rule is start at 1024, divide by 2/halve each time.
Riley’s rule is start at 111, subtract 12 each time.
Karen‘s pattern will reach a term smaller than 10 first.
Math/Explanation:
First I thought the tables were actually input/output machines, so I spent some time on that. Then I realized that it wasn’t, so all I had to do is find out the differences. Karen’s pattern was pretty easy. 1000 ÷ 2 was 500, and 24 ÷ 2 is 12. 1024 ÷ 2 = 512.
Riley’s pattern is also easy. 111 - 11 =100, and 111 - 12 = 99. 99 - 12 = 87.
Now for the last question. I think that Karen’s pattern will reach below 10 first, because since she is dividing by 2 instead of subtracting 11, the term will decrease faster.
And it did. In Karen’s pattern, it took only 8 terms to reach below 10. In Riley’s, it would have taken 11 extra terms to reach below 10, or 10 to reach 10.
Karen Riley
1024 111
512 99
256 87
128 76
64 65
32 54
16 43
8 32
I think that my strategy was the best (or at least good) because all you really need to do is divide or subtract. It's kind of long, but it can be easily shortened. And it is pretty easy so you don't need to make this weird long formula and spend a while to try to figure out how to do it.