As the students initially worked in their “unified” groups (where they were all working on the same Version), they were instructed to write down their thinking about why it made sense for them to solve it the way they did. At the end of class, we collected what they wrote about strategies for MARK and strategies for ALISHA, and have the following examples to share:
Jennifer’s Response for MARK
These rates can tell Mark which ice-cream is the better buy because even though a 64 oz for $6.79 is more costly, you still get more ounces. Plus, you’re only paying a difference of about .2 . Therefore, the difference in ounces is about 15. So, he should pick 48 oz for $4.69.
Jennifer’s Response for ALISHA
Yes, Alisha is correct because she just found another way to find unit price. She did the opposite of Mark and, using the numbers she got, if you multiply them by the price, you get about the correct total ounces.
Cameron’s Response for MARK
$.01 more per ounce, it would be to buy the 64 ounce. So the 64 ounce is a better buy.
Cameron’s Response for ALISHA
She is correct because they are the same.
Heather’s Response for MARK
This can tell me which is better because it tells you the unit rate for each ounce.
Heather’s Response for ALISHA
Yes, Alisha is correct because she still got the unit price for one ounce. I know it is the unit price because if I multiply 10.234… it would equal almost 48 and the same for the other one.
Daniel’s Response for MARK
They can tell Mark which ice cream is the better buy because he just found out how much 1 ice cream costs for each situation, the lower cost is the best buy.
Daniel’s Response for ALISHA
Yes, she is because her answer shows how many ounces you can get for 1 dollar, the most ounces is the better buy.
Alicia’s Response for MARK
The 48-ounce package is a better buy because if you find the price for one ounce, the 48 ounce only costs about 9.8 cents per ounce, but the 64-ounce costs about 10.6 cents per ounce.
Alicia’s Response for ALISHA
Alisha could have used a proportion to solve this problem because if the answer to the proportion costs more than the price of the 48-oz package, the 48-oz package is cheaper than the other package
Matt’s Response for MARK
Matt could divide the 64 oz price by 64 ounces (6.79 ÷ 64) to get the price per oz, about ($.11). Then he could do the same thing with the 48 oz (4.69 ÷ 48 = about $.10 ). The 48 oz is the better buy
Matt’s Response for ALISHA
Alicia could have found the least common multiple of the oz (48 and 64) , which is 192. With 48, 192 is the 4th number, so she had to multiply 48 by 4. Since 64 x 3 is 192 as well, the oz are worked out. To get the price in relation, she had to multiply 4.69 by 4 and 6.79 by 3. The 48 oz has the better buy.
Dustin’s Response for MARK
ArrowHe can tell wich is a better buy by seeing how much it costs per ounce. He can do that by deviding the cost by ounces.
Dustin’s Response for ALISHA
Alisha could have used proportions to solve this problem because she could see how much the 48 ounce one was if they were equal.
Lily’s Response for MARK
We think the $4.69 (48-ounce) package of ice cream is a better deal because it should only cost $6.25 for a 64-ounce package. Since 1 lb. = $1.56 it’s overpriced by about 54 cents. It’s a small matter but it’s still unfair priced.
Lily’s Response for ALISHA
No, she is not correct, because you would get a completely different answer that goes into negative numbers. We got 9.425… for 64 / 6.79 and 10.234… for 48 / 4.69 . These are completely different numbers and they would not be even to Problem #1
Analiese’s Response for MARK
We think that $4.69 is a better ice cream deal because it should cost $1.56 per pound and their is 3 pounds of ice cream. It should only cost $6.25 for a 4 pounds of ice cream and it is over priced by 54¢
Analiese’s Response for ALISHA
No, this is not correct, because when you are dividing a smaller number into a larger number you will be going into the negatives. We got 9.425… for 64 / 6.79 and for 48 / 4.69 we got 10.234… into the negatives.
