The central mathematical idea behind the three versions of this task is to determine which of two products is
the better buy: A 64-ounce container of ice cream selling for $6.79 or a 48-ounce container of ice cream
selling for $4.69.
Mark and Alisha were sent to buy ice cream for a class party.
Their favorite flavors came in a 64-ounce package for $6.79
and a 48-ounce package for $4.69.
- To find which is the better buy, Mark divided like this:
Explain how these ratios can tell Mark which ice cream
is the better buy. - Alisha claimed she could use different ratios to solve
this problem. She divided like this:
Is Alisha correct? Explain your answer.
Mark and Alisha were sent to buy ice cream for a class party.
Their favorite flavors came in a 64-ounce package for $6.79
and a 48-ounce package for $4.69.
- How can Mark tell which is the better buy?
- After looking at Mark’s work, Alisha claimed she could
use a different way to solve this problem. What might
Alisha have done?
Mark and Alisha were sent to buy ice cream for a class party.
Their favorite flavors came in a 64-ounce package for $6.79
and a 48-ounce package for $4.69.
- To find which is the better buy, Mark divided like this:
- Explain how these ratios can tell Mark which ice cream
is the better buy. - Alisha claimed she could use different ratios to solve
this problem. She divided like this:
- Is Alisha correct? Explain your answer.
You can also find:
Printable forms of the three Versions
Our comments on why we chose these three Versions, and some of our initial questions about how
students might respond before we ever tried this in class.
Version 1 provides a dollars-per-ounce strategy for Mark as well as an ounces-per-dollar strategy for Alisha. The correct result for each calculation is also provided. On the surface it would seem to be easy for students who had an understanding of unit rates. But would students actually recognize the meaning behind those calculations, and further, would they understand the interpretations of the results? Note how the directions emphasize students providing an explanation for what Mark and Alisha did. We were especially curious if either of the two strategies (Mark’s or Alisha’s) seemed easier than the other for students to grasp.
If Version 1 can be seen as providing the most information, then Version 2 certainly provides the least information. What kinds of strategies might students come up with for Mark, we wondered? Also, how readily might they come up with a strategy for Alisha that was different from the strategy they used for Mark?
Version 3 is identical to Version 1, except that the results of the division calculation are omitted. On the one hand, we thought students might just do the computation and end up with the same kinds of analysis that would be required on Version 1. On the other hand, we guessed correctly that some students might use the ratio set-up to enact other strategies, such as finding a least common multiple.
