May Problem to Discuss

A cookie recipe calls for 2 1/2 cups of flour for every 1 cup of sugar. Damon has 10 cups of flour and 5 cups of sugar. How many full batches of cookies can he make? Will he have any flour or sugar left over?

  1. What do you notice about this problem?
  2. How could you solve this problem using only pictures?
  3. How would your students solve it?
  4. What would be the least amount of steps to solve this problem?
  5. What would be the most amount of steps to solve this problem?
  6. How could you make this problem easier?
  7. How could you make it more difficult?


Damon can make 4 full batches of cookies with 1 cup of sugar left over.

1. The numbers are easy to work with being multiples of 2 & 5.

2. Use blocks to represent the numbers--like Cuisenaire rods.

3. I would encourage them to use fractions.

4. 4??

5. Not sure did not go there.

6. use only whole numbers.

7. Use decimals.

Thank you for her response.  Would your learners be more inclined to use fractions or something else to solve this type of problem?  Where would they struggle?

No, my former students, I currently am a GED Tester-Evaluator, would avoid fractions like the plague. I would encourage them to increase their comfort level with fractions by exploring how easily some problems are solved using fractions. They usually struggle with higher level critical thinking skills and problem solving. Most would simply want to give up at the slightest hint of challenge from a problem.

1.  I notice that there are two ingredients that could be limiting factors.  I notice right away that this will be at least at least a 2 step problem (how many batches and how much of the ingredients are left.)

2. & 4.   You could use a bar to represent the total amount of each ingredient, label it like a number line and draw corresponding amounts for each batch under each bar.   This would show you can make 5 batches with the sugar and 4 batches with the flour.  This diagram would also show that you would have one batch (or 1 cup) of sugar left over.

I found it interesting that you noticed the limiting factors first.  I hadn't thought about that piece so that was an "ah-ha" for me.  I also like the use of a bar to represent the total.  I wonder if there was a way to use pictures to help find a solution. hmmm