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Bake Sale


Alignments to Content Standards: 6.NS.B.4

Task

  1. Lindy is having a bake sale. She has 48 chocolate chip cookies to put in bags. How many bags can she fill if she puts the same number in each bag and uses them all? Find all the possibilities. Explain your reasoning.
  2. Lindy has 64 vanilla wafer cookies to put in bags. How many bags can she fill if she puts the same number in each bag and uses them all? Find all the possibilities. Explain your reasoning.
  3. How many bags can Lindy fill if she puts the chocolate chip cookies and the vanilla wafers in the same bags? She plans to use all the cookies and wants to include an equal number of chocolate chip cookies and an equal number of vanilla wafers in each bag. Explain your reasoning.
  4. What is the largest number of bags she can make with an equal number of chocolate chip cookies and an equal number of vanilla wafers in each bag (assuming she uses them all)? Explain your reasoning.

IM Commentary

This problem uses the same numbers and asks essentially the same mathematical questions as "6.NS Factors and Common Factors," but requires students to apply the concepts of factors and common factors in a context. A version of this task could be adapted into a teaching task to help motivate the need for the concept of a common factor.

Solution

  1. 1, 2, 3, 6, 8, 12, 16, 24, 48.
    The number of bags she can make are shown in the table:
    Number of CC cookies in each bag 12346 812162448
    Number of bags 482416128 64321
    Since the number of cookies that goes in a bag is a factor of the total number of cookies, all the factors of 48 are listed in the first row of the table. Each column corresponds to a situation where the 48 cookies are divided equally among some bags, and the product of the numbers in each column is 48. The number of bags is also a factor of the total number of cookies.
  2. 1, 2, 4, 8, 16, 32, 64.
    Number of vanilla wafers in each bag 1248163264
    Number of bags 6432168421
    Since the number of cookies that goes in a bag is a factor of the total number of cookies, all the factors of 64 are listed in the first row of the table. Each column corresponds to a situation where the 64 cookies are divided equally among some bags, and the product of the numbers in each column is 64. The number of bags is also a factor of the total number of cookies.
  3. 1, 2, 4, 8, 16
    Since the number of bags must be a factor of both 48 and 64, the common factors of 48 and 64 represent all the possibilities for the number of bags she can make. The table below shows these possibilities along with the number of each kind of cookie that would go in each bag.
    Number of bags 124816
    Number of CC cookies in each bag 48241263
    Number of vanilla wafers in each bag 64321684
  4. Looking at the table from the third part of this solution, we see that the largest number of bags she can make corresponds to the largest common factor, which is 16 in this case. If there are 16 bags, there will be 3 chocolate chip cookies and 4 vanilla wafers in each.

Susie says:

about 4 years

This is a simple, yet relevant task. It is exactly the type of problem we have on our state tests. I like it! Thank you for sharing it.

jmirabel says:

over 6 years

I like these questions, but I think part c should include a statement similar to the other parts regarding the fact that Lindy uses all the cookies. Otherwise, you could have two other combinations than what is listed: 32 bags (1CC cookie and 2 Vanilla) and 48 bags (1 cookie of each type).

Kristin says:

over 6 years

That's a very good suggestion. I reworded part C to include that.

cherila says:

almost 5 years

removed