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I’m struggling a bit with this standard. The example given is to use pictures and create a story to match (2/3) x 4 = 8/3. I”m not seeing how this relates to the start of the standard which seems to ask that students show that (2/3) x 4 = 2 x (4 x 1/3). Or, equivalently, that (2/3) x 4 = 2 x (4 ÷ 3). What are students actually expected to do?
For a story you could use the one in the progression:
Ron and Hermione have 4 pounds of Bertie Bott’s Every Flavour Beans. They decide to share them 3 ways, saving one share for Harry. How many pounds of beans do Ron and Hermione get?
You could talk this through as follows: “If you share 4 pounds among 3 people, each gets 4÷3, and then Ron and Hermione have 2×(4÷3) altogether.”
For a picture, you could use a tape diagram marked 0, 1, 2, 3, 4, take one third of each unit interval to get a division of 4 into 3 equal parts, then take 2 of each of those thirds to get “2 parts of a partition of 4 into 3 equal parts”. (Easier to draw than to describe; the figure should look something like the one in the progression that is used to show (2/3)×(5/2).
I am just wondering if you are also looking for students to create story problems and draw pictures for the equivalent sequence a x q/b. Such as, Ron had 4 pounds of Every Flavour Beans and Harry had twice as much as Ron. If Harry divided his beans between 3 people, how much would each person get? Thank you.
Multiplying fractions by whole numbers occurs in the previous grade, Grade 4. See 4.NF.4. And yes, 4.NF.4c is about story problems, and has an example of one. Your story problem seems to be more about $(a \times q)/b$ than $a \times (q/b)$. That is, we seem to double Ron’s beans before sharing, not after. Note that neither 5.NF.4a nor 4.NF.4c requires students to construct story problems, although that’s a good idea.
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