few_shots: 
Example:
Concept/skill: 
Recognize and represent proportional relationships between quantities.

Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Answer: 
No. Usually problems that teach recognizing and representing proportional relationships between quantities involve deciding whether two quantities are in a proportional relationship or identifying the constant of proportionality, and then representing proportional relationships by equations or explaining proportional relationship using coordinate graphs.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_000972_neg_0

6
standard_description: Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
The purpose of this activity is for students to consider the numbers when they choose a strategy to find the value of a product. Some students might choose to use the same strategy for any multiplication problem. In this activity, the numbers were chosen to encourage students to choose different strategies in order to generate discussion about why certain multiplication problems lend themselves to different strategies.
When students choose a multiplication strategy based on the factors, using the associative and commutative properties of multiplication and the distributive property, along with known facts, they make use of structure to facilitate their calculations (MP7).
MLR7 Compare and Connect.
Lead a discussion comparing, contrasting, and connecting the different strategies students chose to solve the problems. Ask, “Are there any benefits or drawbacks to one strategy compared to another?” and “Why did the different approaches lead to the same outcome?”
Advances: Conversing
Launch
Groups of 2
“Sometimes we use different strategies to solve problems, depending on the numbers in the problem. Without solving, look at the numbers in each expression and think about the strategy you would use to find the value.”
1–2 minutes: quiet think time
“Choose 2 problems you would solve using a different strategy and describe the strategy to your partner. Explain why you chose different strategies.”
1–2 minutes: partner work time
Activity
“Find the value of each expression. If you find the value mentally, record the steps you used in your head to arrive at the product.”
5–10 minutes: independent work time
Monitor for students who used different strategies for the same problem. For example, for
\(14\times25\)
, some students might multiply
\(14\times20\)
and
\(14\times5\)
and some students might double 25 and halve 14 and find
\(7\times50\)
.
8–10 minutes: partner work time
Student Facing
Find the value of each expression. Explain or show your reasoning.
\(14\times3\)
\(14\times101\)
\(14\times25\)
\(14\times9\)
\(14\times136\)
Student Response
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Activity Synthesis
Invite students to share their strategies for finding the value of
\(14 \times 101\)
.
“Is there a mental strategy you can use to find the value of this product?” (Yes. I know
\(14 \times 100\)
is 1,400 and then I can add 14 to that.)
Invite students to share their strategies for finding the value of
\(14 \times 136\)
.
“Which strategy did you use to find the value of
\(14 \times 136\)
? Why?” (I used the standard algorithm because I did not see a quick mental strategy for finding the value.)


aligns: no