few_shots: 
Example:
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?


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

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, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_000972_neg_0

6
standard_description: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
problem_activity: Narrative
The purpose of this activity is for students to find areas of rectangles where one side is a whole number and the other side is a fraction that is greater than 1.  Students should solve the problems in a way that makes sense to them. Ask students to explain how the diagrams show the multiplication expressions.
Engagement: Provide Access by Recruiting Interest.
Synthesis: Optimize meaning and value. Invite students to share how they use the diagram to calculate the area of the desk or the garden and the method they used to do so with a classmate.
Supports accessibility for: Conceptual Processing, Attention
Launch
Groups of 2
Activity
5 minutes: individual work time
5 minutes: partner work time
Student Facing
Write a multiplication expression to represent the area of the shaded region.
[IMG]
What is the area of the shaded region?
Write a multiplication expression to represent the area of the shaded region.
[IMG]
What is the area of the shaded region?
Student Response
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Advancing Student Thinking
If students do not write multiplication expressions to represent the area of the shaded region, prompt them to explain how they found the area of the shaded region. Then, write expressions to represent the student’s strategy and ask, “How do these expressions represent your strategy?”
Activity Synthesis
Ask several students to share their responses to the second problem.
Display:
\(3 \times 3\frac{3}{4}\)
\(3 \times \frac{15}{4}\)
“How do these expressions represent the area of the shaded region?” (They are the width and length of the shaded region. In one, the length is a whole number and some fourths, and in the other, it is all fourths.)
“How is finding the value of these two expressions different?” (For the first one, I can multiply 3 by 3 and then 3 by
\(\frac{3}{4}\)
and add them together. For the second one, I can see how many fourths I have using multiplication.)


aligns: no