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: Write, read, and evaluate expressions in which letters stand for numbers.
problem_activity: Warm-up
Students reflect on equivalent expressions that represent the area of a shaded rectangle which is part of a larger rectangle of unknown width.
Launch
Allow students 2 minutes of quiet work time, followed by a whole-class discussion.
Student Facing
A rectangle with dimensions 6 cm and
\(w\)
cm is partitioned into two smaller rectangles.
Explain why each of these expressions represents the area, in cm
2
, of the shaded region.
\(6w-24\)
\(6(w-4)\)
[IMG]
Student Response
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Activity Synthesis
Ask students to share their reasoning.
\(6w-24\)
should be straighforward: the area of the entire rectangle is
\(6w\)
, and the area of the unshaded portion is
\(6 \boldcdot 4\)
or 24, so the area of the shaded portion is
\(6w-24\)
.
Students may have more trouble with
\(6(w-4)\)
. The key is to understand that the longer side of the shaded portion can be represented by
\(w-4\)
.
[IMG]


aligns: yes