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: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
problem_activity: Narrative
The purpose of this activity is for students to use diagrams to reason about products of a whole number and a non-unit fraction with diagrams, building on their work with diagrams that represent products of a whole number an a unit fraction. They begin to generalize that the number of shaded parts in a diagram that represents
\(n \times \frac{a}{b}\)
is
\(n \times a\)
and to explain that generalization (MP8).
Launch
Groups of 2
“Let's represent some other products of a whole number and a fraction and find their values.”
Activity
“Take a few quiet minutes to work on the activity. Afterwards, share your responses with your partner.”
5–7 minutes: independent work
2–3 minutes: partner discussion
Monitor for the strategies students use to reason about the last two problems.
Identify students who reason visually (using diagrams), additively, and multiplicatively to share in the synthesis.
Student Facing
This diagram represents
\(\frac{2}{5}\)
.
[IMG]
Show how you would use or adjust the diagram to represent
\(4 \times \frac{2}{5}\)
.
What is the value of the shaded parts in your diagram?
This diagram represents
\(\frac{5}{8}\)
.
[IMG]
Show how you would use or adjust the diagram to represent
\(3 \times \frac{5}{8}\)
.
What is the value of the shaded parts in your diagram?
Find the value of each expression. Draw a diagram if you find it helpful. Be prepared to explain your reasoning.
\(2 \times \frac {1}{6}\)
\(2 \times \frac{4}{6}\)
\(2 \times \frac {5}{6}\)
\(4 \times \frac{5}{6}\)
Mai said that to multiply any fraction by a whole number, she would multiply the whole number and the numerator of the fraction and keep the same denominator. Do you agree with Mai? Explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Discuss the four multiplication expressions in the third problem.
Select 1–2 students who might have drawn diagrams for all expressions.
“How does your diagram show the value of
\(2 \times \frac{4}{6}\)
?” (There are 2 groups of
\(\frac{4}{6}\)
, so there are 8 sixths shaded, which is
\(\frac{8}{6}\)
.)
Select 1–2 students who drew a diagram for some expressions and reason numerically for others.
“Why did you choose to draw a diagram for some expressions and to do something else for others?” (After drawing the first two diagrams, I realized that I'd have to draw a lot of groups or parts, so I thought about the numbers instead.)
Select 1–2 students who reasoned about all expressions numerically.
“How did you find the value of the expressions without drawing diagrams at all?” (I saw a pattern in earlier problems, that we can multiply the whole number and the numerator of the fraction and keep the denominator.)
Discuss the last problem in the lesson synthesis.


aligns: no