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: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
problem_activity: Activity
This practice activity is similar to the last activity in the associated Algebra 1 lesson, except that students are asked to find specific information about the contexts before being asked to compare them.
To give students a greater opportunity to communicate their thinking verbally and listen to the reasoning of others, we recommend assigning each student to either work on function
\(m\)
or
\(p\)
for the first question, and then get together in groups of 2–4 to tackle the remaining questions.
Launch
Arrange students in groups of 2. In each group, one partner completes the first question for function
\(m\)
, and the other partner for function
\(p\)
. Then, partners should work together using the information they found in the first question to complete the remaining questions.
It’s a judgment call about whether to ask students to find the maximum of function
\(m\)
without a graphing calculator or provide access to graphing calculators. In the associated Algebra 1 lessons, there are times when students are asked to answer such a question without graphing.
Student Facing
Two objects are thrown into the air. The height of object M in meters is modeled by the function
\(m(x)=(5+10x)(1.5-x)\)
with
\(x\)
representing time in seconds. The height of object P in meters is modeled by the function
\(p\)
, represented by the graph.
[IMG]
For each object, determine:
the time at which the object hit the ground
the height from which the object was thrown
the maximum height of the object
the time at which the object reached its maximum height
Which object was launched from a greater height? Explain your reasoning.
Which object hit the ground first? Explain your reasoning.
Which object reached a greater maximum height? Explain your reasoning.
Student Response
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Activity Synthesis
Much of the conversation will take place within groups. Time permitting, invite students to create a visual display of their solutions and explanations. Give students an opportunity to review other groups’ work, and time to revise and refine their own work. If desired, select a few exemplary visual displays to keep posted in the classroom to support students in later lessons.


aligns: no