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: 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
First, students examine several examples of functions and non-functions from the perspective of “Can we figure out . . . ?” Then, they decide which of the functions can be represented by a given expression.
Launch
Allow quiet think time to consider the situations in the first question and answer yes or no. Ensure students understand which ones are functions, and which are not. Then, give students time to complete the table.
Student Facing
For each question, answer yes or no.
It is 50 miles to Tucson. Can we figure out how many kilometers it is to Tucson?
It is 200 kilometers to Saskatoon. Can we figure out how many miles it is to Saskatoon?
A number is -3. Can we figure out its absolute value?
The absolute value of a number is 8. Can we figure out the number?
A circle has a diameter of 8 cm. Can we figure out its circumference?
A circle has a circumference of
\(10\pi\)
cm. Can we figure out its diameter?
A square has a side length of 6 units. Can we figure out its perimeter?
A rectangle has a perimeter of 30 meters. Can we figure out its width?
Which of the relationships are functions?
For each function definition in the table, match it with the situation, write a statement explaining which variable depends on which, and write an example using function notation. An example is done for you.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "function definition"}, {"_attributes": {"scope": "col"}, "_value": "situation"}, {"_attributes": {"scope": "col"}, "_value": "statement"}, {"_attributes": {"scope": "col"}, "_value": "example"}]}]}], "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "23857"}, "_value": "\\(m(x) = 0.62x \\)"}]}, {"_value": "You know kilometers and want to find miles."}, {"_value": "Distance in miles depends on distance in kilometers, or, distance in miles is a function of distance in kilometers."}, {"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "23898"}, "_value": "\\(m(100)=62\\)"}]}]}, {"td": [{"p": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "23943"}, "_value": "\\(f(x) = x \\boldcdot \\pi\\)"}]}, {}]}, {}, {}, {}]}, {"td": [{"p": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "23991"}, "_value": "\\(g(x) = 1.6x\\)"}]}, {}]}, {}, {}, {}]}, {"td": [{"p": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "24038"}, "_value": "\\(h(x) = 4x\\)"}]}, {}]}, {}, {}, {}]}, {"td": [{"p": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "24087"}, "_value": "\\(k(x) = |x|\\)"}]}, {}]}, {}, {}, {}]}]}]}]}
Student Response
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Activity Synthesis
Invite students to share their responses in the table, and how they know. Emphasize that there are many correct examples one could choose—the thing to understand is how function notation communicates an input and output to the function (or a value of the independent variable and corresponding value of the dependent variable.)


aligns: no