few_shots: 
Example:
Concept/skill: 
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Answer: 
Yes. This task asks students to compare two fractions that are equal. The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_task_000212_pos_0

4
standard_description: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)
problem_activity: Warm-up
The purpose of this warm-up is for students to use repeated reasoning to write an algebraic expression to represent a rule of a function (MP8). The whole-class discussion should focus on the algebraic expression in the final row, however the numbers in the table give students an opportunity to also practice calculating the square of numbers written in fraction and decimal form.
Launch
Arrange students in groups of 2. Give students 1–2 minutes of quiet work time and then time to share their algebraic expression with their partner. Follow with a whole-class discussion.
Student Facing
Fill in the table of input-output pairs for the given rule. Write an algebraic expression for the rule in the box in the diagram.
[IMG]
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "input"}, {"_attributes": {"scope": "col"}, "_value": "output"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "8"}, {}]}, {"td": [{"_value": "2.2"}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "40402"}, "_value": "\\(12\\frac14\\)"}]}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "833"}, "_value": "\\(s\\)"}]}, {}]}]}]}]}
Student Response
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Activity Synthesis
Select students to share how they found each of the outputs. After each response, ask the class if they agree or disagree. Record and display responses for all to see. If both responses are not mentioned by students for the last row, tell students that we can either put
\(s^2\)
or
\(A\)
there. Tell students we can write the equation
\(A = s^2\)
to represent the rule of this function.
End the discussion by telling students that while we’ve used the terms input and output so far to talk about specific values, when a letter is used to represent any possible input we call it the
independent variable
and the letter used to represent all the possible outputs is the
dependent variable.
Students may recall these terms from earlier grades. In this case,
\(s\)
is the independent variable and
\(A\)
the dependent variable, and we say “
\(A\)
depends on
\(s\)
.”


aligns: yes