few_shots: 
Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

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_001097_pos_0

7
standard_description: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
problem_activity: Task
The table below shows some input-output pairs of two functions $f$ and $g$ that agree for the values that are given but some of their output values are missing.
{"table": [{"tbody": [{"tr": [{"th": [{"_value": "$t$"}], "td": [{"_value": "0"}, {"_value": "15"}, {"_value": "30"}, {"_value": "45"}, {"_value": "60"}, {"_value": "75"}, {"_value": "90"}, {"_value": "105"}, {"_value": "120"}]}, {"th": [{"_value": "$f(t)$"}], "td": [{"_value": "0"}, {"_value": "0.5"}, {}, {"_value": "1.3"}, {"_value": "2"}, {"_value": "2.7"}, {}, {"_value": "4"}, {}]}, {"th": [{"_value": "$g(t)$"}], "td": [{"_value": "0"}, {"_value": "0.5"}, {}, {"_value": "1.3"}, {"_value": "2"}, {"_value": "2.7"}, {}, {"_value": "4"}, {}]}]}]}]}
Complete the table in a way so that $f$ could be invertible and so that $g$ is definitely not invertible.
Graph both functions and explain from the graph why $f$ is invertible and $g$ is not.
Come up with two real life situations that $f$ and $g$ could be representing.
Find and interpret the value $f^{-1}(4)$ in terms of these contexts.


aligns: no