few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response:
Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Measure lengths indirectly and by iterating length units.

Convert like measurement units within a given measurement system.

Geometric measurement: understand concepts of angle and measure angles.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Describe and compare measurable attributes.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Tell and write time.

Classify objects and count the number of objects in each category.

Work with time and money.

Measure and estimate lengths in standard units.

Represent and interpret data.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Relate addition and subtraction to length.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
problem_activity: Narrative
In this activity, students learn how to use a protractor. They align a protractor to the vertex and a ray of an angle so that its measurement can be read. The given angles are oriented in different ways, drawing students’ attention to the two sets of scales on a protractor. Students need to consider which set of numbers to pay attention to and think about a possible explanation for when or how to use each scale. Moreover, one of the scales is only marked in increments of 10 degrees so if students use this scale they need to reason carefully about the precise angle measure (MP6).
This activity uses
MLR1 Stronger and Clearer Each Time. Advances: reading, writing.
Action and Expression: Internalize Executive Functions.
Invite students to estimate the size of the angle before finding each precise measurement. Offer the sentence frame: “This angle will be greater than _____ and less than _____. It will be closer to _____.”
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Attention
Launch
Groups of 2–4
Activity
5 minutes: independent work time
2–3 minutes: group discussion
Monitor for students who find each measurement by:
looking for the scale with a ray on
\(0^\circ\)
and counting up on that scale
subtracting the two numbers (on the same scale) that the rays pass through
MLR1 Stronger and Clearer Each Time
“Share your response to the last problem with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3–5 minutes: partner discussion
Repeat with 2–3 different partners.
“Revise your initial draft based on the feedback you got from your partners.”
2–3 minutes: independent work time
Student Facing
Here are four angles whose sizes you may have estimated earlier. A protractor has been placed over each angle. Measure the size of each angle in degrees.
[IMG]
[IMG]
[IMG]
[IMG]
Elena and Kiran are measuring an angle with a protractor. Elena says the angle is
\(80^\circ\)
. Kiran says it shows
\(100^\circ\)
. Why might they end up with different measurements? Which one is correct? Explain your reasoning.
[IMG]
Student Response
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click here to register or sign in
for free access to Student Response.
Activity Synthesis
Select students who used different strategies to share their responses and reasoning.
Display the image of Elena and Kiran’s angle. If no students mentioned that
\(80^\circ\)
is not possible because the angle clearly appears greater than a right angle (
\(90^\circ\)
), consider asking how Elena can use what she knows about right angles to think about her measurement.


correct_option_index: 2