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:
{
  "explanation": "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: Apply trigonometry to general triangles.

Understand similarity in terms of similarity transformations.

Analyze, compare, create, and compose shapes.

Prove geometric theorems.

Make geometric constructions.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Understand congruence in terms of rigid motions.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Translate between the geometric description and the equation for a conic section.

Reason with shapes and their attributes.

Prove theorems involving similarity.

Explain volume formulas and use them to solve problems.

Find arc lengths and areas of sectors of circles.

Define trigonometric ratios and solve problems involving right triangles.

Use coordinates to prove simple geometric theorems algebraically.

Visualize relationships between two-dimensional and three-dimensional objects.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Understand and apply theorems about circles.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Classify two-dimensional figures into categories based on their properties.

Apply geometric concepts in modeling situations.

Solve real-world and mathematical problems involving area, surface area, and volume.

Experiment with transformations in the plane.

Understand and apply the Pythagorean Theorem.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
problem_activity: Narrative
The purpose of this activity is for students to begin to distinguish rectangles from other shapes. By working with variants and non-examples of rectangles, students begin to develop their understanding of what makes a shape a rectangle. When they discuss which group a shape should be placed in, students informally describe the attributes of the shape.
MLR8 Discussion Supports.
Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frames for all to see: “I noticed _____, so I matched . . . .” Encourage students to challenge each other when they disagree.
Advances Conversing, Listening
Required Materials
Materials to Copy
Rectangle Sort Cards
Required Preparation
Cut out rectangle cards from the blackline master. Each group of 4 needs 1 set of cards.
Launch
Groups of 4
Give each group a set of cards.
Draw or display a rectangle:
[IMG]
“Tell your partner two things you know about this shape.” (There are 4 sides. It looks like a door. It is a rectangle. It is long and flat.)
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
If needed, ask “What is the name of this shape?”
30 seconds: quiet think time
“This shape is a
rectangle
.”
Activity
“Work with your group to sort the shapes into two groups. Put the shapes that are rectangles on the left side of your page. Put the shapes that are not rectangles on the right side of your page. When you place a shape, tell your group why you think the shape belongs in that group.”
4 minutes: small-group work time
“Write a number to show how many shapes are in each group.”
1 minute: independent work time
“Which group has fewer shapes? How do you know?”
30 seconds: quiet think time
30 seconds: partner discussion
Student Facing
Let’s put the shapes into 2 groups.
Rectangle
[IMG]
[IMG]
[IMG]
Not a Rectangle
[IMG]
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students put shapes other than rectangles into the group of rectangles, consider asking:
“How did you choose which group to put this shape in?”
“What is alike, or the same, about all of the shapes in this group?”
Activity Synthesis
Invite 1–2 groups to share how they sorted the shapes.
Draw or display a square:
[IMG]
“Which group did you put this shape in?” (We put it with the rectangles because it has 4 sides. We didn’t put it with the rectangles because it is a square.)
“This shape is a
square
, which is a special rectangle because all four sides are the same length.”


correct_option_index: 2