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?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response:
Thought: This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Prove geometric theorems.

Explain volume formulas and use them to solve problems.

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

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Experiment with transformations in the plane.

Apply geometric concepts in modeling situations.

Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

Understand similarity in terms of similarity transformations.

Understand and apply theorems about circles.

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

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

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Reason with shapes and their attributes.

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

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

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

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

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

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

Make geometric constructions.

Understand and apply the Pythagorean Theorem.

Find arc lengths and areas of sectors of circles.

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

Use coordinates to prove simple geometric theorems algebraically.

Analyze, compare, create, and compose shapes.
problem_activity: Task
Let $C$ be a circle with center $O$ and a diameter meeting $C$ in points
$P$ and $S$ as shown below:
[IMG]
With straightedge and compass, show how to find  a point $Q$ on $C$ so that triangle $OPQ$ is equilateral.
Repeating part (a) show how to find points $R, T, U$ on $C$ so that
$PQRSTU$ is a regular hexagon.
Find the area of $PQRSTU$.  How does it compare to the area of $C$?


correct_option_index: 21