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

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

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

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

Prove theorems involving similarity.

Make geometric constructions.

Define trigonometric ratios and solve problems involving right triangles.

Understand and apply the Pythagorean Theorem.

Prove geometric theorems.

Understand and apply theorems about circles.

Use coordinates to prove simple geometric theorems algebraically.

Explain volume formulas and use them to solve problems.

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

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

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

Apply geometric concepts in modeling situations.

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

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

Understand congruence in terms of rigid motions.

Analyze, compare, create, and compose shapes.

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

Experiment with transformations in the plane.

Understand similarity in terms of similarity transformations.

Reason with shapes and their attributes.

Apply trigonometry to general triangles.

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

Find arc lengths and areas of sectors of circles.
problem_activity: Warm-up
The purpose of this activity is for students to practice sketching spheres and labeling the radius and diameter of the sphere.
Launch
Give students 1–2 minutes of quiet work time, followed by a whole-class discussion.
Student Facing
Here is a method for quickly sketching a sphere:
Draw a circle.
Draw an oval in the middle whose edges touch the sphere.
[IMG]
Practice sketching some spheres. Sketch a few different sizes.
For each sketch, draw a radius and label it
\(r\)
.
Student Response
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Activity Synthesis
Invite students to share their sketches. Ask students to share what the diameter would look like if they did not already draw one in. Remind students that sketches can be used to help visualize a problem where an image might not be provided. In today’s lesson, they will be working with activities that might or might not have images provided and they should sketch or label any images provided to use as a tool to help understand the problem thoroughly.


correct_option_index: 2