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

Understand congruence in terms of rigid motions.

Define trigonometric ratios and solve problems involving right triangles.

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

Reason with shapes and their attributes.

Apply trigonometry to general triangles.

Apply geometric concepts in modeling situations.

Analyze, compare, create, and compose shapes.

Understand similarity in terms of similarity transformations.

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

Understand and apply theorems about circles.

Understand and apply the Pythagorean Theorem.

Experiment with transformations in the plane.

Prove geometric theorems.

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

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

Make geometric constructions.

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

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

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

Find arc lengths and areas of sectors of circles.

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

Use coordinates to prove simple geometric theorems algebraically.

Explain volume formulas and use them to solve problems.

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

Prove theorems involving similarity.

Visualize relationships between two-dimensional and three-dimensional objects.
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: 21