options: Prove geometric theorems.

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

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

Apply geometric concepts in modeling situations.

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

Understand and apply the Pythagorean Theorem.

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

Explain volume formulas and use them to solve problems.

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

Understand similarity in terms of similarity transformations.

Define trigonometric ratios and solve problems involving right triangles.

Apply trigonometry to general triangles.

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

Understand and apply theorems about circles.

Reason with shapes and their attributes.

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

Use coordinates to prove simple geometric theorems algebraically.

Make geometric constructions.

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

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

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

Understand congruence in terms of rigid motions.

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

Analyze, compare, create, and compose shapes.

Prove theorems involving similarity.

Translate between the geometric description and the equation for a conic section.
problem_activity: Activity
The purpose of this activity is for students to apply the formula for area of a circle to solve a problem in context. The diameter of the circle is given, so students must first determine the radius.
Launch
Display this image of table top for all to see. Ask students, “What do you notice? What do  you wonder?”
[IMG]
Quiet work time followed by a whole-class discussion.
Student Facing
Elena wants to tile the top of a circular table. The diameter of the table top is 28 inches. What is its area?
Student Response
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Student Facing
Are you ready for more?
A box contains 20 square tiles that are 2 inches on each side. How many boxes of tiles will Elena need to tile the table?
Student Response
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for free access to Extension Student Response.
Anticipated Misconceptions
Students may square the diameter, forgetting that they need to determine the radius first.
Activity Synthesis
Invite students to share their strategies for finding the area of the tabletop. After 3 students have shared their strategies, ask the class what formula all of the students used for finding the area of a circle. Record and display this formula,
\(A = \pi r^2\)
, for all to see. Here,
\(A\)
is the area of the circle, and
\(r\)
is the radius of the circle.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Prior to the whole-class discussion, invite students to share their work with a partner. Display sentence frames to support student conversation such as: “First, I _____ because….”, “I noticed _____ so I….”, “Why did you...?”, and “I agree/disagree because….”
Supports accessibility for: Language; Social-emotional skills


correct_option_index: 16