options: Understand and apply theorems about circles.

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

Experiment with transformations in the plane.

Find arc lengths and areas of sectors of circles.

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

Prove geometric theorems.

Reason with shapes and their attributes.

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

Prove theorems involving similarity.

Understand congruence in terms of rigid motions.

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

Apply geometric concepts in modeling situations.

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

Analyze, compare, create, and compose shapes.

Apply trigonometry to general triangles.

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.

Understand and apply the Pythagorean Theorem.

Use coordinates to prove simple geometric theorems algebraically.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Explain volume formulas and use them to solve problems.

Understand similarity in terms of similarity transformations.

Make geometric constructions.

Solve real-world and mathematical problems involving area, surface area, and volume.
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: 12