options: Use coordinates to prove simple geometric theorems algebraically.

Reason with shapes and their attributes.

Find arc lengths and areas of sectors of circles.

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

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

Define trigonometric ratios and solve problems involving right triangles.

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

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

Understand and apply the Pythagorean Theorem.

Understand congruence in terms of rigid motions.

Explain volume formulas and use them to solve problems.

Experiment with transformations in the plane.

Understand similarity in terms of similarity transformations.

Make geometric constructions.

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

Prove theorems involving similarity.

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

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

Prove geometric theorems.

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

Apply geometric concepts in modeling situations.

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

Understand and apply theorems about circles.

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

Analyze, compare, create, and compose shapes.

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

Apply trigonometry to general triangles.
problem_activity: Warm-up
The purpose of this warm-up is for students to reason about the various measurements of a circle. In each of the pictures, students are given a piece of information about the circle and asked to reason about the other measurements of the circle. Some of these measurements can be found based on the given information while others, without a calculator, would require an estimate.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet think time followed by 2 minutes to discuss their estimates with a partner.
Student Facing
Here are some pictures of circular objects, with measurement tools shown. The measurement tool on each picture reads as follows:
Wagon wheel: 3 feet
Plane propeller: 24 inches
Sliced Orange: 20 centimeters
[IMG]
For each picture, which measurement is shown?
Based on this information, what measurement(s) could you estimate for each picture?
Student Response
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Activity Synthesis
For each picture, ask selected students to share the measurements shown in the pictures. Ask students to explain the strategies or calculations they would use for computing or estimating other measurements (for example, the radius and circumference of the wheel). Record and display student responses on the actual pictures. Refer to MLR 2 (Collect and Display) to highlight student responses and language about what they know and what they estimated.


correct_option_index: 4