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

Reason with shapes and their attributes.

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

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.

Understand similarity in terms of similarity transformations.

Apply geometric concepts in modeling situations.

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

Prove geometric theorems.

Apply trigonometry to general triangles.

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

Understand and apply theorems about circles.

Make geometric constructions.

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

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

Prove theorems involving similarity.

Analyze, compare, create, and compose shapes.

Understand congruence in terms of rigid motions.

Use coordinates to prove simple geometric theorems algebraically.

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.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.
problem_activity: Optional activity
In this optional activity, students use colored pencils (or pens or highlighters) to label the radius and height on different pictures of cylinders. Then they sketch their own cylinders and label the radius and heights of those. The purpose of this activity is for students to practice identifying the radius and height of various cylinders, some of which are in context.
This activity can also be abbreviated if students demonstrate prior understanding of how to draw or label cylinders and only need a brief refresh.
Launch
Distribute colored pencils. Give students 1–2 minutes of quiet work time followed by a whole-class discussion.
Student Facing
For cylinders A–D, sketch a radius and the height. Label the radius with an
\(r\)
and the height with an
\(h\)
.
[IMG]
Earlier you learned how to sketch a cylinder. Sketch cylinders for E and F and label each one’s radius and height.
Student Response
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Anticipated Misconceptions
In diagrams D and E, some students might mistake the diameter for the height of the cylinder. Some students may mark a height taller than the cylinder due to the tilt of the figure.
Activity Synthesis
Select students to share where they marked the radius and height and the cylinders sketched for images E and F. Discuss examples of other cylinders students see in real life.
Speaking, Listening: MLR3 Clarify, Critique, Correct.
Present an incorrect drawing that reflects a possible misunderstanding from the class about the height of a cylinder. For example, draw a cylinder with the diameter incorrectly placed at its height and the height at its diameter. Prompt students to identify the error, (e.g., ask, “Do you agree with the representation? Why or why not?”), correct the representation, and write feedback to the author explaining the error. This helps students develop an understanding and make sense of identifying the heights of differently-oriented cylinders.
Design Principle(s): Support sense-making; Maximize meta-awareness


correct_option_index: 0