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

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

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

Define trigonometric ratios and solve problems involving right triangles.

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

Prove geometric theorems.

Analyze, compare, create, and compose shapes.

Understand and apply theorems about circles.

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

Use coordinates to prove simple geometric theorems algebraically.

Understand congruence in terms of rigid motions.

Reason with shapes and their attributes.

Experiment with transformations in the plane.

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

Understand similarity in terms of similarity transformations.

Explain volume formulas and use them to solve problems.

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

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

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

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

Understand and apply the Pythagorean Theorem.

Make geometric constructions.

Find arc lengths and areas of sectors of circles.

Apply geometric concepts in modeling situations.

Prove theorems involving similarity.

Apply trigonometry to general triangles.

Understand congruence and similarity using physical models, transparencies, or geometry software.
problem_activity: Warm-up
This warm-up reviews the volume work students had done previously to prepare for the work in this lesson. It reinforces the idea of using unit cubes and fractional-unit cubes as a way to measure the volume of a rectangular prism.
Launch
Give students 2–3 minutes of quiet work time. Follow with a class discussion.
Student Facing
How many cubes with an edge length of 1 inch fill this box?
[IMG]
If the cubes had an edge length of 2 inches, would you need more or fewer cubes to fill the box? Explain your reasoning.
If the cubes had an edge length of
\(\frac 12\)
inch, would you need more or fewer cubes to fill the box? Explain your reasoning.
Student Response
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Activity Synthesis
Select several students to share their responses and reasoning. After each person explains, ask students to indicate whether they agree. To involve more students in the discussion, consider asking:
“Who can restate ___’s reasoning in a different way?”
“Does anyone want to add on to _____’s reasoning?”
“Do you agree or disagree with the reasoning? Why?”
Tell students that they will use their understanding of the volume of rectangular prisms to solve other geometric problems.


correct_option_index: 0