options: Explain volume formulas and use them to solve problems.

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

Define trigonometric ratios and solve problems involving right triangles.

Use coordinates to prove simple geometric theorems algebraically.

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

Understand similarity in terms of similarity transformations.

Find arc lengths and areas of sectors of circles.

Reason with shapes and their attributes.

Apply geometric concepts in modeling situations.

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

Make geometric constructions.

Understand congruence in terms of rigid motions.

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

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

Prove geometric theorems.

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

Analyze, compare, create, and compose shapes.

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

Apply trigonometry to general triangles.

Understand and apply the Pythagorean Theorem.

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

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

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

Understand and apply theorems about circles.

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

Prove theorems involving similarity.

Experiment with transformations in the plane.
problem_activity: Narrative
The purpose of this activity is to build towers with solid shapes and count how many solid shapes are in the tower. Students will need to think strategically about which shapes to use and their properties. For stacking shapes, it is important to have flat faces. Students may notice that spheres can not be used to build towers. Pyramids and cones can be used as the top of the tower, but nothing can be stacked on top of them. The purpose of the activity synthesis is to discuss the attributes of shapes and why students chose the shapes they did to build their towers.
MLR8 Discussion Supports.
During group work, invite students to take turns sharing their responses. Ask students to restate what they heard using precise mathematical language and their own words. Original speakers can agree or clarify for their partner.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Geoblocks
Solid shapes
Launch
Groups of 2
Give students access to solid shapes and geoblocks.
“Use solid shapes to make the tallest tower you can.”
3 minutes: independent work time
Activity
“Compare with your partner. How are your towers the same? How are they different?” (Sample response: We both used a lot of cubes. My tower has a point on top. My partner’s tower is taller.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“Write a number to show how many solid shapes you used in your tower.”
2 minutes: independent work time
“Did you or your partner use more solid shapes in their tower?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Student Facing
How many solid shapes did you use in your tower?
_______________
Activity Synthesis
Invite students to share their towers.
“What shapes did ____ use?” (There are some cubes and a pyramid on top.)
“How many shapes did ___ use?” (4)
“Did you use a sphere in your tower? Why?” (No. I could not put anything on top of it because it’s round. It rolled away because it’s round.)
“Did you use a cone in your tower?” (It worked at the very top but I could not put anything on top of the cone.)


correct_option_index: 16