options: Understand similarity in terms of similarity transformations.

Use coordinates to prove simple geometric theorems algebraically.

Prove geometric theorems.

Apply geometric concepts in modeling situations.

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

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

Analyze, compare, create, and compose shapes.

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

Experiment with transformations in the plane.

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

Understand and apply theorems about circles.

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

Understand congruence in terms of rigid motions.

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

Make geometric constructions.

Understand and apply the Pythagorean Theorem.

Reason with shapes and their attributes.

Apply trigonometry to general triangles.

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

Prove theorems involving similarity.

Explain volume formulas and use them to solve problems.

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

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

Define trigonometric ratios and solve problems involving right triangles.

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

Find arc lengths and areas of sectors of circles.

Solve real-world and mathematical problems involving area, surface area, and volume.
problem_activity: Optional activity
In this activity, students take the triangle they selected in the previous activity and use it as the base of their triangular prism. After students have drawn their net and before they cut it out and assemble it, make sure they have correctly positioned their bases, opposite from each other on the top and bottom of the rectangle and reflected. It will also make assembling the net easier for students if they draw lines subdividing the large rectangle into the individual rectangular faces and draw tabs where the faces will be glued or taped together.
Launch
Demonstrate the positions triangles should attach to the rectangle to form a net by displaying an example and describing the important parts:
The triangles must have a vertex at
\(A\)
and
\(C\)
.
The triangles must be identical copies with one “upside down” from the other.
Corresponding sides of each triangle must be along the side of the rectangle.
[IMG]
Engagement: Internalize Self Regulation.
Check for understanding by inviting students to rephrase directions in their own words. Provide a project checklist that chunks the various steps of the activity into a set of manageable tasks.
Supports accessibility for: Organization; Attention
Student Facing
Your teacher will give you an incomplete net. Follow these instructions to complete the net and assemble the triangular prism:
Draw an identical copy of the triangle you selected in the previous activity along the top of the rectangle, with one vertex on point
\(A\)
.
Draw another copy of your triangle, flipped upside down, along the bottom of the rectangle, with one vertex on point
\(C\)
.
Determine how long the rectangle needs to be to wrap all the way around your triangular bases. Pause here so your teacher can review your work.
Cut out and assemble your net.
After you finish assembling your triangular prism, answer these questions. Explain or show your reasoning.
What is the volume of your prism?
What is the surface area of your prism?
Stand your prism up so it is sitting on its triangular base.
If you were to cut your prism in half horizontally, what shape would the cross section be?
If you were to cut your prism in half vertically, what shape would the cross section be?
Student Response
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Activity Synthesis
Select students to share their answers for the cross sections. For cross sections taken in these two ways, all triangular prisms should have the same shapes as answers although the actual size of the cross section will differ based on the size of the base triangle and the height of the prism.
The volume and surface areas will depend on the triangle they have chosen to use as their base.
Select students to share their methods for computing volume and surface area. The base area is important in the calculation of each, so students should use the values they computed in the previous activity.
Writing, Speaking, Listening: MLR1 Stronger and Clearer Each Time.
Use this routine to provide students a structured opportunity to refine their methods for calculating the volume of their prisms. Give students time to meet with 2–3 partners, to share and get feedback on their responses. Provide students with prompts for feedback that will help them strengthen their ideas and clarify their language. For example, “What did you do first?”, “What was your base?”, “Can you draw a picture?” Give students 1–2 minutes to revise their writing based on the feedback they received.​
Design Principle(s): Optimize output (for explanation)


correct_option_index: 18