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

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

Apply geometric concepts in modeling situations.

Prove theorems involving similarity.

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

Apply trigonometry to general triangles.

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

Understand congruence in terms of rigid motions.

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

Prove geometric theorems.

Understand similarity in terms of similarity transformations.

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

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).

Define trigonometric ratios and solve problems involving right triangles.

Make geometric constructions.

Understand and apply the Pythagorean Theorem.

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

Understand and apply theorems about circles.

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

Use coordinates to prove simple geometric theorems algebraically.

Experiment with transformations in the plane.

Find arc lengths and areas of sectors of circles.

Explain volume formulas and use them to solve problems.

Analyze, compare, create, and compose shapes.

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

Reason with shapes and their attributes.
problem_activity: Narrative
The purpose of this activity is for students to build and compare flat and solid shapes. Students are not expected to build precise shapes. Using clay to build the shapes helps students feel the difference between flat and solid shapes. The terms “flat” and “solid” are introduced in the activity synthesis. Students may benefit from getting to hold and see the solid shapes up close as they build them.
Required Materials
Materials to Gather
Clay
Required Preparation
Each student needs a piece of clay.
Gather a cone and cylinder to display.
Launch
Groups of 2
Give each student a piece of clay.
“Use your clay to make a shape that you know.”
1 minute: independent work time
“Share your shape with your partner. How are they the same? How are they different?” (The shapes are different. I made a circle and my partner made a triangle.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Activity
Display a cylinder.
“Make this shape with your clay.”
2 minutes: independent work time
Display a cone.
“Make this shape with your clay.”
2 minutes: independent work time
“Describe the shape that you made to your partner. What does it look like?” (It looks like an ice cream cone. It’s tall. It has a point on the bottom.)
30 seconds: quiet think time
2 minutes: partner discussion
Share responses.
Student Response
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Activity Synthesis
Display a group of flat shapes and a group of solid shapes that students created.
“What is different about the shapes that we made first and the rest of the shapes that we made?” (The shapes that we made first are all flat. The other shapes stick up.)
“The first shapes that we made were flat shapes, like circles and rectangles. Then we built some other shapes. What can we call these shapes?” (solid shapes, big shapes)
“These shapes are solid shapes.”
“Use your clay to make a flat shape.”
“Use your clay to make a solid shape.”


correct_option_index: 13

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