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

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

Understand congruence in terms of rigid motions.

Define trigonometric ratios and solve problems involving right triangles.

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

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

Understand and apply the Pythagorean Theorem.

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

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply theorems about circles.

Experiment with transformations in the plane.

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

Understand similarity in terms of similarity transformations.

Explain volume formulas and use them to solve problems.

Apply geometric concepts in modeling situations.

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

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

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

Reason with shapes and their attributes.

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

Prove theorems involving similarity.

Prove geometric theorems.

Make geometric constructions.

Analyze, compare, create, and compose shapes.

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

Graph points on the coordinate plane to solve real-world and mathematical problems.
problem_activity: Narrative
In this warm-up, students practice identifying obtuse angles in an image. They may, for instance, rely on the symmetry of the figure or on a grouping strategy, or otherwise scan the figure in a methodical way.
Launch
Groups of 2
“How many angles do you see? How do you see them?”
Display the image.
1 minute: quiet think time
Activity
Display the image.
“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Student Facing
How many angles do you see in the folded paper heart?
[IMG]
Student Response
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Activity Synthesis
“How did you make sure all the angles are accounted for?”(I put a mark through them or numbered them.)
“How many obtuse angles are in this image?” (10)
Label each obtuse angle with reasoning from students.
Consider asking:
“Who can restate in different words the way _____ saw the angles?”
“Did anyone see the angles the same way but would explain it differently?”
“Does anyone want to add an observation to the way _____ saw the angles?”


correct_option_index: 5