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

Explain volume formulas and use them to solve problems.

Apply trigonometry to general triangles.

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

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

Prove geometric theorems.

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Reason with shapes and their attributes.

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply theorems about circles.

Understand similarity in terms of similarity transformations.

Analyze, compare, create, and compose shapes.

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

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

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

Apply geometric concepts in modeling situations.

Make geometric constructions.

Understand congruence in terms of rigid motions.

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

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

Understand and apply the Pythagorean Theorem.

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).

Experiment with transformations in the plane.

Find arc lengths and areas of sectors of circles.

Visualize relationships between two-dimensional and three-dimensional objects.
problem_activity: Optional activity
The purpose of this activity is for students to create their own stained-glass design for a given amount of money. The activity is purposefully left open to allow students to either tweak the previous design or create something completely new.
As students work, monitor and select students who either tweaked a previous design or created a new, interesting design to share during the whole-group discussion.
Launch
Students in same groups.  Remind students to include whole or partial circles in their designs.
Student Facing
Draw a stained-glass window design that could be made for less than
$
450. Show your thinking. Organize your work so it can be followed by others.
Student Response
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Anticipated Misconceptions
Some students may think they need to create a new design and struggle getting started. Point these students to the designs in previous activities and ask how they could modify these designs to meet the cost requirement.
Activity Synthesis
Display students’ designs for all to see and ask students to explain how they knew their design met the cost requirement. Allow other students to ask questions of the student who is sharing their design.
Speaking, Listening: MLR7 Compare and Connect.
As students prepare their stained-glass window designs, look for students with different solution methods. As students investigate each other’s work, ask students to share what worked well in a particular approach. During this discussion, listen for and amplify any comments about what might make the calculation of the cost more precise. Then encourage students to make connections between the quantities used to calculate the cost of the glass and the circles in the stained-glass window design. During this discussion, listen for and amplify language students use to interpret quantities as the total area of the whole or partial circles in their design. This will foster students’ meta-awareness and support constructive conversations as they compare strategies for calculating the cost of a stained-glass window and make connections between quantities and the area of circles.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


correct_option_index: 13