options: Understand congruence in terms of rigid motions.

Understand and apply theorems about circles.

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

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

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

Understand and apply the Pythagorean Theorem.

Find arc lengths and areas of sectors of circles.

Reason with shapes and their attributes.

Apply geometric concepts in modeling situations.

Understand similarity in terms of similarity transformations.

Use coordinates to prove simple geometric theorems algebraically.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

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

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

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

Make geometric constructions.

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

Apply trigonometry to general triangles.

Analyze, compare, create, and compose shapes.

Experiment with transformations in the plane.

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

Prove geometric theorems.

Explain volume formulas and use them to solve problems.
problem_activity: Narrative
The purpose of this activity is to deepen students’ understanding that a shape can belong to multiple categories because of its attributes. Students analyze shapes and determine all the ways that each one could be named. The names may refer to a broad category such as triangle or quadrilateral, or a narrower subcategory such as rhombus or rectangle. As they name the different categories students need to be precise both about the meaning of the categories and verifying the properties of the different shapes (MP6).
MLR8 Discussion Supports.
Synthesis: For each observation that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Advances: Listening, Speaking
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select at least 4 of the 6 problems.
Supports accessibility for: Organization, Attention, Social-Emotional Skills
Launch
Groups of 2
“Look at the quadrilateral in the first problem. Work independently to circle all the names that you could use to describe the quadrilateral. Be prepared to share your reasoning.”
1 minute: independent work time
“Discuss your responses and reasoning with your partner.”
2 minutes: partner discussion
Share responses.
Activity
“Complete the rest of the problems independently. Be prepared to explain your reasoning.”
3–5 minutes: independent work time
“Now, discuss your answers with your partner. Be sure to explain your reasoning for each way you described the shape. Also, be sure to ask your partner if you have any questions about their reasoning.”
5–7 minutes: partner discussion
Monitor for students who notice that some shapes can be described using multiple terms.
Student Facing
Select
all
the ways you could describe each shape. Be prepared to explain your reasoning.
1
[IMG]
triangle
quadrilateral
square
rhombus
rectangle
2
[IMG]
triangle
quadrilateral
hexagon
rhombus
rectangle
square
3
[IMG]
triangle
quadrilateral
pentagon
rhombus
rectangle
square
4
[IMG]
triangle
quadrilateral
hexagon
rhombus
rectangle
square
5
[IMG]
hexagon
quadrilateral
triangle
square
rectangle
rhombus
6
[IMG]
hexagon
quadrilateral
triangle
rhombus
rectangle
square
Student Response
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for free access to Student Response.
Advancing Student Thinking
If students use only one name for a shape that can be named in multiple ways, consider asking:
“How did you describe the shape?”
“Are there any other names that could be used to describe the shape?”
Activity Synthesis
Select 1–2 students to share the terms they selected for each of the last four quadrilaterals and their reasoning.
Consider asking:
“Who can restate _____’s reasoning in a different way?”
“Does anyone want to add on to _____’s reasoning?”
“Do you agree or disagree? Why?”
“The last shape can be described with 4 of the choices. How is it possible that it can be described in so many ways?” (It is a quadrilateral because it has 4 sides. It is a rhombus because it’s a quadrilateral with 4 sides that are the same length. It is a rectangle because it has 4 right angles and 2 pairs of sides that are the same length. It is a square because it has 4 sides that are the same length and 4 right angles. The last three are more specific descriptions of a quadrilateral.)


correct_option_index: 7