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

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

Explain volume formulas and use them to solve problems.

Apply geometric concepts in modeling situations.

Use coordinates to prove simple geometric theorems algebraically.

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

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

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

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

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

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

Understand and apply theorems about circles.

Prove geometric theorems.

Apply trigonometry to general triangles.

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

Make geometric constructions.

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

Prove theorems involving similarity.

Find arc lengths and areas of sectors of circles.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Experiment with transformations in the plane.

Reason with shapes and their attributes.
problem_activity: Narrative
The purpose of this activity is for students to begin to distinguish triangles from other shapes. By working with variants and non-examples of triangles, students begin to develop their understanding of what makes a shape a triangle. Students may more easily identify equilateral triangles as triangles but may also identify other examples as triangles. When students discuss with their group which group a shape should be placed in, students informally describe the attributes of the shape (MP6).
Required Materials
Materials to Copy
Triangle Sort Cards
Required Preparation
Cut out triangle cards from the blackline master. Each group of 4 needs 1 set of cards.
Launch
Groups of 4
Give each group a set of cards.
“Work with your group to sort the shapes into 2 groups. Put the shapes that are triangles on the left side of your page. Put the shapes that are not triangles on the right side of your page. When you place a shape, tell your group why you think the shape belongs in that group.”
Activity
4 minutes: small-group work time
Monitor for students who discuss attributes of triangles when sorting.
“Write a number to show how many shapes are in each group.”
1 minute: independent work time
“Walk around to see how the other groups organized their shapes. Did they organize them the same way that your group did?”
6 minutes: work time
Student Facing
Let’s put the shapes into 2 groups.
Triangle
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[IMG]
[IMG]
Not a Triangle
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Student Response
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Advancing Student Thinking
I
f students put shapes other than triangles into the group of triangles, consider asking:
“How did you choose which group to put this shape in?”
“What is alike, or the same, about all of the shapes in this group?”
Activity Synthesis
Display cards O, K, and G next to each other.
“Noah says that the shape in the middle is not a triangle because it is pointing down and triangles have to point up. Do you agree with Noah? Why or why not?“


correct_option_index: 15