options: Apply trigonometry to general triangles.

Experiment with transformations in the plane.

Define trigonometric ratios and solve problems involving right triangles.

Make geometric constructions.

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

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

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

Apply geometric concepts in modeling situations.

Analyze, compare, create, and compose shapes.

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

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

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

Find arc lengths and areas of sectors of circles.

Understand congruence in terms of rigid motions.

Understand and apply theorems about circles.

Understand similarity in terms of similarity transformations.

Prove geometric theorems.

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

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

Explain volume formulas and use them to solve problems.

Understand and apply the Pythagorean Theorem.

Reason with shapes and their attributes.

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

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

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

Prove theorems involving similarity.

Use coordinates to prove simple geometric theorems algebraically.
problem_activity: Narrative
In this activity, students are given the result of folding a shape along one or more lines of symmetry and asked to reason about the original shape. No lines of symmetry are specified, so students must consider all sides of a folded shape as a possible line of symmetry and visualize the missing half accordingly.
The first question offers opportunities to practice choosing tools strategically (MP5). Some students may wish to trace the half-shapes on patty paper, to make cutouts of them, or to use other tools or techniques to reason about the original shape. Provide access to the materials and tools they might need.
During the activity synthesis, discuss the different ways students approach the second question. Consider preparing cutouts of shapes A–F to facilitate the discussion. (The shapes are provided in the blackline master.)
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy, including the tools they will use, for the task. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Conceptual Processing, Organization, Attention
Required Materials
Materials to Gather
Paper
Patty paper
Protractors
Rulers or straightedges
Scissors
Materials to Copy
Before and After
Launch
Groups of 2
Give a ruler or a straightedge to each student.
Provide access to protractors, patty paper, scrap paper, and scissors.
Activity
5 minutes: independent work time
2–3 minutes: partner discussion
Monitor for the different strategies students use to identify the original shape of the half-shapes (as noted in the activity narrative).
Student Facing
Mai has a piece of paper. She can get two different shapes by folding the paper along a line of symmetry. What is the shape of the paper before it was folded?
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Diego folded a piece of paper once along a line of symmetry and got this right triangle.
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Which shapes could the paper have before it was folded? Explain or show how you know.
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Student Response
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Activity Synthesis
Invite students to share their responses and strategies.
When discussing the second question, ask students why B, C, and E are not possible shapes of the original piece of paper even though there’s a line that breaks each figure into two right triangles that match the given triangle. (B and E have no line symmetry. C has lines of symmetry but not diagonally from corner to corner. If you fold there, the triangles would not be on top of one another.)


correct_option_index: 11