Exploring Rotation Symmetry

Objective:

Students will be able to identify rotation symmetry in figures, determine the order of rotational symmetry, and visualize figures rotating around a given point.

Assessment:

Students will be given a set of geometric figures and asked to identify the order of rotational symmetry for each figure. They will also have to draw the figures after a specific rotation to demonstrate their understanding.

Key Points:

• Rotation Symmetry: A figure has rotational symmetry when it can be rotated (less than 360 degrees) and still look like it did before the rotation.

• Center of Rotation: The point a figure is rotated around such that the rotational symmetry holds.

• Order of Rotational Symmetry

• Identifying Figures with Rotational Symmetry

• Visualizing Figures After Rotation

Opening:

• Introduce the concept of rotation symmetry by showing students a figure and asking them to think about if the figure looks the same after being rotated around a point.

• Pose the question: "What do you think happens to a shape when it is rotated around a fixed point?"

Introduction to New Material:

• Explain the definition of rotation symmetry and the concept of a center of rotation.

• Discuss how to determine the order of rotational symmetry in a figure.

• Anticipated misconception: Thinking that all shapes have rotation symmetry.

Guided Practice:

• Show examples of figures with different orders of rotational symmetry and have students identify the order for each.

• Guide students through rotating figures on a coordinate grid and determining the new position after rotation.

• Monitor student progress by asking probing questions and providing feedback.

Independent Practice:

• Students will be given a worksheet with various geometric figures and asked to identify if they have rotation symmetry, determine the order of symmetry, and draw the figure after rotation.

• Behavioral expectations: Students should show all work neatly and clearly label their responses.

Closing:

• Have students share one thing they learned about rotation symmetry today.

• Ask students to reflect on why understanding rotation symmetry is important in geometry.

Extension Activity:

• For early finishers, provide a set of more complex figures and ask them to determine the order of rotational symmetry and justify their answers.

Homework:

• Homework Activity: Students will find real-life examples of objects that exhibit rotation symmetry and discuss their findings in the next class.

Standards Addressed:

• G-CO.A.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs.

• G-CO.A.2: Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.