
Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
Using GeoGebra (http://www.geogebratube.org/student/m1595), students will be able to derive the rules for rotating a point on the coordinate plane about the origin for a 90 degree, 180 degree, 270 degree, a 360 degree rotation. Students will be able to identify images of rotated points in the coordinate plane for a 90 degree, 180 degree, and a 270 degree counterclockwise rotation.
Transformations  Rotation GeoGebra Applet

Prior Knowledge: What prior knowledge should students have for this lesson?
MAFS.5.G.1.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate).
MAFS.5.G.1.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
MAFS.6.G.1.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems.

Guiding Questions: What are the guiding questions for this lesson?
Can anyone tell me what it means to rotate an object? (i.e. turning an object)
Can you give me an example of a rotation in everyday life? (i.e. clock hands moving, earth turning on its axis)

Teaching Phase: How will the teacher present the concept or skill to students?
After using questions 14 in the formative assessment, continue using the GeoGebra applet at http://www.geogebratube.org/student/m1595. (Make sure the "show original" and "show center" checkboxes are checked. Make sure the center of rotation point (blue point) is on the origin. Make sure the show image checkbox is unchecked.)
 Move the points of the triangle to 3 other points in the first quadrant.
 Ask the students to predict what a 90 degree counterclockwise rotation will look like.
 Ask the students what quadrant a 90 degree counterclockwise rotation of the triangle would be in.
 Have students draw the image and their prediction of the rotation on their graph paper.
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 90 degrees.
 Ask students to identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
 Uncheck the "show image" box.
 Move the points of the original figure to a location in the second quadrant.
 Repeat steps 49.
 Move the points of the original figure to a location in the third quadrant.
 Repeat steps 49.
 Move the points of the original figure to a location in the fourth quadrant.
 Repeat steps 49.
 Move the points of the original figure to be contained in different quadrants (i.e. (2,2), (3,2), and (1,1)).
 Repeat steps 49.
 Ask students if they see a pattern or a relationship between the original points and their rotated points.
 Ask students, what are the coordinates of the image of a point (a,b) that is rotated 90 degrees counterclockwise about the origin? (b,a)

Guided Practice: What activities or exercises will the students complete with teacher guidance?
If students have computers, they can do the following activities individually or in pairs. If not, the teacher can project the applet and have students complete the worksheets as the teacher manipulates the applet.
180 Degree Rotations Guided Practice Worksheet
270 Degree Rotations Guided Practice Worksheet
Instructional Tips:
 A 180 degree counterclockwise rotation about the origin transforms (a,b) into (a,b).
 A 270 degree counterclockwise rotation about the origin transforms (a,b) into (b,a).
 Students should create triangles in the first quadrant, second quadrant, third quadrant, and fourth quadrant, and a triangle with points that "straddle" three different quadrants.
Summarized here are the worksheet activities:
180 Degree Rotations  Student Guided Practice
 What will a figure look like after a 180 degree counterclockwise rotation?
 Open the GeoGebra applet at http://www.geogebratube.org/student/m1595. Make sure the show origin and show center checkboxes are checked. Move the center of rotation point (blue point) to the origin. Make sure the show image checkbox is unchecked.
 Before using the applet, predict which quadrant will the image of the triangle be in after a 180 degree counterclockwise rotation?
 Draw the original triangle and your prediction of the rotation on graph paper.
 Perform the following steps:
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 180 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
180 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Perform the following steps:
 Uncheck the "show image" box.
 Move the points of the original figure to another location in the first quadrant.
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 180 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
180 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Perform the following steps:
 Uncheck the "show image" box.
 Move the points of the original figure to a location in the second quadrant.
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 180 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
180 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Perform the following steps:
 Uncheck the "show image" box.
 Move the points of the original figure to a location in the third quadrant.
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 180 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
180 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Perform the following steps:
 Uncheck the "show image" box.
 Move the points of the original figure to a location in the fourth quadrant.
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 180 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
180 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Describe a pattern or a relationship between the original points and their rotated points.
 What are the coordinates of the image of a point (a,b) that is rotated 180 degrees counterclockwise about the origin?
270 Degree Rotations  Student Guided Practice
 What will a figure look like after a 270 degree counterclockwise rotation?
 Open the GeoGebra applet at http://www.geogebratube.org/student/m1595. Make sure the show origin and show center checkboxes are checked. Move the center of rotation point (blue point) to the origin. Make sure the show image checkbox is unchecked.
 Before using the applet, predict which quadrant will the image of the triangle be in after a 270 degree counterclockwise rotation?
 Draw the original triangle and your prediction of the rotation on graph paper.
 Perform the following steps:
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 270 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
270 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Perform the following steps:
 Uncheck the "show image" box.
 Move the points of the original figure to another location in the first quadrant.
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 270 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
270 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Perform the following steps:
 Uncheck the "show image" box.
 Move the points of the original figure to a location in the second quadrant.
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 270 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
270 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Perform the following steps:
 Uncheck the "show image" box.
 Move the points of the original figure to a location in the third quadrant.
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 270 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
270 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Perform the following steps:
 Uncheck the "show image" box.
 Move the points of the original figure to a location in the fourth quadrant.
 Change the rotation slider to 0 degrees.
 Check the box "show image."
 Move the rotation slider to 270 degrees.
 Identify the points of the original figure and compare them to the coordinates of the points of the rotated image.
270 Degree Rotation

Coordinates of Original Point

Coordinates of Rotated Point

Point A



Point B



Point C



 Describe a pattern or a relationship between the original points and their rotated points.
 What are the coordinates of the image of a point (a,b) that is rotated 270 degrees counterclockwise about the origin?

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Have students complete the independent practice worksheet.
Rotations Independent Practice Worksheet
Rotations Independent Practice Worksheet with Answers

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Ticketoutthedoor (this strategy will allow you to assess whether students have mastered the content in the lesson. In the last 510 minutes of class, give students a slip of paper and have them respond to the following questions. Collect them as they leave the room and review to identify how well students mastered the content).
 What are the coordinates of point (a, b) after a counterclockwise rotation about the origin of:
 90 degrees? (b, a)
 180 degrees? (a, b)
 270 degrees? (b, a)
 360 degrees? (a, b)
Explanation of answers:
 90 degree CCW rotation transforms (a, b) into ((b), a) = (b, a).
 180 degree CCW rotation transforms (a, b) into ((a), (b)) = (a, b).
 270 degree CCW rotation transforms (a, b) into (b, (a)) = (b,a).
 360 degree CCW rotation transforms (a, b) into (a, b), bringing the triangle back to the original position.
 Create your own rotation problem by identifying the original points of the figure and identifying the degree of rotation about the origin. Provide the solution to your problem.

Summative Assessment
Review answers for independent practice.
Review answers on Ticket Out the Door to ensure students have mastered the concept of geometric rotations.

Formative Assessment
Open the GeoGebra applet at http://www.geogebratube.org/student/m1595. Make sure the show origin and show center checkboxes are checked. Move the center of rotation point (blue point) to the origin. Make sure the show image checkbox is unchecked.
 Discuss the words "clockwise" and "counterclockwise" and make sure students have an understanding of those terms.
 Ask the students to predict what a 90 degree counterclockwise rotation will look like.
 Ask the students what quadrant a 90 degree counterclockwise rotation of the triangle would be in.
 Have students draw the image and their prediction of the rotation on their graph paper.
Monitor student responses during the teaching phase of this lesson to gauge mastery of the concepts explored.

Feedback to Students
As students work through guided practice problems, teacher should circulate and give individual feedback to students. After each problem, teacher can allow students to share their solutions and diagrams with the class.