Translations, reflections, rotations

This lesson will allow students to explore translations, reflections, and rotations using a resource of Shodor Education Foundation, Inc. Permission has been granted for the use of the materials as part of the workshop Interactivate Your Math Students. Students explore the world of translations, reflections, and rotations in the Cartesian coordinate system by transforming squares, triangles and parallelograms. Parameters: Shape, x or y translation, x or y reflection, angle of rotation. (Italics are a direct quote from Shodor.org.)

A lesson plan for grades 6–8 Mathematics

By Deborah Bourne

Learn more

• NCDigIns Help students become proficient in mathematics with this formative assessment diagnostic tool.

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• Flipping around pentominoes: The students will use Unifix cubes to create the twelve different pentominoes. The students will join 5 Unifix cubes to make different shapes that will lie flat on a table or level surface. The students will then test for new shapes by flipping, sliding, or turning to create each different pentomino.
• Tabletop grids: Students will play a review game in small groups using large grids to develop skill in locating and naming points on grid maps.
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Related topics

• Learn more about coordinate planes, geometry, mathematics, reflections, rotations, and translations.

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Learning outcomes

Upon completion of this lesson, students will:

• have been introduced to the concepts of translation, reflection, and rotation.

• have practiced translating, reflecting, and rotating two-dimensional objects on the coordinate plane.

Teacher planning

Time required for lesson

50 Minutes

Materials/resources

• graph paper
• construction paper
• glue
• markers

Technology resources

computer with internet access for each pair of students

Pre-activities

Students should be able to graph and locate points using ordered pair and understand the concept of symmetry.

Prior to teaching the lesson students need to

1. Create a coordinate plane on graph paper - label the x and y axis 0 - 12 - label the 4 quadrants.
2. Using construction paper, cut out 4 identical 6 cm squares. Color each angle a different color. (This simulates the transmographer activity on the Interactivate website.)

Activities

1. Discussion of the meaning of translations, reflections, and rotations. (An excellent example can be found on the Interactivate website.)
2. Guided Practice: Students access the Interactivate Transmographer. Teacher walks the students through at least two simulations in each category - translations, reflections, rotations.
3. Independent Practice: Students explore the activities in pairs. Students use the previously created graphs and squares to model rotations around the y axis beginning in quadrant 1.
   • Paste a square in quadrant 1 and label the x and y coordinates of each corner - the students select the coordinates
   • The students select a second square to show the location of the original square when rotated 90 degrees - paste the square in the new position and label the coordinates of the corners
   • Select a third square to model a 180 degree rotation from the original position
   • Select the final square to model a 270 degree rotation from the original position

   Students should be encouraged to refer to the computer activity for assistance.

Assessment

Use each student’s graph:

• Mastery: 3 out of 4 rotations with appropriate labeling of ordered pairs
• Understanding: 2 out of 4 rotations with labeling of ordered pairs
• Needs Practice: 1 out of 4 rotations

Comments

This lesson was written in an attempt to address the issue of learning differences. The concepts can be very difficult for students with learning disabilities. Using the computer simulation as well as the construction model can be very effective.