Beacon Lesson Plan Library
DescriptionThis activity allows students to design their own letter graph, and then produce the resulting graphs after a translation, reflection, and rotation.
ObjectivesUnderstands geometric concepts such as perpendicularity, parallelism, tangency, congruency, similarity, reflections, symmetry, and transformations including flips, slides, turns, enlargements, and fractals.
-Four colored pencils or crayons per student
-Graph board or transparency with Cartesian Coordinate Plane
Preparations1. Prepare a graph board or transparency with the Cartesian Coordinate Plane.
2. Collect four colored pencils or crayons for each student.
3. Secure extra graph paper.
Procedures1 Introduce the lesson by discussing the meaning of the words: transformation, translation, reflection, and rotation. Students should state ways in which the words are used in everyday life. As an example, the teacher can mention that when someone looks at their reflection, it is a mirror image of them.
2. Have students write the mathematical definitions of the words in their glossary or notes (see attached file). Teachers may want to encourage students to associate the following words: change with transformation, slide with translation, flip with reflection, and turn with rotation.
3. Choose a simple geometric figure such as a triangle or quadrilateral to graph.
4. Use a graph board or transparency with the Cartesian Coordinate Plane, and construct the graph for all students to see. Choose the location and size of the graph so that the vertices are easily identified using ordered pairs consisting of integers.
5. Students graph the exact figure on their graph paper.
6. Review the meaning of translation, and have the students translate the original figure five (or any number) units to the left (or right). Guide the students in discovering that the original ordered pairs (x, y) are now (x-5, y). For this, and all new figures, the graphs are drawn using different colors.
7. Give the students time to draw the translation, and then construct the correct result on the board or transparency.
8. Review the meaning of reflection with the students, and then instruct the students to reflect the figure over the x-axis (or other chosen line). Show the students how they can fold the paper on the line they are reflecting across in order to find where the result will be placed. Also, guide the students in discovering that each ordered pair (x, y) is now (x, -y) if reflecting across the x-axis, or (-x, y) if reflecting across the y-axis.
9. Give the students time to do this, and then construct the correct result.
10. Next, review the meaning of rotation with the students. Then, instruct the students to rotate the original figure 90 degrees or 180 degrees about a center of rotation, probably the origin. Encourage students to turn their papers if needed, but remind them to keep the center of rotation stable.
11. Give the students time to complete this, and then construct the correct result on the board or transparency.
12. Now, have students draw another graph on a clean sheet of graph paper. To do this, all students construct the x-axis and y-axis, and then choose a block letter of the alphabet. The letter can be lower case or upper case.
13. Students choose a translation, a reflection, and a rotation that they will construct.
14. Students identify the transformations at the bottom of the page in the color matching the resulting graph. For example, if they graph their translation using blue, then they would write in blue, -translation six units to the right- at the bottom of the page.
AssessmentsAs a formative assessment, the students' completed letter graph and resulting transformations could be used. Each graph should be a different color, and the description it matches should be written in the same color. Students who have not grasped each concept could be paired with a student who shows mastery of the concepts, or could meet individually with the teacher.
ExtensionsStudents could use figures other than block letters of the English alphabet, including geometric figures, mathematical symbols, or block letters of the Greek alphabet.
Students could identify the vertices of the original figure, and the vertices of each resulting graph.
Attached FilesGeometry definitions. File Extension: pdf
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