Grade Six - Session 5 Transformations with Technology Facilitator Packet
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1 Mathematics Grade Level Assessments and Content Expectations Grade Six - Session 5 Transformations with Technology Facilitator Packet Modules Developed by Macomb County Teachers under the leadership of Marie Copeland Page 1 of 5 Revised
2 Developers Mathematics Grade Level Assessments and Content Expectations M-GLAnCE Project Directors Debbie Ferry Macomb ISD Mathematics Consultant Carol Nowakowski Retired Mathematics Consultant K-4 Project Coordinator Marie Copeland Warren Consolidated Macomb MSTC 5-8 Project Coordinator 2004 Project Contributors David Andrews Sharon Chriss Kimberly Dolan Amy Holloway Clintondale Schools Therese Miekstyn Rebecca Phillion Richmond Comm. Schools Ronald Studley William Ashton Fraser Public Schools Kimberly DeShon Jodi Giraud L Anse Creuse Schools Barbara Lipinski James Navetta Charlene Pitrucelle Lynn Bieszki Barbara Diliegghio Julie Hessell Linda Mayle Gene Ogden Shirley Starman Van Dyke Public Schools 2005 and 2006 Session/Module Developers Carol Nowakowski Kathy Albrecht Terri Faitel Trenton Public Schools Deb Barnett Lake Shore Public Schools Jo-Anne Schimmelpfenneg Debbie Ferry Macomb ISD Luann Murray Genesee ISD Marie Copeland Warren Consolidated Page 2 of 5 Revised
3 GLCE for Grade 6 Transformations with Technology 5 minutes Congruence Discovering Translations Rules Using Technology to Graph Transformations Discuss instructional sequence Be sure to highlight tips and misconceptions of students Indicate that paper and pencil, graphing calculators, and Geometer s Sketchpad (GSP) will be used to show relationships. Participants will make congruent figures and name the correspondences. Participants will discover translation rules and use the graphing calculators to model the translation rules. Set up the original triangle in L1 (x coordinates) and L2 (y coordinates). Put the first coordinate also as a fourth point so that a line graph will complete the triangle. Set up the Pages 1 3 Pages 4 5 Page 6 9 Graph paper Scissors Graphing calculator Page Point out the connections to congruence that many transformations change the orientation but not the size. Understanding which sides and angles map to each other. The abstract rules are difficult for students. Be sure they are relating the rules to the translations correctly. Take this slowly so that the participants follow how to graph the different triangles. Page 1 of 5 Revised
4 translated triangle in L3 and L4. Set up the stat plot with a line graph Have participants graph their original triangle and Reflections with a Mira 15 minutes Reflection Rules Reflections and Translations the translated triangle. Participants will use a mira to reflect different objects over a given line. Then they will use that concept to bisect angles and line segments. Participants will use a mira on the first three reflection problems. Then they will discover how they could have reflected over that line without a mira or a rule. Given the rules for the transformation in words, participants will graph the original figure and the image and write the Page 13, 14 Miras Page 15, 16 s Mira Pages s Make sure the participants are positioning the miras correctly. Make sure students understand that x does not necessarily indicate a negative number. Also be aware that triangles were used to show a clear difference of the figures as they are reflected (no rectangles or squares!) While participants are working use both the graphing calculator and GSP to give them immediate feedback. Page 2 of 5 Revised
5 Constructed Response Rotations Rotating around a center point general rule. Participants will see what a constructed response might look like. Participants will use patty paper to rotate figures around the origin on a coordinate plane so that students can learn general rules for rotation. Participants will use a compass and protractor to rotate figures around a center point. Pages 20 Colored pencils Pages Scissors Protractor Pages compass ruler protractor Be sure participants are using a colored pencil to graph the first image in order to see the relationship between the original triangle and the ending triangle. Begin rotations by starting with a vertex at the origin and one side on an axis. Participants need to know the difference between a positive or negative rotation. With so many lines on the construction it can become confusing; therefore, use different colored pencils to rotate each point. Page 3 of 5 Revised
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