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Math Alliance February 2, 2011 Judy Winn Beth Schefelker, Melissa Hedges

Exploring Rigid Motion: Symmetry. Math Alliance February 2, 2011 Judy Winn Beth Schefelker, Melissa Hedges. Homework Discussion: Rocket Activity. Prior to instruction, how did you plan to address anticipated student struggles?

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Math Alliance February 2, 2011 Judy Winn Beth Schefelker, Melissa Hedges

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  1. Exploring Rigid Motion: Symmetry Math Alliance February 2, 2011 Judy Winn Beth Schefelker, Melissa Hedges

  2. Homework Discussion: Rocket Activity • Prior to instruction, how did you plan to address anticipated student struggles? • What did you learn about your students spatial abilities as they engaged in the activity? • How did you address student struggles as they surfaced during the exploration? • How did you summarize the mathematics of the lesson so your students understood the foundations of rigid motion (composing and decomposing of shape).

  3. Thinking about the charts • As you discussed each of the charts with your group… • Which chart conversation made you think deeply about your approach to this activity with your students? • Share out ideas with the whole group

  4. What is symmetry?Where in the World do we find Symmetry? Create a list of items that have symmetry. What is your criteria for deciding if your items have symmetry?

  5. Possible examples you might have shared.... • Symmetry exists all around us and many people see it as being a thing of beauty.

  6. This photograph has 2 lines of symmetry. Can you find them?

  7. What is Symmetry? • Read pg. 391 – 392 Beckmann book In what way does the author use real-world connections to help launch our study of symmetry? At your table create a definition of symmetry. • Record it on an index card • Put it away to return to later.

  8. Exploring Reflection (Line) Symmetry with Pattern Blocks Part 1: • Fold a vertical line through the middle of plain piece of paper. • Use 6-8 pattern blocks to make a design on one side of the line. • The design must touch the line in some way.

  9. An Exploration of Reflection Symmetry with Pattern Blocks • Part 2 • Once your design is complete, stand up and move one table to the right. Find a seat at the new table. • Make the mirror image of the design in front of you. • Part 3 • Place a mira on the line of symmetry. • What do you notice?

  10. Reflection Symmetry with Patten Blocks - An Extension Use a new piece of paper to make a horizontal line of symmetry. • Repeat the steps with this new line of symmetry. How did the orientation of the line of symmetry effect the task?

  11. Checking your definition How does this task support your definition of symmetry? What changes would you make to your index card?

  12. Activity 2: Geoboards • Using one band, make one line of symmetry. • (horizontally or vertically)‏ • Make a design on one side of the line. • Make it’s mirror image on the other • side of the line. • What challenges would surface if the • line of symmetry were made diagonally? • Try it!

  13. Reflection Symmetry Dot Paper Practice • Use dot paper to draw a line of symmetry. • The line of symmetry can be vertical, horizontal or diagonal. • Make a shape/image on one side of the line. • Draw its reflection on the other side of the line. Check with the mira. • What is the underlying mathematics we need students to develop as they engage in this task?

  14. Revisiting the definition of symmetry • Read Defining Symmetry in your handout. • With a partner: • Discuss the meaning of reflection symmetry as developed in the reading • In what way did the three activities connect to the ideas in the reading? • How would you add to the definition of symmetry on your index card?

  15. What’s the math? • What are the critical skills students are developing as they engage in conversations about symmetry? • Visualization skills • Language involving ideas of rigid motion • Allows opportunity to connect to other topics of geometric study.

  16. Planning for Instruction and Anticipating Student Misconceptions How might these activities benefit students with identified learning barriers? What would you need to think through before trying this with your students?

  17. Polygons and Reflection SymmetryTriangle Exploration • Try the following: • Make a triangle that has one line of symmetry • Make a triangle that has more than one line of symmetry • Make a triangle that has NO lines of symmetry • How did you test for reflection symmetry? • Isosceles Equilateral Scalene

  18. Investigating Symmetry • Use the regular polygons below to complete the homework.

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