Math AllianceFebruary 2, 2011

Judy Winn Beth Schefelker,

Melissa Hedges

Exploring Rigid Motion: Symmetry

Homework Discussion: Rocket ActivityPrior 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).

Thinking about the chartsAs 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

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?

Possible examples you might have shared....

Symmetry exists all around us and many people see it as being a thing of beauty.

This photograph has 2 lines of symmetry.

Can you find them?

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.

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.

An Exploration of Reflection Symmetry with Pattern BlocksPart 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?

Reflection Symmetry with Patten Blocks - An ExtensionUse 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?

Checking your definition

How does this task support your definition of symmetry?

What changes would you make to your index card?

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!

Reflection Symmetry Dot Paper PracticeUse 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?

Revisiting the definition of symmetry

Read Defining Symmetry in your handout.With a partner:

Discuss the meaning of reflection symmetry as developed in the readingIn 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?

What’s the math?

What are the critical skills students are developing as they engage in conversations about symmetry?Visualization skillsLanguage involving ideas of rigid motion

Allows opportunity to connect to other topics of geometric study.

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?

Polygons and Reflection Symmetry

Triangle Exploration

Isosceles EquilateralScalene

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?

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

01/30/11