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What is your favorite color?

(Please share your answer in the chat)

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How many ways can you color the design?

https://bit.ly/6InterlockingCircles

http://bit.ly/CircleColorDesign

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Examples

Non-Examples

SYMMETRY

ASYMMETRY

Take a moment to appreciate the colorings students have done.

These images are all made from the same design as the six interlocking circles you played around with in the beginning.

We’ve used color to bring out a particular feature in the design.

In fact, we can say that the designs on the left, because of how they are colored, all share a feature that the designs on the right do not.

Ask: What do you notice about the colorings on the left? What characteristic is shared by these (the examples) but not these (the non-examples)?

Monitor the chat and call out some interesting ideas and useful language.

One thing I’m seeing in many of your observations is this idea of <folding, reflection, same on both sides, etc - use language from observations in chat>

Animation: First click shows lines of symmetry in the designs on the left. For the images that have more than one line of symmetry, only one appears.

Ask: Are there any other ways we could “fold” (use language drawn from learner observations) any of the figures on the left to similar result? If you have an idea how, you can unmute yourself.

Animation: Second click adds the second lines of reflection to the examples on the top row.

If it doesn’t come up, you can ask about the image on the lower left. Does it get a second line? (If anyone has an idea, they can unmute themselves and share).

If words “symmetry” and/or “asymmetry” haven’t come up,

Ask: There is a name what we’re talking about with our examples and non-examples. Does anyone know what it is?

Animation: Final animation changes headings from Examples and Non-Examples to Symmetry and Asymmetry

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Working Definition of Symmetry

Has at least one imaginary line where you could fold the image along that line and both parts would match up exactly.

(The line acts like a mirror.)

Image: by Sarah Lonberg-Lew

LINE

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M S R J A L T F H

C P R F O G D E L

Remove the letters without line symmetry from each line and type what’s left in the chat (but don’t hit ENTER yet!)

Decipher the Message

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M S R J A L T F H

C P R F O G D E L

Remove the letters without line symmetry from each line and type what’s left in the chat (but don’t hit ENTER yet!)

Decipher the Message

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Examples

Non-Examples

Another Kind of SYMMETRY

Designs with Rotational Symmetry Designs without Rotational Symmetry

When we looked at line symmetry, we talked about imaginary lines where you could fold the image along that line and both parts would match up exactly.

Here we have another type of symmetry. There is something else you can do to get the image to match up with itself again.

ASK: Again, use the chat to make some observations about characteristics that are shared by the examples but are not found in the non-examples?

Monitor the chat and call out some interesting ideas and useful language

One thing I’m seeing in many of your observations is this idea of <turning, rotating, spinnings, etc - use language from observations in chat>

Animation: Replaces Examples and Non-Examples with Designs with Rotational Symmetry and Designs without Rotational Symmetry.

ASK: When we looked at the designs with line symmetry, we saw some designs had multiple line symmetries.

Does anyone see a way to quantify the turns or rotations? Share any ideas you have in the chat.

If someone observes that some of these designs have line symmetry, mention that there are examples of line symmetry on both sides here. Meaning sometimes a design with rotational symmetry has line symmetry and sometimes it does not.

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Working Definition of Rotational Symmetry

You can turn the image some fraction of a turn or some number of degrees and it will look the same as before you turned it.

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The Language of Rotational Symmetry

A full turn of any image is 360°.

We say this clover has...

4-fold rotational symmetry
90° rotational symmetry

We say 4-fold because you can turn it one-quarter (¼) turn and get it to match up with itself.

We say 90° because a one-quarter turn

(of 360°) is 90°

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Let’s Describe the Rotational Symmetry We See in this Flower

Sentence Starters...

This flower has ___-fold rotational symmetry
This flower has ___° rotational symmetry
You can turn this flower _______�to get it to match up with itself.

5

72

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Let’s Describe the Rotational Symmetry We See in this Flower

Sentence Starters...

This flower has ___-fold rotational symmetry
This flower has ___° rotational symmetry
You can turn this flower _______�to get it to match up with itself.

5

72

… one-fifth (⅕) of a turn

72°

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Symmetry Challenges: Create or identify a design that has...

Rotational symmetry and line symmetry
Rotational symmetry but no line symmetry
Line symmetry but no rotational symmetry
No symmetry at all
A shape that has symmetry but the coloring does not / a design where the coloring breaks the symmetry of the shape
Exactly one line of symmetry,

Exactly two lines of symmetry, etc.

2-fold (180°) rotational symmetry, 3-fold (120°) rotational symmetry, 4-fold (90°) rotational symmetry, etc.
A rotational symmetry that’s different from the number of circles (like 4-fold rotational symmetry in 8 interlocking circles)
6-fold (60°) rotational symmetry and no line symmetry
Create your own challenges!

Post your efforts to the padlet. http://bit.ly/CircleColorDesign

If you think a challenge is not possible, explain why.

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Tools for the Symmetry Challenges

https://bit.ly/6InterlockingCircles

http://bit.ly/7InterlockingCircles

http://bit.ly/8InterlockingCircles

http://bit.ly/9InterlockingCircles

http://bit.ly/10InterlockingCircles

http://bit.ly/11InterlockingCircles

http://bit.ly/12InterlockingCircles

In addition to creating, you can look back at the ANN Gallery of Interlocking Circles.

Do any of the designs there fulfill the criteria of the challenges?

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http://bit.ly/ANNsymmetrychallenge

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One thing I learned about symmetry is…

One thing I am wondering about symmetry is...