Station # 1A: Geometric Flips

At this station you will explore words and try to decide if the words are symmetircal--or not. You will also try to think of words that are symmetrical.

What you need:

1. Paper to write on
2. A word list (this list will have words on it like MOM, OTTO, BOB)
3. A MIRA
4. The chart below to record words in

What to do:

1. On a piece of paper, write the word MOM. Draw a horizontal line above the word MOM.
   
   
2. Using a MIRA reflect this word over a horizontal line of reflection at the top of the word.
   
   
3. Repeat with the line of reflection at the bottom of the word.
   
   
4. Try to come up with other words that can be reflected horizontally.
   
   
5. Now look at the word MOM again. Draw a straight line vertically to the left or right of the word MOM. Would the reflection of MOM over a vertical line be a real word?
   
   
6. Try to come up with other words that can be reflected vertically.
   
   
7. Also try to come up with words that make different (real) words through vertical reflection.
   
   
8. Can you think of any words that reflect real words when reflected both horizontally and vertically?
   
   
9. Use the following chart to find words that fit one or more of the following categories. Can any one word fit all categories? Please refer to the word list for examples of words that you may wish to use.

written horizontally flipped horizontally	written horizontally flipped horizontally
written vertically flipped horizontally	written vertically flipped vertically

10. What is the longest word that you can find that will reflect itself when flipped horizontally? Flipped vertically?

Station 1B: Mira Math

This station uses a concrete manipulative called a MIRA (like a mirror, only you can see through it). A MIRA will help you know if something is symmetrical. You place the MIRA in the center of the shape and if a shape is symmetrical then what you see on one side of the MIRA should be identical to what you see through the MIRA.

What you need:

1. A MIRA

2. A tub of butterflies, insects, books and pictures

3. A handout of MIRA activities

What to do:

First of all use the Mira to examine the butterflies and also to explore some pictures in the books in the tub. Are the butterflies completely symmetrical? Can you find some shapes in the books that are completely symmetrical?

In the tub with the Miras is a four-page handout with Mira activities. Go through this handout, using the Mira to do the activities. Try to complete this handout. Make sure your name is on it. Take the handout with you when you go to the next station. Make sure you try to DRESS THE COWBOY; to do this you need to place the MIRA beside each item of clothing and move it around (rotate the MIRA) to move the clothing to the cowboy's body.

Station 1C: Pattern Blocks

At this station you will explore symmetry with pattern blocks. You will explore two kinds of symmetry: reflection symmetry and rotation symmetry.

What you need:

1. Pattern Blocks

2. Hinged mirrors

What to do:

Everyone:

Take a hinged mirror and place each pattern block in turn in the hinge part of the mirror--right where the two parts of the mirror meet, and then close the mirror around the block so that the hinger mirro touches the block. What do you see when you look into the mirror? How many reflections of the original shape are there? If you count the shape that you have placed in the center, AND the reflections of your shape, how many of your shape can you see?

Place about 4-6 blocks in the hinge of the mirror and close the mirror as best you can around the blocks. Now look into the mirror, but DO NOT move the mirror. Try to construct AROUND THE OUTSIDE OF THE MIRROR what you seeh IN the mirror.

Do this activity again but this time, after you have placed about 4-6 blocks in the hinge part of the mirror and have examined the reflection in the mirror, REMOVE the mirror and try to recreate the reflected image.

Grade 5:

1. When you place any one block in the hinge part of the mirror, try to predict--before you look into the mirror--how many reflections you will get. Be ready to tell us why you think your prediction would be correct. How would you know if you were correct WITHOUT looking into the mirror?
2. If you know for sure how many green triangles make up your circle, how can you use that information to predict how many yellow hexagons, how many blue diamonds, how many red trapezoids would make up your circle--WITHOUT actually placing the blocks in the hinge of the mirror.
3. Now place each block in turn into the hinge part of the mirror and see if you predicted correctly.

Children, make sure that your teacher takes a picture of your work so that it can be saved to show others.

Station 1D: Geoboards

At this station you will use geoboards to explore symmetry.

What you need:

1. Geoboards

2. Elastics

3. Geoboard dot paper

What to do:

Work with a partner. Each of you should have your own geoboard. Sit beside your partner and place your geoboard right beside your partner's geoboard. The axis or line of symmetry will be in between the two geoboards. If you are sitting BESIDE your partner the line of summetry will be vertical. Later, you can sit ACROSS from your partner and have a horizontal axis. You can mark this 'line' with a ruler if you wish. One of you should make a shape with elastics on your board. Your partner should then try to create the reflection of that shape. If you are not sure if you have truly made the reflection then place a MIRA between the two boards and look into the MIRA to check on your reflection. Each of you should create 3 shapes and your partner should make the reflections. On your geoboard dot paper draw one of the shapes and its reflection (use two of the small geoboards on the dot paper).

Station 1E: Interactive Symmetry

At this station you will go onto the Internet and explore a website that has an interactive geoboard.

What you need:

1. Access to a computer with an Internet connection.

At this station you will visit websites where you can explore symmetry. At the first site you select the type of symmetry you are interested in and the color you want to use and before your eyes you will see examples of this type of symmetry. At the second site you need to use the online interactive geoboard to create your own symmetrical shapes.

What to do:

1. Go to the following website:

http://www.gwydir.demon.co.uk/jo/learn/symmetry.htm

Play inside the white square for a few minutes and then try to complete the activities under the white square.

2. The new Principles and Standards for School Mathematics has an interactive geoboard at the following site: http://standards.nctm.org/document/eexamples/chap4/4.2/

Use one band to make a verical 'line' down the center of the goeboard. Create a shape on one side of the band and mirror it on the other.

Station 2: Snowflakes

Has anyone ever managed to catch a snowflake on their mitten and taken a very close look? Wilson Bentley spent his life looking at snowflakes and photographing them. Take some time and look at the book Snowflake Bentley by Jacqueline Briggs Martin. Find an adult or older child to read this story to you and then do the following:

What To Do:

1. Find an available computer and log-on.
2. Visit the following website:
http://www.explorescience.com/activities/activity_list.cfm?categoryID=4
3. Choose the shape of snowflake you'd like to make.
4. Follow the instructions and experiment with the symmetry found in snowflakes!

Station 3: Symmetrical Moves

Each person take a task card and prepare to lead the group in the activity on the card.

Grade 2 Leader: Mirror Imagery
Play Simon Says. You be Simon and do actions that involve hands and legs, staying in the same place. If you say "do this" and the others follow, you say "I didn't say Simon says" and continue the game.

Grade 2 Leader: Marching in Place
Face the group and ask the others to march with you in place. Say "do what I do." Turn around so that your back is to the group. When you step with your right foot, swing your left hand forward. Then do the opposite with your left foot and right hand. Alternating hands and feet (left and right) is called "cross extension."

Marching Poem
A marching we will go
A marching we will go
Left and right, we sail tonight
A marching we will go.

Stop!

Grade 2 Leader: Ask your group to gently get down on their hands and knees in crawling position. You stay standing and say: "See how you change hands and feet when you crawl."

Ask the crawlers to crawl while you say the poem.

Crawling Poem
Crawling is good for your brain.
Crawling is good for your brain.
Crawl and walk,
Then learn to talk
Crawling is good for your brain.

Stop!

Grade 2 or 5 Leader: Rotational or Turning Symmetry
This is the kind of symmetry used when you see yourself in a video monitor in a store: you move your right arm and your TV image moves its right arm. Have a pair of people stand in front of the video camera. One person is the leader and the other is the follower. Do five hand/arm moves and follow. Then take turns.

Mirror Symmetry in Conversation

Introduction

When you are listening to a friend talking, you can give them messages that you are listening by mirroring some of their gestures. How you mirror may give the person a non-verbal message about your interest in the conversation.

Copy Cat: If you do exact and precise mirroring of the person's movement and posture, it often causes embarrassment as it makes fun of the person talking. This is not such a good idea.

Do your own thing: If you take positions that are totally unlike what the speaker is doing, they are likely to think that you are not really interested. This might make them think that you are rude.

Good listener: Slowly and gradually move to include some of the talker's movements using a smaller size. Do not copy all of the movements, just some of them.

Grade 5 Task Card:
In pairs, have one person be the talker and listener. Have them sit in chairs facing each other.

Tell the talkers that they are to talk for one minute (12+ sentences) to their listener. See the list of topics below.

Students can take turns being the listener, and choose one of the three possibilities: copy cat, do your own thing, good listener.

See if the group can guess which you are doing. Talk about how it feels and what it looks like. Have someone else be the talker and listener.

Topics for Conversations:
Funny pets
The problem with peanut butter.
What to pack before a long trip
Explain to an adult why you need an increase in allowance.

Station # 4: Miming and Mirroring

Mirroring: Looked in a mirror lately? What does your reflection do when you move? In this activity we will explore how your reflection moves. In groups of two, one person (the leader) will move in front of a mirror or window and the other person (the follower) will be that person's reflection.

What To Do:

1. Divide your group into teams of two. (If someone doesn't have a partner, take turns so everyone has a chance to participate.)
2. In each group, choose one person to be the leader, and one to be the follower.
3. Choose one group to start.
4. The starting group selects a slip of paper, and mimes the scenario described. The other group will try to guess what the scenario is.
5. Repeat until everyone has a turn leading, following and guessing!

You are sitting in front of a mirror combing and gelling your hair.


You are standing at the kitchen counter making a sandwich (and pouring juice).


It is a very hot day. You are giving your dog a bath.


You are making your bed (or helping to make your bed).


You are playing on the monkey bars.

You are climbing a ladder to save a kitty in a tree. You need to come down the ladder holding onto the ladder with one hand and the kitty with the other hand.

You are brushing and flossing your teeth.

You are watering a row of plants (house, classroom, or garden)

You are washing and drying dishes.

You are sharpening a new box of pencils.

You are cleaning a dirty window.

You are erasing a blackboard

You are a hockey player skating towards the boards. Another player body-checks you, and you crash into the glass.

Station # 5: Symmetry in Music

Note: It is important for students to experience other symmetry stations before this one because musical symmetry adds new meanings. This station expands the concepts of symmetry that students have learned so far.

Many musicians have a strong interest in Mathematics, so it is no surprise that concepts such as mirror-image and symmetry occur in music. There are several kinds of symmetry in music.

The music program Music Note Pad that is used for this station is available on the Internet. If you have an e-mail address, you can download this music notation program for free from http://www.codamusic.com/coda/

A. Note-by-Note Symmetry in Music

Examples of note-by-note symmetry in music are very rare, but a few composers played with mathematical ideas and worked them out in music.

Nancy has composed a short tune called "Forwards and Backwards" to show how a melody can be symmetrical. When the melody is very short you can sometimes hear the symmetry. In a long symmetrical piece, you can not tell unless you look at the score.

Task 1: Open F to B. Play the piece. Press stop. Look at the melody to see if you can find the center, that is, where the mirror image begins.

Task 2: Open the file called note-note, that gives you the first half of a new melody. Compose the rest of the piece so that it is symmetrical. Play your piece. Can you hear the pattern in reverse?


Enrichment

The Crab Canon by J. S. Bach is a duet for two instruments where one instrument plays a line of music that is the mirror image of the other instrument. The Crab Canon is on a paper at the station.

If you were to listen to the Crab Canon, you would not be able to tell that the music is symmetrical.

Task 3: Compare the beginning of Instrument 1 and the end of Instrument 2. Can you see the mirror image? Check a little further, does the pattern continue?

What shape is a crab? How does a crab move? Can you guess why this title might fit?

Grade 5 students --If you have musical background and/or can think hard about this piece you might figure out that it is symmetrical in the auditory sense (through the ears) because if you could imagine or calculate the middle of the piece, you would find that the pattern of notes on either side is the same. This is a mental/technical kind of symmetry.

B. Symmetrical Forms (Auditory)

Musicians use ideas of symmetry to describe larger musical forms where listeners can hear large sections of music that are repeated. Rather than do the analysis note-by-note, the music is chunked into phrases/sentences or sections.

Open the file "Twinkle, Twinkle". Press play and listen to it. Notice that "Twinkle, Twinkle" has three phrases with the first and third being identical. It is not the words (called lyrics), but the musical line that makes it symmetrical.

This is called A B A form, a symmetrical form.

Some familiar objects can remind you of this ABA form, for example, Oreo cookies [cookie, filling, cookie] and sandwiches [bread, jam, bread].

Task 1: Listen to "Hot Cross Buns" from the CD. It has a repetition of the first A, so it is AABA. This is one of the most common song forms.

Listen to "The More We Get Together". Which form is it? ABA or AABA

Enrichment
Task 2: In pairs, go to a lap top where music notation has been down-loaded for you. As a group you are going to compose a short tune in ABA form. You need to start a new page and give it a title and composer. Select your instrument and add this instrument. Start composing. Play it back. Can you hear the repetition of the A section? Save it with your names + ABA.

Station 6: Symmetrical Poetry

The materials at this table will help you to write a short poem. It is fine to use both symmetrical and non-symmetrical words in your poem. The following is a list of 6 kinds of symmetry. Do not try to use them all. Read through these ideas for symmetry before deciding on your poem title. There are specific instructions for Grade 2 and Grade 5 students.

1. Pairs of words where one is the reverse of the other:

deer reed
draw ward
leg gel
live evil
not ton
no on
pets step
rat tar
rats star
saw was
sleep peels
ten net
trap part
war raw
won now


2. Words that are symmetrical, with each letter being symmetrical: MOM, EYE, WOW, WOW, EVE, EVE, OTTO.

3. Words that are symmetrical (palindromes): dad, did, level, kayak.

4. Two word combinations that are symmetrical:
A Toyota
A nut (tuna)
Wonton (not now)
Race fast safe car (the line of symmetry is through the middle of the t)
Don't nod (the line of symmetry is through the middle of the t)

5. Three words where the first and last are the same (ABA form). Examples:
Laugh and laugh
Warm cold warm

6. Reflection. See the Peace Poem, the words "peace" and "now".

• Make a drawing of a symmetrical object: boat, circle, a t-shirt, a house, or other object. See examples.
• Write a poem with one or two symmetrical word patterns.

Grade 5 Students:

• Make a drawing of a symmetrical object: boat, circle, a t-shirt, a house, or other object. See examples. Write a poem with three or more symmetrical word patterns.
• OR Print your poem so that the overall shape is symmetrical.Include three or more symmetrical work patterns.

If you would like to review what symmetry is you can visit this website:

http://pbskids.org/cyberchase/classroom/games/symmetry/index.html

Station 7--A Visual Arts -- Alphabet Symmetry
Materials: plastic letters, playdoh, plastic knife, miras.

What to do: Place a letter of the alphabet in front of you. Put a mira beside the letter. With your playdoh make a mirror image of your letter. When you look into the mirror what you see IN the mirror should be identical to the letter you placed in front of you. Is it?

Station 7--B Visual Arts -- Building Symmetry
Materials - photographs, Lego, pattern blocks, black construction paper, scotch tape

People who design buildings (architects) often use symmetry. Can you find the line of symmetry in the photographs of these buildings?

What To Do:

1. Choose a photograph.
2. What is symmetrical about the picture you chose?
3. Can you find the line of symmetry.
4. Cover half of the photograph with a piece of black paper.
5. Tape the paper down so it doesn't move.
6. Using Lego or pattern blocks, try to make the covered half of your picture by looking only at the uncovered side. Remember it is symmetrical!

Entrance to Sacred Heart School

House near Sacred Heart School

Station 7--C Visual Arts -- Remembering Symmetry
Materials - half-photographs, paper/pencils, crayons etc, scotch tape

What To Do:

1. Choose half a photograph.
2. Each picture is symmetrical. If I give you one side, can you draw the other side?
3. Tape the photograph to a piece of paper, and try to draw the other side.

Resources

Resources used in the preparation and implementation of this mini-unit.

http://www.gwydir.demon.co.uk/jo/learn/symmetry.htm

http://standards.nctm.org/document/eexamples/chap4/4.2/

http://www.explorescience.com/activities/activity_list.cfm?categoryID=4
http://www.codamusic.com/coda/
http://www.math.iastate.edu/mathnight/activities/modules/music/musicmiddle.pdf

http://pbskids.org/cyberchase/classroom/games/symmetry/index.html

www.pbs.org/teachersource
www.mathdance.org
www.scottkim.com
www.explorescience.com