Lesson Title: “Is Symmetry Useful?”
Creator: Billie Jo Falcon
Grade Level: 3rd
BigIdea: Geometry – Symmetry in our world
EssentialQuestions:
1.)Why is it that some two dimensional shapes have one or more lines of symmetry and others have none?
2.)How is symmetry used in our world?
3.)How can we use symmetry to showother relationships between shapes?
CSO:
M.S. 3.3 Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, student will
- analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships,
- specify locations and describe spatial relationships using coordinate geometry and other representational systems,
- apply transformations anduse symmetry to analyze mathematical situations, and
- solve problems using visualization, spatial reasoning, and geometric modeling.
M.O.3.3.4 identify, describe and draw lines of symmetry in two-dimensional shapes.
Learning Standards:
21C.03-4.1.LS.3 Student, cognizant of audience and purpose, articulates thoughts and ideas accurately and effectively through oral, written or multimedia communications.
21C.O.3-4.3.LS.4 Student appreciates, accepts and works cooperatively with others, in both academic and social contents, shares responsibility for continued improvement of the academic performance and climate of the school, and exhibits ethical behavior while working alone or communicating with others.
TechnologyTools: (Available – Elmo, 2 classroom computers, mobile presenter,)
21C.O.3-4.3TT.6 Student selects appropriate technology tools and resources needed to communicate information to others, to achieve personal goals, and to support independent learning.
Launch/Introduction:
1.)Ask students to cut out a heart from a piece of construction paper, place their name on it and tape it to the front board to form a class row of hearts. Have volunteers tell how they created their hearts. Ask: “If you worked for a greeting card company and had to pick the heart you felt your customers would most want to buy, what would you look for in a heart? And why?”
2.)Read to the class: Let’s Fly a Kite by Stuart J. Murphy. Then demonstrate use of a plastic mirror to show how they can check for symmetry without cutting or folding the pictures in the book.
ActivatePriorKnowledge:
1.)Create a class KWL chart for what we know about symmetry. Ask the students to repeat the word symmetry. Have the students state what they know about symmetry as you list it under “K”. Then ask if there are any questions they may want to ask about symmetry and write those under the “W”. Throughout the lesson have students add what they learn under the “L” on our chart.
SpecializedVocabularyDevelopment:
1.)Have students read the vocabulary words listed on our large chart paper (symmetric, lineofsymmetry, two-dimensional shapes). Encourage students as they work through the investigations to watch for other words that they’d like to add to our list.
2.)Using the Frayer model discuss and share meanings for thesewords.(The Frayer model is found on the Teach21 site under strategy bank, and is used as a graphic organizer for each vocabulary word.) We will fill one out for each new term as a whole group spending about 2-3 minutes on each section of the organizer. Students will keep these in their 2pocket Math folder. Example:
Definition in your own words / Facts/characteristicsExamples / Nonexamples
Investigate/Explore:
A.)Tell the students that you will give them a baggie of letters to share with the partner sitting beside them.They are to fold the letters as we try to discover what letters have one or more lines of symmetry. (We are using upper case 4” block letters pre-cut from our school’s Ellisondie cutter.) Since these letters may have curves that do not fold perfectly, students can check their lines of symmetry by using the plastic mirrorsto test the letters on the interactive Learning Recording sheet #19. As we fold and/or check each letter they should draw the lines of symmetry for the corresponding letters on recording sheet #19.
B.)Areas of the room have been set up with materials the teams will use to do activitiestoday.
*Students will be working in pre-assigned teams of four to explore:
Step 1.)Ask students “How we canidentify, describe, and create shapes with and/or without a line of symmetry?”[Team members will take turns drawing all possible lines of symmetry for the shapes on Class Activity sheet B-1. They have a second copy of this sheet to use if they need to cut and fold any of the shapes to help them describe its line of symmetry. Next, the teams will play the game on Activity Sheet # 11-2 to identify which lines are lines of symmetry in the figures given. Then they will create their own shapes and work as a team to decide if these shapes are symmetrical.
Step 2.) Each team will plan a way to organize their results to share with the classand explain what they discovered about various shapes they created or used.They may use a chart like the one below from page 112 in the Marilyn Burns’ book, About Teaching Mathematics.
These shapes fold one way: / These shapes fold more than one way: / These shapes do not fold to make matching sides:Step 3.) Next, the teams willbrainstorm and research a list of things in our world that show symmetry; jobs that might requireknowledge of symmetry; and othermath concepts we might be able to show using our knowledge of symmetry.
*Firsthave teams start by taking a team assignment sheet, and then each member picks a tongue depressor stick labeled as either recorder #1 or #3 or as reporter #1 or #3 to determine their job.
Summarize/Debrief the Lesson:
Reflections:
1.)Review the class chart of Share Time Rules.
2.)Share time: Teams return to whole class area and one team at a time comes up front:their first reporter shares and displays their team’s results for step1(What shapes did your team discover had lines of symmetry, and how do you know?); then their second reporter shares their discoveries from step 3 (How is symmetry used in our world and/ or for other math lessons?); after each report the team members may answer any questions from the class.
3.) Does anyone have something they learned about symmetry that they would like to add to the “L” section of our class KWL chart?
4.) Ask for volunteers to use our new vocabulary words in meaningful sentences.
5.) Do you think what you have learned about symmetry could make something you try to do easier than before? What?Why?
6.) Has anyone else discovered something about symmetry that we have not discussed yet? Or a new question that anyone would like to add to the “W” section of our KWL chart about symmetry?
Extensions:
1.)Problem Solving Activity #11-4 using tangrams to construct symmetrical figures.
2.)Brain Game Book activity sheet from pages 414-415 to draw the missing half of pictures on grid paper.
3.)Symmetry Art Lessons on pages 15 and 17 fromMath Art Projects and Activities book by Carolyn Ford Brunetto, or make collages of symmetrical pictures.
4.)Students could use blocks to design 3-D symmetrical figures;pattern blocks to design 2-D symmetrical figures; or geoboards to make symmetrical designs.
5.)Take a nature walk looking for leaves, flowers, and bugs that have symmetry.
6.)Suggest students check their closets at home to fold clothes to check to see if they are symmetrical.
Materials:
Copies of the team assignments; construction paper for hearts;tape;scissors;KWL Chart;Enough sets of pre-cut letters(for partners);2-D shapes/or templates; pencils;rulers; and the following activity sheets: From Houghton Mifflin Math Expressions lesson B-1 backline masters on pages100-101; from Scott Foresman-Addison Wesley enVision Math Teacher Resource Masters for Recording Sheet # 19 and Center Activities #11-2. *For Extension Activities add problem solvingreteach/practice #11-4; Teacher Created Resources in the Brain Game Book pages 414 -415; tangrams; building blocks; and the book Math Art Projects and Activities by Carolyn Brunetto.
*Helpful, but optional: clip boards, mirrors, Elmo, mobile presenter, computers/ internet, possibly have available old catalogs and magazines for students to cut out any pictures that have symmetry; Books and magazines about art, architecture, and designers such as: St. Louis Architecture for Kids (Scholastics) by Lee Ann Sandweiss; Architecture ABC by Michael J. Crosbie; *Bookmark these Google searches for webQuest:Symmetry in Our World; Symmetry in Art; Symmetry in Nature; Symmetry in Architecture; Symmetry in Logos; and websites:
Duration: 90 minutes(If you have 60 min. Math Periods you could do steps 1 & 2 one day and step 3 the next day.)
Assessment: Informally assess students as they share what they recorded on Record sheet # 19, and as they report their discoveries and answer questions from theirteam activities. (Can students identify, describe, and draw lines of symmetry correctly?)
Discussion/ TeacherNotes: Our lesson is on symmetry and its importance and use in the real world. We start with a simple activity to cut out heart shapes to observe what skills or understanding of symmetry the students may already use. Next, I shared a book about two kids who always want things divided in two matching parts. Then we introduce the term and ask what they know or would like to know about symmetry.
I chose to have my students work in pairs for the whole group letter folding activity to encourage them to describe how they were checking for lines of symmetry and communicate why it did or did not work. Doing this with a partner first gives all the students more courage to share with the whole group later. Then I chose to put them in pre-assigned groups of 4 to work as a team with heterogeneous abilities and cooperation skills.
Through hands on activities the teams exploreshapes that do or do not have lines of symmetry. They will be cutting, folding, and/or using plastic mirrors to look for lines of symmetry. Once the students do several activities identifying, describing, and drawing lines of symmetry, they will look for symmetry in their world. They will also predict and research possible uses for symmetry.Students will have the opportunity to use the internet (we have 2 internet connected computers in our classroom), books, catalogs, and magazines to look for how we use symmetry in our world. As I walk around the room observing the teams I will offer guidance or suggestions if needed to help them find other things that have symmetry such as clothing, art work, and things in nature.
After a set amount of time, I will encourage the teams to work on a presentation of what their team has discovered about symmetry in shapes and other things in our world. The students may choose to create charts, use the Elmo or mobile presenter, or if they have the skills by the time we do this lesson they may create a computer presentation. (My students who go to enrichment may help others try this.)
One of my goals is to encourage my students to use 21st century technology to communicate mathematical discoveries they have made about symmetry. Another goal I had in preparing this lesson is to motivate my students to think beyond theone page lesson they have each year in their Math textbook on symmetry.By looking for symmetry and its uses in the real world they can take ownership of this Math concept and actually use it and recognize places it may have been used. Hopefully, by the end of this lesson the students will not forget ‘symmetry’ or confuse it with other Math terms. I also plan to have them use their new knowledge of folding to create equal or matching parts in future lessons on fractions and problem solving.
Resources:
Other Children’s literature books with similar concepts:
Reflections by Ann Jonas
LAO LAO of DRAGON MOUTAIN by Margaret Bateson-Hill
KITES by Demi
Math Art Projects and Activities by Carolyn Ford Brunetto (Scholastics)
TEAM ASSIGNMENTS
*First, draw a job stick to see who will do each of the following jobs:
- Recorder for step 1. You will get a clip board to record the shapes and mark which ones have lines of symmetry as you and your team work through step 1.
- Reporter for step 1. Present your team’s discoveries from step 1 to the class.
- Recorder for step 3. You will get a clip board to list people, places, and things you and your team found that use symmetry.
- Reporter for step 3. Present your team’s discoveries for step 3.
Follow these steps:
Step 1. Do the activity sheet B-1, then play the game on activity sheet #11-2 to practice identifying, describing, and drawing lines of symmetry, and creating shapes that have symmetry. Why do some shapes have symmetry and others do not?
Step 2. Plan a way to organize your team’s results to share with the class what you discovered about the various shapes you folded, created, or used in step 1. (You may share their results using the Elmo or creating a table on Microsoft Word.)
Step 3. Brainstorm and research a list of things in our world that show symmetry; jobs that might require knowledge of symmetry; and other math concepts we might be able to show using our knowledge of symmetry.
Possible Rules for use on class charts:
SHARE TIME RULES
1.)Raise your hand and wait to be acknowledged.
2.)Share your ideas.
3.)Listen, with your hand down, when someone else is talking.
4.)Ask questions or share comments related to what is being discussed.
GROUP RULES
1.)YOU are responsible for your own work and behavior.
2.)YOU must be willing to help any group member who asks.
3.)YOU may ask the teacher for help only after you have asked everyone in your group for help. (Ask threebefore me!)
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