Discovering the Meaning of Line Symmetry

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SWBAT identify the lines of symmetry in a two dimensional figure.

Big Idea

Creating a beautiful design from three polygonal figures helps a student discover and understand the meaning of symmetry.

Warm Up: Finding Symmetry in a Square

10 minutes

Materials Needed: Squares cut out from construction paper or sticky notes.

I opened the lesson today by questioning students about what they understood about symmetry. I wanted to get some understanding of what they perceived as symmetry. I wrote the word on the whiteboard as we started the short discussion. I held up a sticky note and asked: What does it mean to fold something in half? I asked students to share their thoughts.

Then I asked them to find a way to fold the square in half again. Afterward, I told them to open up their squares an take a look at them. I asked them to describe what they saw. One student said that we had folded it into fourths. I agreed and then steered them back to the concept of lines fearing that they would focus on fractions.  I asked them to find two more ways to fold their squares in half and we continued to discuss the concept of lines until I was satisfied that all had mastered the part of the standard that requires them to recognize lines of symmetry. 

I led them into discussion of the vocabulary word "symmetry" by asking for a show of hands if they had heard the word. I half expected they had heard it and had some concept of what it was since I know that they covered this in third grade last year, even though it is not a third grade standard.

After this simple task, I was confident all students would be able to master the task of identifying line symmetry. I wanted to challenge them!




Symmetry in Nature

15 minutes

Math in Nature: This standard requires that students recognize lines of symmetry. What better place than in nature? I showed them this cute video to help them get used to looking for symmetry and activate their "symmetry vision."

I carefully coached them as the video moved from picture to picture because I wanted them to be engaged in thinking about looking for symmetry. They especially were intrigued with the buildings.I made sure in my comments as the video progressed to connect the real world with the mathematical concept. When the video was finished, we took time to discuss their favorite picture and go back to take second peeks. It was fun to share and talk about symmetry in nature through this video.

Moving on: I asked them to log onto Educreations and find one object in the room to photograph that they thought had lines of symmetry. After they photographed the object, I wanted them to draw as many lines of symmetry, using their app, as they could on the photographed object and record their explanation of what symmetry means. They were asked to save their lesson. This way, this video became a reference. If they found something without symmetry or could not recognize it, I could easily assess where they were in their thinking process. It also allowed them to experiment, guess, and predict. I roved the classroom to assess their understanding. Everyone had a photo of something with symmetry. Students supported one another if they were having difficulty identifying lines of symmetry.

 I told them that finding lines of symmetry in more complicated patterns becomes harder. The next part of our lesson will help them understand that. The next part of the lesson steps up the level of rigor and not all students will master it, but they will strengthen their understanding of the standard.



Creating Symmetry with Polygon Shapes

20 minutes

Materials: 3 Polygon Shapes of choice, computer paper, three different colored colored pencils, black construction paper for background.

I created examples of the following steps and displayed them on the whiteboard for them to refer to throughout the lesson. Once students chose three polygons they were to do the following:

1. Take a piece of computer paper and fold it in half lengthwise. Then open it and fold it the widthwise . Folded paper example

2. Open it up and find the center intersection of the lines and place your first piece in the center. Starting the design....

3. Then, trace around the first piece. From that piece you can build your design.

4. The pieces may not overlap, but butt up side to side or corner to corner.

5. You may not draw a design beyond the edge of the paper.

6. Color each shape one color. For example, the square is one color, the triangle another and the rectangle another. You must adhere to these colors for these shapes.

7. Cut out your design when you are done. Do not cut out the individual pieces.

8. Fold the design to find as many lines of symmetry as possible.A design completed by a student.

9. Write on the note card and describe how many lines of symmetry your design has.

10. Glue the shape to the black construction paper. The design will pop!

 Math Practice Standard 5 and 7 are being exercised here as students need to use the polygonal shapes correctly and strategically in order to produce a symmetrical design. They are continually reasoning the concept of balancing the half with the other half of the design as they place their shapes with edges or vertices touching as required.




5 minutes

When several students had finished cutting out their designs, it was time to stop and share some work. Not all were finished and it was assigned for homework. I knew sharing would assist them in their understanding as they complete the symmetrical design.

I led the discussion with asking two different students to explain their designs and the symmetry. We wrapped up the lesson with discussing whether we had mastered the standard yet. I reviewed the goals with them and we decided that we:

1. Mastered recognizing line symmetry. We could fold the square, find the lines of symmetry and we all understood.

2. Can draw line symmetry on a 2 d shape. When we chose an object to photograph and explain in an Educreations Video on iPads, we proved  that we had solid evidence of mastering this standard.We could recognize a symmetrical object and draw lines of symmetry as the standard required.

 However, we all agreed that creating  a 2d shape was much more difficult than the earlier work! This is rigorous and we need more practice as a whole. They photographed the steps and examples on their iPads for instruction to support their work at home. I told them to please enjoy this design and thinking process as they practiced mastering a much more rigorous task to discover how symmetry works.