Line of Symmetry

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SWBAT identify and draw the lines of symmetry by folding two-dimensional shapes.

Big Idea

Folding a two-dimensional shape can help a student identify the lines of symmetry.


5 minutes

In today's lesson, the students learn to recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Also, the students identify line-symmetric figures and draw lines of symmetry (4.G.A3).  

To begin the lesson, I give each student a sheet of copy paper.  I ask the students to fold the sheet of paper in half horizontally.  (I model this for the students with a sheet of paper.)  What can you say about both parts of the paper?   (I want the students to tell me that both parts of the paper are the exact same size.)  Student response: 1) They look like a fraction of 1/2, 2) They both are rectangles, 3) They are symmetrical.  This student is exactly right.  

Just to make sure that the other students understand, I ask this student, What exactly do you mean when you say that they are symmetrical? Student response:  They are the same on both sides.  I let the students know that this is a line of symmetry.  A line of symmetry is when a two-dimensional shape is folded and you get a mirror image of the other part.  Can a shape have more than one line of symmetry?  Student response:  Yes.  Let's find out.

Whole Class Discussion

10 minutes

To get the students to understand that a shape can have more than one line of symmetry, I have the students fold the piece of paper vertically.  I tell the students that the paper must match up perfectly when they fold it.  If it does, then that is a line of symmetry.  The students now know that a shape can have more than one line of symmetry.

The Line of Symmetry power point is displayed on the Smart board.   I call the students, who are sitting in the back of the room, to the carpet so that they can see the board clearly.  There are two shapes with lines drawn through them.  I want the students to tell me if these lines are lines of symmetry.  (This is important because, for our state test, the students will have to be able to look at a shape to determine if there is a line of symmetry.)  I remind the students that in a line of symmetry, whatever we see on one side, we need to see the exact same thing on the other side.  I point to the first shape and ask if it is a line of symmetry.  Student response:  No, because it is not equal on both sides.  I ask the students to tell me a word that can describe a symmetrical shape.  The students had a hard time remembering this word, so I remind them that we have talked about congruency.  Congruent means same size, same shape.  In the first shape, the two sides are not congruent.  One side has an angle and the other side does not.  Next, the students studied the second shape.  I ask, If I fold this shape along the line, would I have a line of symmetry?  Student response:  Yes, because both sides are equal. If I moved the line in the shape up some.  Would it be a line of symmetry? Student response:  No, because one side would have more than the other side.  

I let the students know that a shape can be divided in three different ways to find a line of symmetry:  horizontally, vertically, and diagonally.  

To give the students practice, I allow the students to work in pairs to explore the skill.

Skill Building/Exploration

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others.

For this activity, I put the students in pairs.  I give each pair a bag of cut out shapes.  The students must work together to find all of the lines of symmetry for the shapes.  Also, on each table, there is a bag of wooden geometric shapes.  The pair of students must take a shape, trace it, then draw the line(s) of symmetry for the shape (MP4). Repeat with a different shape.  It is important that the students can draw lines of symmetry for printed shapes because on the end-of-the-year state test, the students will not have cut out shapes to fold.

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.  The students communicate with each other and must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students.  As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6).  As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.  

As they work, I monitor and assess their progression of understanding through questioning. 

1.  When you fold the shape, do you get a mirror image of the shape?

2.  How many lines of symmetry does the shape have?

3.  What can you do to find other lines of symmetry for the shape?

Early Finishers: Identify shapes in the classroom that have a line of symmetry.


15 minutes

To close the lesson, I have students share their answers.  This gives those students who still do not understand another opportunity to learn it.  The students show how they folded their shapes in order to get a line of symmetry.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples (Student Work - Symmetry and Student Work - Symmetry), as well as work that may have incorrect information.  

 Each student is given an Exit Ticket - Line of Symmetry to complete individually.  Group activities are great, but I need to know how well each student is doing on their own. The exit tickets are collected at the end of class (Exit Test - Line of Symmetry).  This gives me further data on how the students are comprehending individually.   All struggling students identified from the data on the exit tickets will receive further instruction in small group.

Results from exit ticket:

Only 6 students out of 16 students found the 2 lines of symmetry for the exit ticket.  Most of the other students thought that there were 4 lines of symmetry for this shape.  Even though the students did well during the lesson with the cut out shapes, we still have a lot of work to do on drawing lines of symmetry on a shape that we can not fold.