Rotational Symmetry

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SWBAT determine if a figure has rotational symmetry.

Big Idea

By turning a shape to different measurements, the students can determine if a shape has rotational symmetry.

Whole Class Discussion

15 minutes

Rationale:  This lesson allows me to review angles with the students.  In previous lessons, the students learned that a right angle is a 90 degree angle.  In this lesson, we take what we know about a right angle and use it to determine if a figure has turned 90 degrees, 180 degrees, 270 degrees, or 360 degrees.

To begin the class, I review with the students what they have already learned about symmetry.  I ask the students to raise their hands and tell me what they know about symmetry.  One students says, "Symmetry is when you fold something and it matches up on both sides."  I remind the students that it is called a line of symmetry when you fold along a line and both sides match perfectly.  Another student adds, "If you cut something in half, both sides are the same."  I ask, "If you fold a shape along a line and it does not match up perfectly, is that a line of symmetry?"  Student response:  No.  

I go on to tell the students that today's lesson is rotational symmetry.  The Rotational Symmetry powerpoint is displayed on the Smart board.  We begin by reviewing the vocabulary:

rotate - to turn

rotational symmetry - when a figure can rotate onto itself in less than a full turn.

I point out to the students that the definition says "less" than a full turn.  I tell the students that they can not say that a shape has rotational symmetry if you have to turn the shape a full turn to get the original shape.  If you turn the shape 1/4, 1/2, or 3/4 turns and it looks the way it did originally, then that shape has rotational symmetry.

I demonstrate this in the power point.  I display the arrow in its original position.  Next, the arrow is turned 1/4.  I demonstate that this is a 90 degree turn by drawing a clock on the white board.  I put the following numbers on the clock:  12, 3, 6, and 9.  I explain to the students that when we turn a shape a 1/4 turn, it is a 90 degree turn.  I draw the line from the 12 to the 3. I ask the students to explain why this is a 90 degree turn.  The students could see that the lines going from 12:00 to 3:00 forms a right angle.  The students have already learned that a right angle is a 90 degree angle.   I ask, "Does this shape at a 90 degree turn look like the original shape?"  The students could see that it did not.  Therefore, we do not know if the figure has rotational symmetry yet.  On the Smart board, I display the shape at a half turn.  I explain to the students that this is called a 180 degree turn.  On the clock I display this by showing that the figure started at 12 and now is at 6.  I draw the line from the 12 to 6 to give the students a visual of the straight angle.  Next I ask, "Does this shape at a 180 degree turn look like the original shape?"  The students all agreed that the arrow did look the same as the original shape.  This means that this figure has rotational figure because I turned it less than a full turn and it looked like it did at first.

To give the students a little more guided practice, I display a trapezoid on the Smart board.  The original shape is displayed, then it is turned 90 degrees.  I ask, Does this shape look as the original shape did?  Student response:  No.  The next slide shows the trapezoid at 180 degrees.  The students said that this was not rotational symmetry.  The next slide displays the trapezoid at a 270 degree turn.  The students said that this was not rotational symmetry.  Last, the trapezoid is shown as a full turn, and it is back in its original position.  Does this shape have rotational symmetry?  Student response:  No.  Why does this shape not have rotational symmetry?  One student responded, "Because it took a full turn to look like the first one."  

Skill Building/Exploration

20 minutes

I give the students practice on this skill by letting them work independently.  By doing this activity independently, each student will get the hands-on experience of rotating the shapes to see if they have rotational symmetry. 

I give each student a rotational symmetry activity sheet and scissors.  The students must cut the shapes out and turn them 1/4, 1/2, and 3/4 turns to see if they have rotational symmetry (MP5).  If they do, the students must write "yes" on the shape.  If they do not, the students write "no" on the shape.  Displayed on the Smart board is a copy of the activity sheet.   This will help the students remember how the original shape should look. 

The students are guided to the conceptual understanding through questioning by me.  As I walk around while the students are working, I assess the students understanding by questioning the students about their answers.  As you can see and hear in the Video - Rotational Symmetry, I use questioning to help guide this student to conceptual understanding.

1.  When you turn the shape less than a full turn, does it look like the original position?

2.  Explain why you said that this shape has rotational symmetry.

3.  Explain why you said that this shape does not have rotational symmetry.

Early Finishers: Draw shapes that have rotational symmetry.  Cut out the shape and turn it 1/4, 1/2, or 3/4 turns to see if you are correct.


15 minutes

To close the lesson, I call the class back together as a whole.  I point to the shapes displayed on the Smart board and call on students to tell me if the shape has rotational symmetry.  The other students tell me if they agree or disagree with the answer.    

I feel that by closing each of my lessons as a whole class is important for students to hear how their classmates think.  If a student does not understand, then this is an excellent teaching opportunity to help those students that did not master the skill.  Students need to see hear and see good work samples (Student Work - Rotational Symmetry).