Reflectional and Rotational Symmetry

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SWBAT Identify objects with reflectional and rotational symmetry.

Big Idea

This is the first lesson in a unit on transformations. Students will examine different objects and identify their symmetries and orders of rotation based on their prior knowledge from the eighth grade.

Do Now

7 minutes

For the Do Now, students identify the various line symmetries of letters in the alphabet. I use this simple activity to activate student's prior knowledge of symmetry. They don't have any problem identifying letters with line symmetry, but they sometimes have difficulty identifying letters with rotational (point) symmetry when we get to them. After about 3 or 4 minutes, we go over the Do Now as a group. I call on various students to state their letters.  Then I ask other students to decide if all of the letters with a specific symmetry have been identified. 

Every time I do this activity, I have several students identify the letters S, N, or Z as having line symmetry. A discussion about the symmetry of these letters leads into the Mini-Lesson where we investigate point symmetry.

I have also included a scaffolded version of the Do Now for students who may not remember much about symmetry.



10 minutes

I begin the Mini-Lesson with a discussion of line symmetry. I say to students, “Another name for line symmetry is reflectional symmetry. Why do you think it’s called that?” Although students can answer this question, they have difficulty verbalizing exactly what they are trying to say. Through further questioning, I elicit that an object has reflectional symmetry if there is a straight line passing through the object and dividing it in half where one side of the shape is the same as the other except it is inverted.

 Next, we move on to point symmetry.  I ask the students, “Are the letters S, N, and Z symmetrical?” In the Do Now, we decided these letters do not have line symmetry; however, these letters are symmetrical. I instruct students to turn their Do Now slip upside down. Students can see that the letters S, N, and Z look the same upside down as they do right side up.  These letters have rotational or point symmetry. They can be rotated 180o around a point in the center of the letter and look the same. I ask, “Which other letters have point symmetry?” Students identify H, I, O, and X correctly, but often include some incorrect letters. Because M becomes W and vice versa when they are rotated 180o about a point in the middle of the letter, students often think they have point symmetry. Additionally, students also identify C and E as having point symmetry. To address this misconception, I remind students that the letters must have the exact same orientation when they are rotated in order to have point symmetry.

We then go into rotational symmetry more in depth by discussing order and angle of rotation. Students sometimes have difficulty identifying an object’s order at first, but with practice, they catch on quickly.   


23 minutes

Before handing out the worksheet, I show students the cross from the Greek flag. We discuss the reflectional and rotational symmetry of the cross. The worksheet has similar types of practice examples. 

Since the examples on their worksheets are in black and white and incomplete, I put pictures of the international flags on the Smartboard. This helps to give students some context when looking at the flags. 

As the students are working, I circulate and ask guiding questions, such as, “If you fold the paper along the lines of symmetry you have drawn, do the halves match up?” and “What happens when you turn the paper upside down?”  Some of the examples are a bit tricky. I instruct the students to look carefully.

After about 15 minutes of working, I stop the students and we go over their responses. I call on students to come to the Smartboard and draw lines of symmetry. We can also see rotational symmetry by actually rotating the objects. 



5 minutes

Exit Ticket:  Is the number of lines of symmetry in a regular polygon always the same as its order of rotation? Justify your answer.

Most students will initially say “yes,” but as they investigate further, they will find it is not always true. Students can use the examples from the lesson activity to justify their answers.