Grade Level: 5th grade

Lesson Objective(s): The student(s) will:

Compare reflectional and rotational symmetry.

Practicum Classroom Teacher: Mrs. Coelho

Indiana Standard: Geometry

Indiana Indicator/ Substandard:

Identify shapes that have reflectional and rotational symmetry.

Materials/Media:

Picture of a man

Picture of an iceberg reflecting into the water

Picture of snowflake

Several sheets of white paper

Pencil

Scissors

Precut Shapes (rectangle, circle, square, triangle, star)

I. Motivation:

1. Put the students in groups of four.

2. Give each group of student's five pictures. (The pictures of the man, iceberg, snowflake, building, and bus from the materials list.) Each picture should show reflection symmetry.

3. Give students directions: "Work together to figure out what all the pictures have in common. Look for patterns in the pictures. Also notice the differences in the pictures. Conclude how all the pictures are alike."

4. Ask Student when they are finished: What do you think all of these pictures have in common? Do you think they have anything in common? Did any of you think of geometry when you were looking at these pictures?

a. When students raise their hands call on them for answers.

5. After all students have been given a chance to answer make sure that the students know that all of the pictures have geometry and symmetry in common.

6. Next tell the students: "Today we are going to learn what reflectional and rotational symmetry is, and where we see it in our environment. (Goal for learner)

II. Procedure:

A. Reflectional Symmetry Within shapes.

1. Write on chalkboard and say: "Reflectional symmetry is when there are two equal sides or two parts that balance on each side of a line." (New Information)

a. Show students shape of rectangle.

b. Ask students to identify the shape in my hands.

c. Watch me I want you to use this process next.

d. Show students how to hold and fold the rectangle so that all the edges match up. (Modeling)

e. Have them fold their rectangle in half, just like they were shown, so that all the edges match up.

f. Give each student a precut rectangle made out of construction paper from the materials list.

g. Have students hold their rectangle with both hands.

h. Each student may only fold the rectangle one time, and if the edges don't match up they need to refold the rectangle so that the edges do match up.

i. Have students reopen their rectangle, and notice the crease (valley).

j. Have students draw a line down the inside crease (valley) on the rectangle they just folded.

k. Ask students: "What do you notice about your rectangle?"

l. Have students fold their rectangle again, but in a different place than the first time the students folded the rectangle.

m. Tell students to make sure that all the edges match up when they fold their rectangle again. (Guided Practice)

n. When students are done ask them: "Does your new crease (line or valley) show reflectional symmetry? How can you tell?" (Check for understanding)

2. Hold the rectangle back up for the students to see.

a. Fold your rectangle for the students incorrectly, the diagonal way.

b. Draw a line down the crease you just made on your rectangle.

c. Show students the line you just drew on your rectangle. (Modeling)

d. Ask students: "Is the line I just made a line of reflectional symmetry? (Check for Understanding)

3. Reflectional symmetry within circles.

 a. Hold up a circle.

b. Ask students: "How many lines of reflectional symmetry do you think a circle has?"

c. Let students answer.

d. Physically fold the circle over and over again showing students that there are many lines of reflectional symmetry.

e. Tell students that a circle has an infinite number of lines of reflectional symmetry, but it is still possible to have a line in a circle that does not show reflectional symmetry.

f. Fold the circle so that it is not a line of reflectional symmetry for the students. (Modeling)(New Information)

g. Give each student three different shapes, (square, rectangle, triangle) made out of construction paper.

h. Tell students: "Put your name on the back of each shape so that the shapes won't get lost."

i. Tell students: "In a minute you will be trying to find at least one line of reflectional symmetry and one line that does not have reflectional symmetry on each of your shapes."

j. Tell students: "Some of the shapes will have more than one line of reflectional symmetry."

k. Tell students to find at least one line of reflectional symmetry and one line that doesn't have reflectional symmetry in each of the three shapes you just gave them. (Practice/Application)

l. When they are done have them set their shapes aside for later use.

 

B. Showing reflectional symmetry by sliding and flipping.

1. A different way to show reflectional symmetry is by having identical shapes or objects side by side or overlapping one another.

a. One way we can find reflectional symmetry is by sliding shapes to form a new picture. In this picture we can find different lines of reflectional symmetry other than just inside a shape. (New Information)

2. Take a circle and trace it on the chalkboard.

a. Show the students how to slide the circle, and then retrace the shape.

b. Show the students a line of reflectional symmetry. (Modeling)

c. Ask students: "Can you see any other lines of reflectional symmetry?"

d. Have a student come up to the board.

e. Have the rest of the students do at their seats what the student does on the board.

f. Have the student trace the circle up on the board.

g. Tell the student to slide the circle, and then trace the circle where they slid it.

h. Ask other students to find lines of reflectional symmetry. (Guided Practice)

3. It is also possible to flip shapes and find lines of reflectional symmetry just like we did when we slid the shapes. (New Information)

 a. Take a triangle made out of construction paper.

b. Trace the triangle on the board.

c. Demonstrate to the students how to flip the triangle.

d. Show students one line of reflectional symmetry. (Modeling)

e. Ask students to find other lines of reflectional symmetry, if any?

f. Have a student come up to the board.

g. Have the rest of the students do at their seats what the student at the board is doing.

h. Have student trace the triangle.

i. Have student flip triangle in a different way than I just did.

j. Ask other students to point out lines of reflectional symmetry. (Guided Practice)

4. Have each student get the three shapes that they put aside earlier.

a. Give each student a sheet of white paper from the materials list.

b. Tell the students to trace a shape.

c. Then they are to practice sliding and flipping the shape.

d. They are to trace the shape once they have flipped or slid the shape.

e. They are also to draw at least one line of reflectional symmetry. (Practice/Application)

C. Rotational symmetry with snowflake.

1. Write on the board and tell students: "Rotational symmetry is when an object spins around an axis and the object appears to look the same two or more times. (New Information)

 a. "A tire rotating around an axle is a good example of rotational symmetry. As the tire rotates around the axle it always looks the same. You can not tell what is the top of the tire, because it always looks the same."

b. Snowflakes are a lot like this as well. We are going to make a snowflake.

c. Give each student a 6x6 square of construction paper from the materials list.

d. Ask students to fold their paper in half.

e. Tell them to fold their folded paper in half.

f. Then have the students fold the paper in half one more time.

g. Have students cut out shapes along the edges of their folded paper.

h. "Make sure not to cut all the edges away so that the paper does not fall apart when you open it."

i. When students are done cutting tell them to open up their snowflakes. (Guided Practice)

j. Ask students: What do you notice about your snowflake? Can you find any lines of reflectional symmetry? (Check for understanding)

2. Give each student a plain piece of paper.

 a. Have students put a big dot approximately in the center of the plain white piece of paper.

b. Explain to students: "This is the axis for our snowflake. The point in which we will rotate our snowflake.

c. Have students lay their snowflake over the piece of paper, with the big dot being in the center.

d. Show students how to rotate the snowflake by 1/4th turns on the sheet of paper. (Modeling)

e. Have students rotate their snowflake on their paper.

f. Have all the students write top on one of the flat side of the snowflake. This will represent the top of our snowflake so that we don't get confused when we rotate the snowflake.

g. Show students how when the snowflake is rotated there are certain points where the snowflake looks like it is in the original position in which we started.

h. Show students that when we see a point in which the snowflake looks like the original we will write out to the side of that point "one point of rotational symmetry".

i. Rotate your snowflake so that it looks the same as the original.

j. Ask students: Is this a point of rotational symmetry?

k. Make sure they understand that this is a point of rotational symmetry.

l. Rotate your snowflake so that it is not at a point of rotational symmetry.

m. Ask students: Is this a point of rotational symmetry?

n. Make sure they understand why this is not a point of rotational symmetry. (Guided Practice)

o. Have students work in pairs to discover where their snowflake has rotational symmetry. They are to label all points of rotational symmetry on the paper. (Practice/Application)

C. Rotational symmetry with shapes.

 1. Give each student the shape of a star made out of construction paper from the materials list.

 a. Give each student a plain sheet of paper.

b. Have each student put a big dot on his or her paper symbolizing the axis.

c. Have each student trace his or her star.

d. Show students that they can tell the star has a point of rotational symmetry when the star matches up with the traced star.

e. Have each student find all the points of rotational symmetry while in groups of two. (Practice/Application)

f. Ask students: If we rotated the shape one complete time would the shape look the same? If the shape looks the same after only one complete turn does the shape have rotational symmetry? (Checking for understanding)

D. Get back out the four pictures the students worked with in the motivation of the lesson.

1. Ask students to point out were the lines of reflectional symmetry are on the man, bus, iceberg, snowflake, and building.

a. Ask students: How do you know were the line of reflectional symmetry is?

b. Ask students: Which of these five pictures has rotational symmetry? How do you know the snowflake has rotational symmetry?

c. Ask students: Name some other objects or things you see in everyday life that have symmetry.

c. "What is the difference between reflectional and rotational symmetry?" (Closure)

III. Evaluation of Student Learning:

 1. Have each student get out the three shapes I had him or her put aside earlier in the lesson.

 a. Give each student a sheet of paper.

b. Have each student fold the sheet of paper in half long ways or hot dog ways.

c. Then have them unfold the paper.

d. Have students fold their paper in half hamburger way or the short way, and then have them fold it in half again while the paper is still folded. This time it will look hot dog ways or long ways.

e. Have students open their paper.

f. They should have eight boxes.

g. Have students number each box in the upper left-hand corner.

2. In the first three boxes the students should draw each of the three shapes that I just had them get out.

 a. Have students put a line of reflectional symmetry in each shape

b. In boxes 4, 5, and 6 have the students draw each shape that they drew in boxes 1-3, only this time with lines that are not lines of reflectional symmetry.

3. In box 7 I want each student to draw a shape, pretend to slide the shape, and then draw the shape were they would have slid the shape on the paper.

 a. Also draw one line of reflectional symmetry in box 7.

b. In box 8 I want each student to draw a shape, pretend to flip the shape, and then draw the shape were they would have flipped the shape on the paper.

c. Also have students draw one line of reflectional symmetry in box 8.

4. On the back of the paper have student draw a line to separate the top half of the paper from the bottom half of the paper.

 a. Tell each student to get out his or her rectangle and triangle.

b. In the top box have students trace a rectangle and label how many points of rotational symmetry the rectangle has.

c. In the bottom box have students trace the triangle.

d. Have students label how many points of rotational symmetry the triangle has.

 

Symmetry Worksheet Scoring Rubric
Categories	Unsatisfactory 0	Unsatisfactory 1	Basic- Proficient 2	Proficient 3
Shape Drawn with one line of reflectional symmetry (boxes 1-3)	No Answer/ Problem was not done	Shape drawn; no line or line present but not correct	Shape drawn; line present and correct
Shape drawn with one line that's not a line of reflectional symmetry (boxes 4-6)	No Answer/ Problem was not done	Shape drawn; no line or line present but not correct	Shape drawn; line present and correct
Shape and slid shape present with one line of reflectional symmetry (box 7)	No Answer/ Problem was not done	Shape drawn; no line or line present but not correct	Shape drawn; line present and correct
Shape and flipped shape present with one line of reflectional symmetry (box 8)	No Answer/ Problem was not done	Shape drawn; no line or line present but not correct	Shape drawn; line present and correct
Rectangle traced and shows all points of rotational symmetry (back of paper)	No Answer/ Problem was not done	Shape drawn; no points of rotational symmetry labeled: points labeled but incorrect	Shape traced; one point of rotational symmetry present and correct	Shape traced; Two points of rotational symmetry present and correct
Triangle traced and shows all points of rotational symmetry (back of paper)	No Answer/ Problem was not done	Shape drawn; no points of rotational symmetry labeled: points labeled but incorrect	Shape traced; one point of rotational symmetry present and correct	Shape traced; Three points of rotational symmetry present and correct
Points Possible: 14		Total Points earned:		___________

IV. Lesson Extension:

1. The next day we would go outside with a digital camera, and the students would find things that they could either pick or that we could take pictures of that reflect reflectional and/or rotational symmetry. Then we could go inside and relate the reflectional and rotational symmetry to another subject we are learning about. For example we could discover if buildings had reflectional symmetry in other time periods as well as our own. Many groups of people use to or still do make masks to represent their way of life. We could make masks that have reflectional symmetry, and would represent our way of life.