Lines of Symmetry. Grade 3. Amy Hahn. Education 334: MW 8 9:20 a.m.

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1 Lines of Symmetry Grade 3 Amy Hahn Education 334: MW 8 9:20 a.m. GRADE 3 V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT A. Spatial Sense Understand the concept of reflection symmetry as applied to geometric shapes. Understand how representations of shapes are affected by various motions. 1. Identify lines of symmetry in geometric shapes. 2. Recognize and predict the position and orientation of a shape after a single flip, slide or turn.

2 Unit Objective: The students will understand more what symmetry means and be able to identify lines of symmetry in shapes, letters, and everyday objects. Daily Objectives: Day 1: Fold paper cutout shapes to find the line of symmetry and define the line of symmetry. Day 2: Analyze shapes to find their line of symmetry and draw lines of symmetry. Day 3: Analyze shapes, letters, signs, and nature to find their line(s) of symmetry. Day 4: Create symmetrical patterns and designs and find lines of symmetry. Day 5: Identify lines of symmetry in shapes. Classroom Description: There is a hearing impaired student in this class.

3 Are the Sides the Same? 1. Objective: By the end of this lesson students will be able to: a. Fold paper cutout shapes to find the line of symmetry. b. Define line of symmetry. 2. Materials a. Cutout shapes circle, square, rectangle, equilateral triangle, oval, and diamond for each student. 3. Standard: GRADE 3 V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT A. Spatial Sense Understand the concept of reflection symmetry as applied to geometric shapes. Understand how representations of shapes are affected by various motions. 1. Identify lines of symmetry in geometric shapes. 2. Recognize and predict the position and orientation of a shape after a single flip, slide or turn. 4. Motivation: a. Half each half of yourself different i.e. one shoe on and one shoe off, one pant leg down and one rolled up, one side of hair up and the other down, wear sweater on one arm up not on the other, etc. b. What do you all notice about what I look like? Does each side of me look different, or the same? What if I were to cut my body down the middle, would each side of me match? You look different on each side and your sides wouldn t match up. c. Fix clothes and hair so each side looks the same. What do you all notice about what I look like? Does each side of me look different, the same? What if I cut myself down the middle now, would each side of me match? You look the same on both sides now and your sides would match up. 5. Procedure: a. Today we are going to be talking about lines of symmetry. i. Does anyone know what symmetry means? It means two things are the same or equal.

4 ii. Does anyone know what line of symmetry would mean then? It s a line that can be drawn through a figure that divides it into two equal parts. iii. Can anyone tell me something that is symmetrical if we drew a line through the middle? Heart, circle, our bodies, letters, window, etc. iv. If we drew a line through the middle of me right now, how would I be symmetrical? Your hair is down on both sides; shoes are both on, etc. v. How was I symmetrical when I first came in the room? You weren t because things were different on each side of you i.e. hair, shoes, pants, sweater, etc. vi. If I were to unfold this shape, does anyone know what shape it might make? (Hold up a cutout heart folded in half) It would be a heart. b. We are going to be exploring different shapes and finding their lines of symmetry by folding. i. Pass out cutout shapes to each student. ii. Let s start by exploring our squares together. If we fold the square in half, what do you notice? It s symmetrical. iii. If you unfold your square, can you find any other lines of symmetry? How many other lines of symmetry can you find? (Have students try finding more lines of symmetry individually for about 1 minute, then have them work with their neighbors for another 2 3 minutes). iv. What did you notice about the squares lines of symmetry? There is more than one there are 4. v. Some shapes can have more than one line of symmetry. vi. Now lets take out our circles and find if there are any lines of symmetry. What do you notice? It s symmetrical. vii. How many other lines of symmetry can you find? Predict how many lines of symmetry you think the circle has (Have students try finding more lines of symmetry individually for about 1 minute, then have them work with their neighbors for another 2 3 minutes). Circle has an infinite amount of lines of symmetry. viii. Repeat steps ii to iv for the rest of the shapes. Have them try and find as many lines of symmetry as they can. Remind them that when they fold, each side has to be equal for it to make a line of symmetry. For each, still have them work individually at first, and then finish up with their neighbors. ix. When they finish, have them go back to their own seat. c. Review what was covered today. i. What does symmetry mean? When two things are the same or equal.

5 ii. What is a line of symmetry? It s a line that can be drawn through a figure that divides it into two equal parts. iii. What are some things that are symmetrical? Squares, circles, our bodies, etc. 6. Closure: a. Alright, boys and girls, what have we learned today? We learned about symmetry and how to find lines of symmetry in shapes. b. You did a great job today in math boys and girls! Clean up your desk and get ready for gym! 7. Modification: a. I would also want to place him or her in the front of the room especially for this lesson because in the beginning, I am demonstrating symmetry by altering my appearance and also holding up examples. Also, since it s the first day a lot of the information is important to understand. Placing them up front would give them a better opportunity to hear. 8. Informal Assessment: a. I asked numerous questions throughout this lesson. b. Students also explored shapes to find if they were symmetrical and how many lines of symmetry they had individually and in groups. 9. Formal Assessment: a. There is not formal assessment in today s lesson. 10. References: Moore, Janna. (March 17, 2009). Folding Shapes: Are the Sides the Same? Retrieved March, 18, 2009, from ndletters1.htm

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8 Reflection, Reflection, on the Wall 1. Objective: By the end of this lesson students will be able to: a. Analyze shapes to find their line of symmetry b. Draw lines of symmetry 2. Materials: a. GeoReflector mirror for each student b. How Many Lines of Symmetry? Activity Sheet for each student c. Overhead Projector 3. Standard: GRADE 3 V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT A. Spatial Sense Understand the concept of reflection symmetry as applied to geometric shapes. Understand how representations of shapes are affected by various motions. 1. Identify lines of symmetry in geometric shapes. 2. Recognize and predict the position and orientation of a shape after a single flip, slide or turn. 4. Motivation: a. Remember when we found lines of symmetry by folding shapes on Monday? b. How many of you have looked into a mirror before? What do you notice when looking into it? What could the mirror be called if the reflection is the same as you? Yes I ve looked into a mirror before. A mirror could be like the line of symmetry because it s divides two symmetrical things. 5. Procedure: a. Today we are going to be using reflections to find lines of symmetry. i. Has anyone ever used a GeoReflector before? Today we are going to be using them to show reflections. GeoReflectors are transparent so you can see a reflection on its surface. ii. Pass out a GeoReflector to each student. iii. I want all of you to look at your GeoReflectors as I explain how they work. Do you notice an edge that has a slant to it? That is the bottom of the GeoReflector and the side you place on the

9 table. Also, the side the slant is on will face the hand you DO NOT write with. So, I am right handed so I will place the slanted edge facing my left hand. For those of you who are left handed, you will place the slanted edge facing your right hand. Have each of the students set their GeoReflector up on their desks like this and walk around checking if they are correct. iv. Does anyone know how we might be able to use these to find lines of symmetry? The edge of the GeoReflector is where a line of symmetry is. v. Remember yesterday when we were folding shapes to find their lines of symmetry? Well, a GeoReflector can find the same thing without folding a shape. If you place the GeoReflector on a line of symmetry, the two halves will match. b. To get all of you familiar with a GeoReflector, I would like each of you to take out a piece of paper and pencil. i. What I would like each of you to do is draw half of a square on your paper. (Draw this on the overhead so students can see an example). ii. Next, place your GeoReflector on your paper like we practiced before, but line the edge of it up with the ends of your drawing. Make sure the slanted edge is facing the hand you DO NOT write with. (Again, show this on the overhead so they can follow along easier). iii. Then what I would like you to do is look through the GeoReflector on the side where the slant is. Raise your hand if you see a reflection of your drawing on the other side. (Help any students who don t see the reflection). iv. Without moving your GeoReflector, trace the lines you see in the reflection with your pencil. You should still be looking through the slanted side to see the reflection. When you are done, take away your GeoReflector. What do you see? It made the same thing on both sides, a square. v. Since both of the sides were the same, what can we say about our GeoReflector and where it was? It was like a line of symmetry for the square. c. Now that we have practiced together how a GeoReflector works, I have some more shapes I want all of you to explore. i. I m going to pass out a worksheet with some shapes on it and I would like you to use your GeoReflectors to find all the lines of symmetry. ii. Pass out How Many Lines of Symmetry? Activity Sheet. Let s start with the triangle together. iii. When working on this, remember how you set up your GeoReflectors to see the reflection. Try thinking about yesterday when we folded shapes to find their lines of symmetry to help.

10 iv. I would like each of you try finding a line of symmetry. (Give them about a minute. While they work draw a triangle on the overhead). Can someone show me on the overhead the line of symmetry they found? How did you find your line? I looked through the GeoReflector and each side was symmetrical because the lines matched up. v. Alright, now I would like each of you to start by working on this alone, then I ll give you time to work with a neighbor. (Give students 2 4 minutes to work on this alone, and then have them work with their neighbor for about 6 8 minutes). vi. Did anyone notice anything between the number of lines of symmetry and the number of sides the shape had? The more sides a shape had, the more lines of symmetry it had as well. vii. What about a circle? It has one continuous side, how many lines of symmetry does a circle have? It has an infinite amount of lines of symmetry. d. Review what was covered today: i. What can GeoReflectors be used for to find? They can be used to help find lies of symmetry in shapes. ii. How do you know when you find a line of symmetry using a GeoReflector? The lines on the paper line up with the reflection on the GeoReflector. iii. Collect How Many Lines of Symmetry? Activity Sheet. 6. Closure: a. Alright, boys and girls, what have we learned today? We learned how to find and draw lines of symmetry in shapes by using a GeoReflector. b. You did a great job today in math boys and girls! Clean up your desk and get ready for gym! 7. Differentiation: a. Some students may struggle with using the GeoReflectors, and others may pick up on the technique quickly. For those students who are excelling, I would want to have copies of other shapes for them to work on in case they finish early, or even if the worksheet provided is too easy. For those students who are struggling, the worksheet provided starts with simpler shapes. Also, by having students work with their neighbors it gives students at all levels a chance to learn from their classmates, or teach their classmates techniques. 8. Informal Assessment: a. I asked numerous questions throughout this lesson. b. I also collected the How Many Lines of Symmetry? Activity Sheet and will use that as an informal assessment.

11 9. Formal Assessment a. There is no formal assessment in today s lesson. 10. References: Thorton, Carol, & Lowe Parrino, Gail. (2004). Hands on teaching H.O.T. strategies for using math manipulatives. (p ). Illinois: ETA/Cuisenaire.

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13 Lines of Symmetry Video 1. Objective: By the end of this lesson students will be able to: a. Analyze shapes, letters, signs, and nature to find their line(s) of symmetry. 2. Materials: a. Computer b. Internet c. Projector to show video on board d. Speakers 3. Standard: GRADE 3 V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT A. Spatial Sense Understand the concept of reflection symmetry as applied to geometric shapes. Understand how representations of shapes are affected by various motions. 1. Identify lines of symmetry in geometric shapes. 2. Recognize and predict the position and orientation of a shape after a single flip, slide or turn. 4. Motivation: a. We have been talking a lot about lines of symmetry this week so I would like to ask all of you a question. How many of you think you see symmetrical things every day? What are some things outside that you may see that are symmetrical? Signs, cars, ball, window, flower, etc. 5. Procedure: a. Alright well today we are going to be at lines of symmetry in our surrounding. Some of these things we may see everyday. i. Before we get started, I would like to talk about the video we are going to watch. There are activities built into it that we will stop and work through together, so make sure you are paying attention! ii. Start up online video and dim the lights. Let the students watch until the first activity. (Whole lesson should take about min). iii. Activity 1:

14 1. Let s look at this first object. Does anyone see any lines of symmetry? Pick a student to come up and show the line of symmetry they found. Alright goo job! The line of symmetry in this object is vertically. Who can tell me what vertically means? It goes up and down or top to bottom. 2. Okay, now let s look at the next object. Does anyone see any lines of symmetry? What do you notice about this object? There are no lines of symmetry it is not symmetrical. Good job! This shape is not symmetrical. 3. Now let s look at this object, can anyone come up and show me any lines of symmetry they see? How did you know that was a line of symmetry? If you fold the plane in half on that line, both sides would match making it symmetrical. Good job, that s right! The line of symmetry on this plane is horizontal, can anyone tell me what horizontal means? It means across something from left to right. iv. Continue watching the video. v. Activity 2: 1. Which of these two letters is symmetrical? T. How do you know it is symmetrical? If you fold the letter in half from top to bottom or vertically then the sides would match. 2. Great! Now let s look at these two letters. Can anyone tell me which of these is symmetrical? The letter C is. Good, how do you know that it s symmetrical? If you fold it in half in the middle horizontally, the sides would match and be symmetrical. 3. Alright now let s look at the next one. Can anyone tell me which of these letters is symmetrical? All of them! Good! Do any of these have more that one line of symmetry? Yes, the letter H has two lines of symmetry. vi. Continue watching the video. vii. Activity 3: 1. Does anyone know which of these lines is the line of symmetry for this shape? Line 3. Great! How did you know that was the answer? The other two lines wouldn t have made each side of the shape symmetrical. 2. Does anyone know which of these lines is the line of symmetry for this shape? Line 2. How did you know that was the answer? The other two lines wouldn t have made each side of the shape symmetrical. 3. Good job! Can anyone tell me which of these lines is the line of symmetry for this shape? None of them are. How did you know that none of them worked? None

15 of the lines would have split the shape into two equal halves. 4. Awesome job! Now, this one is a little different. Which of these lines is NOT a line of symmetry? Think back to when we found all the lines of symmetry by folding and using the GeoReflectors. Line 5. Great! How did you know that this was the one that wasn t a line of symmetry? It was the only line that wouldn t have split the shape into two equal halves. viii. End video after the third activity. 6. Closure: a. Alright, boys and girls, what have we learned today? We learned about lines of symmetry in signs, letters of the alphabet, shapes, things in nature, etc. b. You did a great job today in math boys and girls! Clean up your desk and get ready for gym! 7. Modifications and Extensions: a. A modification for this lesson would be to have my hearing impaired student sit up in the front of the room or by a speaker. Since most of this lesson is electronic and over speakers it would be important for me to place that student near a speaker so he or she would have the best opportunity to hear. An extension for this activity could be to have the students either think of something that has lines of symmetry they see everyday, or to have them bring something in from home. This would be a good way for them to explore outside of school to find something that is symmetrical. 8. Informal Assessment: a. I asked numerous questions throughout this lesson. 9. Formal Assessment: a. There is no formal assessment in today s lesson. 10. References: Links Learning. (2004). Line Symmetry. Video posted to Line_Symmetry/index.html

16 Snowflakes 1. Objective: by the end of this lesson students will be able to: a. Create symmetrical patterns and designs. b. Find lines of symmetry. 2. Materials: a. Paper (square pieces) any colors b. Scissors for each student c. Construction paper d. Rulers e. Glue f. Markers 3. Standard: GRADE 3 V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT A. Spatial Sense Understand the concept of reflection symmetry as applied to geometric shapes. Understand how representations of shapes are affected by various motions. 1. Identify lines of symmetry in geometric shapes. 2. Recognize and predict the position and orientation of a shape after a single flip, slide or turn. 4. Motivation: a. How many of you like winter and the snow? Do you know anything interesting about snowflakes? All snowflakes are different and they have patters. 5. Procedure: a. Great! Well, today we are going to making our own snowflakes and looking for lines of symmetry. i. Pass out paper and scissors to all of the students. ii. Alright to get started I just want to walk through how to fold you paper to make snowflakes. I would like each of you to fold your paper in half diagonally. iii. Then, I would like each of you to fold your triangle in half like this. (Show students yours).

17 iv. This next part is tricky so I need each of you to pay close attention to what I m doing. The next step is to fold the triangle into thirds. (Show students yours then have them do it). v. The last step is to cut the extra paper on the bottom. (Show students yours) vi. Each of you can use your scissors to cut into this piece of paper and make a design for your snowflake. Make sure that you are carful cutting! Also, remember, the more you cut into the paper, the more decorative your snowflake will look. When you are done, carefully open up your paper and look for the symmetry in your snowflake. Feel free to share with your neighbors! vii. Give students more paper as needed and about min to keep making snowflakes. viii. Alright boys and girls, put your scissors down! I would like each of you to show the class your favorite snowflake you made and say why you like it. Have each student share a snowflake with the class. ix. What did you notice while making your snowflakes? When you opened them they were different every time and they had the same pattern repeated on them. b. Now that we have made some snowflakes, we are going to find the lines of symmetry in them. i. What I would like each of you to do is pick one of your snowflakes that you would like to explore more. What you are going to do is glue your snowflake to a piece of construction paper, and then draw in all the lines of symmetry you can find. ii. Give the students about 5 8 minutes to work on this. iii. Did anyone find any lines of symmetry in theirs? How did you look for them? Yes, I looked at the patterns and where lines could be draw to split the snowflake into two equal parts. iv. Did anyone notice anything else? Where we made fold lines to make the snowflakes are where lines of symmetry could be. v. Great, you all did a wonderful job! 6. Closure: a. Alright, boys and girls, what have we learned today? We learned about making symmetrical patterns and finding lines of symmetry in snowflakes. b. You did a great job in math today! Please pick up all of your scraps and recycle them, then get ready for gym. 7. Differentiation and Extension: a. For differentiation, a great way to make this activity more challenging for more advanced students could be to have them fold their

18 snowflake more times. On the last step where you fold the triangle into thirds, you could challenge them to fold their paper into eighths or sixteenths. This also will create more lines of symmetry to look for at the end of the lesson when they glue a snowflake on paper and draw in the lines of symmetry. An extension you can do with this activity is to hang all of the extra snowflakes around the room with the students so their work can be on display. 8. Informal Assessment: a. I asked numerous questions throughout today s lesson. b. I will use the student s snowflake on construction paper as an informal assessment. 9. Formal Assessment: a. There is no formal assessment in today s lesson. 10. References: a. No References.

19 Find the Symmetry 1. Objective: by the end of this lesson students will be able to: a. Identify lines of symmetry in shapes. 2. Materials: a. Symmetry worksheet one copy per student b. Finish the Pictures! worksheet one copy per student 3. Standard: GRADE 3 V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT A. Spatial Sense Understand the concept of reflection symmetry as applied to geometric shapes. Understand how representations of shapes are affected by various motions. 1. Identify lines of symmetry in geometric shapes. 2. Recognize and predict the position and orientation of a shape after a single flip, slide or turn. 4. Motivation: a. Alright, boys and girls, we have been talking a lot about lines of symmetry the last week and you all have done wonderful! Remember when we used our GeoReflectors? Well, we are going to finish up lines of symmetry today and use our GeoReflectors to do some more exploring. 5. Procedure: a. First, can anyone remember what we can use our GeoReflectors for? Finding lines of symmetry b. Yes that s right! Today, we are going to start with finding lines of symmetry in shapes using our GeoReflectors. We did something similar to this earlier this week. i. Pass out Symmetry worksheet and GeoReflector to each student. ii. Now, what I would like each of you to do is to work on this worksheet individually and find the lines of symmetry in each of the shapes. You can use your GeoReflectors to help and I would like you to find as many as you can in each of the shapes.

20 Also, remember that if you re right handed to place the slanted edge facing your left hand, and if you re left handed to place the slanted edge facing your right hand. I ll give you about minutes to work on this. When you finish, flip your paper over and draw a picture of what you are going to do this weekend. c. Alright, now what if we were only given half a shape, what do you think we could use our GeoReflectors to find? The other side of the shape or the symmetrical side of the shape. d. Great job! That is what we are going to work on next! i. Pass out Finish the Pictures! worksheet to each student. ii. Since we already know that we can use our GeoReflectors to find lines of symmetry, we are going to be doing the opposite now. If you look on your worksheet what do you notice? Half of a shape is there with it s like on symmetry. iii. Yes, great! On your worksheet you are given half of a shape, and it s line of symmetry. What I would like each of you to do is use your GeoReflectors to draw in the missing half of the shape. Think about when we have used the GeoReflectors before and how the lines overlap when they are symmetrical. Since there isn t another side of the shape to overlap, you are going to have to draw it in. I would like each of you to work on this individually. I ll give you about 5 10 minutes. When you finish you can get a matching game and quietly work on it at your desk. 6. Closure: a. Boys and girls you did a great job in math today! Please bring your papers up to my desk and you may line up for gym. 7. Informal Assessment: a. I asked numerous questions during today s lesson. 8. Formal Assessment: a. The formal assessment will be completion of Symmetry worksheet and Finish the Pictures! worksheet. 9. References: Education.com. ( ). Symmetry. Retrieved April 11, 2009, from grades//?q=symmetry EnchantedLearning.com. ( ). Retrieved April 11, 2009, from

21 SYMMETRY Draw a line of symmetry on each shape. M E C D H Copyright Education.com Created by :

22 Finish the Pictures!

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