# Drawing Lines of Symmetry Grade Three

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1 Ohio Standards Connection Geometry and Spatial Sense Benchmark H Identify and describe line and rotational symmetry in two-dimensional shapes and designs. Indicator 4 Draw lines of symmetry to verify symmetrical twodimensional shapes. Mathematical Processes Benchmarks D. Use mathematical strategies to solve problems that relate to other curriculum areas and the real world; e.g., use a timeline to sequence events; use symmetry in artwork. J. Read, interpret, discuss and write about mathematical ideas and concepts using both everyday and mathematical language. Lesson Summary: In this lesson, students explore the concept of symmetry using geometric shapes, capital letters and various other shapes. They will fold shapes to show symmetry, draw lines of symmetry and create symmetrical designs. Estimated Duration: 60 minutes Commentary: This lesson builds on students prior experiences with symmetry. Students learn that symmetry is an attribute that can be used to describe and classify shapes and that shapes can have more than one line of symmetry. They can conjecture that shapes with more than one line of symmetry have rotational symmetry. By using transformations, such as rotations, they can prove which shapes have rotational symmetry. Pre-Assessment: Distribute Is That a Line of Symmetry? Pre-Assessment, Attachment A, to each student. Have students complete this worksheet independently. Collect papers when finished. Scoring Guidelines: Use the rubric to guide instructional decisions. Readiness Performance Description Ready for Correctly identifies lines of symmetry or Instruction incorrect symmetry. Clearly explains Monitor during Instruction Intervention Required symmetry correctly. Correctly identifies 7-8 lines of symmetry or incorrect symmetry. Adequately explains symmetry. Correctly identifies six or fewer lines of symmetry or incorrect symmetry. Inadequately explains symmetry. Requires further intervention activities to recognize symmetry before proceeding with instructional lesson. Post-Assessment: Distribute and assign Drawing Lines of Symmetry Post- Assessment, Attachment D to each student. In the activity, students identify and draw lines of symmetry on common shapes and letters and write an explanation of what symmetry is. 1

2 Scoring Guidelines: The focus for the evaluation of each student s progress should be accuracy and understanding of the concept of symmetry. Use the following rubric to score students work: Level of Performance Descriptors Understanding 4 Accurately draws lines of symmetry for all shapes including shapes with multiple lines of symmetry. Clearly explains how to determine symmetry correctly. 3 Accurately draws most lines of symmetry with no more than three errors. Adequately explains how to determine symmetry. 2 Draws some lines of symmetry accurately, but also draws some incorrect lines of symmetry showing 4-6 errors. For exampl e: draws only one line of symmetry for shapes with multiple lines of sym metry or draws line(s) of symmetry for basic shapes or letters, but not both. Explanation is unclear or inaccurate in describing how to determine line(s) of symmetry. 1 Draws some lines of symmetry accurately, but also draws some incorrect lines of symmetry showing more than six errors. Explanation shows limited to no understanding of how to determine line(s) of symmetry. Instructional Procedures: Part One 1. Distribute Shapes, Attachment C, and Symmetry Chart, Attachment E to each student. Have students cut out each shape. 2. Have students describe the attributes of the shapes (strai ght lines, equal sides, right angles, etc.) Record the attributes on the board. 3. Have students investigate th e number of lines of symmetry for each shape by folding the shapes and recording information on the Symmetry Chart, Attachment E. a. Explain to students that they are to find th e number of lines of symmetry for each shape. b. Tell them that they can fold the shapes to determine the number of lines of symmetry. c. Direct them to the chart and explain how they are to fill out the two columns. d. Have students draw the lines of symmetry on the shapes in the first column of the chart. 4. Observe students as they work. Provide assistance or pair students as needed. Allow students to use a straight-edge or ruler to draw the lines. If students experience difficulty drawing the lines of symmetry, have them draw lines on the folds of their cut-out shapes and then use that to draw on the chart. 5. Gather students into small groups to compare their responses. Have students prove their conjectures of the number of lines by folding the shapes. 6. Use a transparency of Symmetry Chart, Attachment E, on the overhead to record the correct answers. 7. Summarize the investigation and ask questions about what students have learned. What shapes have only one line of symmetry? What shapes have two lines of symmetry? Which shape has the most lines of symmetry? (circle) Can you determine how many? (No, it is an infinite number.) 2

3 Find the shapes that have sides that are all the same. What do you notice about the number of sides and the number of lines of symmetry? Which shapes were difficult to determine? (It is common for students to indicate that the diagonals of rectangles and rhombi are lines of symmetry.) 8. Pair the students. Have each student draw four shapes. Tell them that at least three of their shapes should have symmetry. Have the partners exchange papers and draw the lines of symmetry. 9. Distribute Capital Letters, Attachment F to each student. Ask students to look at letters A-I and s ort them into categories by symmetry. Draw a three-column chart on the board or overhead projector. No Lines of Symmetry One Line of Symmetry More Than One Line of Symmetry 10. Have students complete Capital Letters, Attachment F, by drawing all the lines of symmetry. Part Two Instructional Tip: The concept of rotational symmetry is introduced at this level as it is part of the benchmark. A plane figure has rotational symmetry if at times it appears in the same orientation as it is rotated. Shapes with more than one line of symmetry have rotational symmetry. 11. Distribute Investigating Rotational Symmetry, Attachment G to students, and direct them to cut out each shape. Ask students: What do all of these shapes have in common? (Each shape is symmetrical.) How many lines of symmetry does each of the shapes have? Have them sort the shapes into groups: shapes with one line of symmetry and shapes with more than one line of symmetry. 12. Develop a student-friendly definition for rotation. Familiar contexts include spinning tops, merry-go-rounds, Ferris wheels and spinners. 13. Model the activity for students. a. Place a large model of a hexagon on the board. b. Trace around the hexagon. c. Write the number 1 near the top edge of the hexagon with a marker. d. Explain to students to rotate the shape until it fits over the traced drawing. e. Rotate the hexagon until it fits into the traced drawing. (appears in the same orientation as the original position) f. Count the number of times that the hexagon fits into the shape until the 1 is back at the top. (6) 14. Direct students to trace the other shapes and rotate the shapes over the traced figure. 15. Hav e students sort the shapes that fit into the traced drawing more than one time and those that only fit into the traced drawing once. 16. Explain to students that the shapes that fit in the traced drawing more than once have rotational symmetry. Ask students if they notice a relationship for the shapes that have 3

4 rotational symmetry and the number of lines of symmetry the shape has. Students should conclude that shapes with more than one line of symmetry have rotational symmetry. Shapes that have one line of symmetry do not have rotational symmetry. 17. Ha ve students determine which letters have rotational symmetry. Allow them to discuss with a partner. Select students to share with the class. 18. Pair the students and have them draw four pictures of shapes, three which have rotational symmetry. Have the students exchange pictures and determine which have rotational symmetry. Select students to share pictures and describe rotational symmetry. 19. Have student explain rotational symmetry in their journals and draw pictures to show their understanding. Collect the journals and informally assess progress. Differentiated Instructional Support: Instruction is differentiated according to learner needs, to help all learners either meet the intent o f the specified indicator(s) or, if the indicator is already m et, to advance beyond the specified indicator(s). Provide cut-out letters to fold when determining lines of symmetry of letters. Using a small mirror on its side in the middle of cutout shapes, letters, numbers, etc., may help students understand symmetry. Tell them to look in the mirror. If the reflection looks how the object normally looks, then it is symmetrical. If it does not, it is not symmetrical. Challenge students exceeding expectations to use construction paper to make new shapes with a given number of lines of symmetry. Explore words such as MOM and WOW to discuss words that show a vertical line of symmetry. Use examples DEED and DECIDE to discuss horizontal symmetry in words. Allow time for students to find more examples of word symmetry. They may use the completed worksheet Capital Letters, Attachment C, to list possible letters to make symmetrical words. Add these words to a symmetry bulletin board showing lines of symmetry. Extensions: Create a bulletin board to post student creations, artwork, magazine cutouts, etc., that are examples of symmetry (see Home Connections). Have one-half construction paper shapes available to explore. Predict and draw how the whole shape would appear if the straight edge were a line of symmetry. Use small mirrors to check predictions. Using various pattern blocks (squares, hexagons, rhombi, trapezoids, triangles), allow students to explore and create various designs and patterns. Circulate as students create patterns and ask, Is this symmetrical? Where would the line of symmetry be? Could there be more than one line of symmetry? To transfer the design to colored paper, have students trace blocks on matching colors, cut out each shape and recreate the design by attaching to black construction paper. Add these designs to a symmetry bulletin board. For a class project, have students create a symmetrical scene (such as a classroom or town) on large roll paper. Everything in the scene must be symmetrical, e.g. people, desks, books, etc. Use paper cutouts or markers to decorate. 4

5 Home Connections: Have a parent or sibling draw and color a design or picture on ½ of a folded paper. The student draws and colors the other half to show symmetry. Have students find examples of symmetry in magazines or catalogues and bring these to school to display on a bulletin board. Interdisciplinary Connections: Content Area: Science Standard: Life Sciences Ben chmark: 3. Classify animals according to their characteristics (e.g., body coverings and body structure). When observing animals to note characteristics, students need to recognize symmetry as a characteristic of an animal s structure or appearance. Materials and Resources: The inclusion of a specific resource in any lesson formulated by the Ohio Department of Education should not be interpreted as an endorsement of that particular resource, or any of its contents, by the Ohio Department of Education. The Ohio Department of Education does not endorse any particular resource. The Web addresses listed are for a given site s main page, therefore, it may be necessary to search within that site to find the specific information required for a given lesson. Please note that information published on the Internet changes over time, ther efore the links provided may no longer contain the specific information related to a given lesson. Teachers are advised to preview all sites before using them with students. For the teacher: chart paper, markers, overhead, chalkboard, construction paper shape cutouts, large paper cutouts of a heart, a tree, a butterfly, cutouts of asymmetrical shapes for display, two identical paper snowflakes, transparency of Symmetry Chart, Attachment B (or chart made on chart paper or at chalkboard), and Capital Letters, Attachment C, construction paper block capital letter cutouts For the student: crayon or marker, ruler Vocabulary: diagonal horizontal mirror image symmetry vertical Technology Connections: Students may use a drawing program for the computer to draw shapes, add lines of symmetry, and sort shapes into symmetrical and asymmetrical groups. 5

6 Research Connection: Marzano, Robert J., Jane E. Pollock and Debra Pickering. Classroom Instruction that Works: Research-Based Strategies for Increasing Student Achievement, Alexandria, VA: Association for Supervision and Curriculum Development, G eneral Tips: Prior to class: Cut out construction paper shapes, one of each per student or each pair of students: square, rectangle, equilateral triangle, regular hexagon, regular octagon, circle, parallelogram, and trapezoid. Make a transparency of Symmetry Chart, Attachment E, and Capital Letters, Attachment F. Attachments: Attachment A, Is That a Line of Symmetry? Pre-Assessment Attachment B, Drawing Lines of Symmetry Post-Assessment Attachment C, Post-Assessment Answer Key Attachment D, Shapes Attachment E, Symmetry Chart Attachment F, Capital Letters Attachment G, Investigating Rotational Symmetry 6

7 Attachment A Is It a Line of Symmetry? Pre-Assessment Name Date Directions: Is the dotted line a line of symmetry? Circle yes or no. 10. Choose one shape from above that has a line of symmetry. Number of selected shape Tell why this shape is symmetrical. 7

8 Attachment B Post-Assessment Name Date Directions: Look for symmetry on each shape and letter. If the shape or letter shows symmetry, use a ruler to draw all lines of symmetry on it. Explain why the lines drawn for the square are lines of symmetry. 8

9 Attachment C Post-A ssessment Answer Key Name Date Directions: Look for symmetry on each shape and letter. If the shape or letter shows symmetry, use a ruler to draw all lines of symmetry on it. Explanations indicate that when the shape is folded on the line drawn, the sides on each side of the fold are congruent or match up exactly. 9

10 Attachment D Shapes 10

11 Attachment E Symmetry Chart Name Date 11

12 Attachment F Capital Letters Name Date Directions: Decide if each letter shows symmetry. If the letter does show symmetry, use a ruler to draw the lines of symmetry on the letter. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 12

13 Attachment G Investigating Rotational Symmetry 13

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