5 Objective Symmetrical Figures In this lesson, students solve problems involving symmetry. Because relationships across a line of symmetry correspond exactly in terms of size, form, and arrangement, students can begin to develop a sense of formal balance, which will serve as a foundation for geometric equations. 4.G.3 Common Core State Standards Talk About It Discuss the Try It! activity. Say: An image that has symmetry can be divided into two halves that are mirror images of each other. Ask: What is a mirror image? Draw two shapes on the board, one that is symmetrical and one that is not. Point to the symmetrical shape. Ask: Is this shape symmetrical? How can you tell? Point to the asymmetrical shape. Ask: Is this shape symmetrical? How can you tell? Solve It With students, reread the problem. Have students create their own symmetrical masks by folding construction paper in the center and placing Pattern Blocks along the fold to make the first half of the mask. Students then trace the blocks and unfold the paper. Using blocks, they should complete the other half of the mask so that it is symmetrical and trace the other half. More Ideas For other ways to teach about symmetry Have students use a GeoReflector Mirror on the shapes they made in the lesson. With one half of the shape in place, students can place the mirror along the line of symmetry and observe the reflection. Have students work in pairs. Students should divide a Geoboard in half with a rubber band. One student then makes a shape or pattern on one half of the Geoboard. The other student must then make a mirror image of the first shape or pattern on the second half of the Geoboard so that the design is symmetrical. Students then switch roles and repeat the activity. Have students make symmetrical designs out of Centimeter Cubes. Students can then use crayons to draw their designs on a Centimeter Grid (BLM 12). Formative Assessment Have students try the following problem. Which shows a line of symmetry? 144 A. B. C. D.
Try It! 30 minutes Pairs Here is a problem about symmetry. Andrew wants to make a face mask of his favorite action hero to wear on the night of his class costume party. The mask he wore last year was torn in half, but Andrew is hoping to use it as a pattern. How can symmetry help Andrew create a whole face mask from the half he has? Introduce the problem. Then have students do the activity to solve the problem. Give Pattern Blocks, crayons, and blank sheets of paper to each pair. Introduce and model the concept of symmetry. Materials Pattern Blocks (50 assorted per pair) crayons (10 per pair) paper (5 sheets per pair) pencils (1 per student) 1. Take the blue rhombus. Use the green triangles to show a line of symmetry. Invite students to trace the blue rhombus and draw other lines of symmetry. Do the same with the yellow hexagon and red trapezoid. 2. Say: We can make a group of shapes that has symmetry, too. Have one student in each pair create one half of a shape; then the other student should complete a symmetrical side. Have students draw a vertical line on their paper to help. 3. Students should trace their figures onto the paper and color the shapes. Have students check to make sure that they can draw a line of symmetry that will divide the design into two halves that are mirror images of each other. Partners then switch roles and repeat the activity. Some students may try to complete the pattern by repeating the shapes (i.e., triangle, trapezoid, triangle, trapezoid) instead of creating a mirror image (triangle, trapezoid, trapezoid, triangle). You may wish to use a hand mirror or GeoReflector Mirror to help students check their design for symmetry. Hold the mirror so that students can see half their design reflected along the line of symmetry. Then remove the mirror and have students check that the other half of the design matches what they just saw in the mirror. 145
Lesson 5 Name Answer Key Use Pattern Blocks to model the symmetrical figure. Name the figure and the two parts. (Check students work.) 1. 2. hexagon; trapezoid rectangle; square Using Pattern Blocks, model a symmetrical figure. Sketch the shape. Name the shape that you sketched. Name the shape formed by both sides together. (Check students work.) 3. 4. square; rectangle triangle; rhombus Sketch the other half of each shape to make a symmetrical figure. 5. 6. 7. 8. 146 Download student pages at hand2mind.com/hosstudent.
Answer Name Key Challenge! If a shape is drawn on a piece of paper, explain how you can tell if the shape is symmetrical. Draw a picture to help. Challenge: (Sample) Fold the paper so that the fold line is along the center line of the shape. If the two halves of the shape match, the shape is symmetrical. Download student pages at hand2mind.com/hosstudent. 147
Lesson 5 Name Use Pattern Blocks to model the symmetrical figure. Name the figure and the two parts. 1. 2. Using Pattern Blocks, model a symmetrical figure. Sketch the shape. Name the shape that you sketched. Name the shape formed by both sides together. 3. 4. Sketch the other half of each shape to make a symmetrical figure. 5. 6. 7. 8. 146 www.hand2mind.com
Name Challenge! If a shape is drawn on a piece of paper, explain how you can tell if the shape is symmetrical. Draw a picture to help. www.hand2mind.com 147