Symmetry. Objectives To review symmetry; and to provide opportunities to explore properties of symmetric shapes. Assessment Management

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1 Symmetry Objectives To review symmetry; and to provide opportunities to explore properties of symmetric shapes. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Identify equal parts of shapes. [Number and Numeration Goal 3] Draw line segments to connect points. [Geometry Goal 1] Draw missing parts of symmetric figures. Locate lines of symmetry in 2-dimensional shapes. Key Activities Children fold and cut out a symmetric figure, explore the properties of symmetric figures, connect matching points on mirror images, and draw the missing parts of symmetric shapes. Ongoing Assessment: Recognizing Student Achievement Use journal page Playing Angle Race Math Masters, p. 430 (optional); p. 441 Student Reference Book, pp. 271 and 272 per partnership: 24-pin circular geoboard and 15 rubber bands or Math Masters, p. 430, straightedge, and pencil Children practice measurement skills. Math Boxes Math Journal 1, p. 147 Children practice and maintain skills through Math Box problems. Home Link Math Masters, p. 186 Children practice and maintain skills through Home Link activities. READINESS Reviewing Symmetry pattern blocks paper Children fold paper into halves and copy pattern-block designs. ENRICHMENT Solving Pattern-Block Symmetry Riddles Math Masters, p. 187 pattern blocks Pattern-Block Template Children solve pattern-block puzzles involving shapes with symmetry. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 132 Children add the term symmetry to their Math Word Banks. Key Vocabulary symmetric symmetry mirror image line of symmetry Materials Math Journal 1, p. 146 Student Reference Book, pp. 122 and 123 Home Link 6 8 Math Masters, p. 185 scissors straightedge cm ruler hand mirror (optional) hole punch (optional) Advance Preparation Copy and cut out Angle Race degree-measure cards from Math Masters, page 441. Teacher s Reference Manual, Grades 1 3 pp. 149, Unit 6 Geometry

2 Getting Started Mental Math and Reflexes Pose equal-sharing and equal-grouping number stories. Children share solution strategies. Suggestions: 2 children share 7 sweet pickles equally. How many pickles does each child get? 3 pickles How many pickles are left over? 1 pickle 4 children share 14 envelopes equally. How many envelopes does each child get? 3 envelopes How many envelopes are left over? 2 envelopes 4 children share 33 crayons equally. How many crayons does each child get? 8 crayons How many crayons are left over? 1 crayon Math Message Take one Math Masters, page 185. Use a straightedge to draw line segments to connect the dots in order: A to B, B to C, and so on. Fold along the dotted line, keeping the picture on the outside. Keep it folded. Cut along the solid lines. Home Link 6 8 Follow-Up Briefly go over the answers. Make sure children understand that the curved arrow shows the path and the direction of the rotation. PROBLEM SOLVING 1 Teaching the Lesson Math Message Follow-Up (Math Masters, p. 185) ELL WHOLE-CLASS Ask children to name the unfolded cutout figure. kite Remind children that kite has 2 meanings: it can be a toy or a mathematical shape. It is important to distinguish this kite from the polygons discussed in Lesson 6-5. Ask children to explain why we can say that the kite is symmetric, or has symmetry. When the shape is folded, the two halves match. To support English language learners, discuss when to use the adjective symmetric versus the noun symmetry. Exploring Properties of Symmetric Figures (Math Masters, p. 185) WHOLE-CLASS Name Date Time Teaching Master Mirror Image Ask children to refold their cutout kites. Explain that now they will make their kite symmetric. Show them how to hold the kite up to a light source and mark the points on the unmarked half with a pencil or marker. They may also punch a hole with a pencil point or hole puncher through both halves at each of the labeled points, except A and J. Children then use a straightedge to connect the holes or dots on the blank half of the kite in the same pattern as on the printed half. When they unfold their kites, children will notice that they have drawn a pattern like the existing pattern. If you have a hand mirror, place it upright along the fold line. Ask a volunteer to describe what is in the mirror. The pattern is called the mirror image of the existing pattern. Discuss the relationship between the printed pattern and its mirror image. Ask: How are they alike? Math Masters, p. 185 B A C E F I H J D G Lesson 451

3 A B C E I F J H D G A line connects point B to its mirror image point. NOTE For practice decomposing polygons, go to They are the same size and have the same shape. How are they different? They face in opposite directions. Have children use a straightedge to connect a pair of matching points (a point on the right side to its corresponding point on the left side). Repeat for two other pairs of matching points. For each pair of matching points, children measure the distance in centimeters from each point to the fold line. Children share their observations. The distance from one point to the fold line is the same as the distance from its matching point to the fold line. Some children may mention that the line segments connecting pairs of matching points form right angles with the fold line. After children have connected all pairs of matching points and measured each point s distance to the fold line, discuss the following concepts: A shape is symmetric about a line if it can be folded in half along that line so the two halves match. The fold line is called the line of symmetry. The mirror image of a design is the same size and shape as the design, but it faces in the opposite direction. Completing Symmetric Figures (Math Journal 1, p. 146; Student Reference Book, pp. 122 and 123) PARTNER PROBLEM SOLVING Partners draw the missing halves of symmetric figures. Have children describe how they solved Problem 9. Children can read more about line symmetry on pages 122 and 123 of the Student Reference Book. Date 6 9 Student Page Symmetric Shapes Time Each picture shows one-half of a letter. The dashed line is the line of symmetry. Guess what the letter is. Then draw the other half of the letter. Draw the other half of each symmetric shape below. Adjusting the Activity Children use hand mirrors to see the missing parts of the figures and complete the drawings. They may also check that the missing parts of the figures are completed correctly. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L The picture at the right shows one-fourth of a symmetric shape, and two lines of symmetry. Draw the mirror image for each line of symmetry. Ongoing Assessment: Recognizing Student Achievement Journal page 146 Use journal page 146, Problems 1 4 to assess children s ability to complete symmetric shapes. Children are making adequate progress if they are able to draw the other half of the letters in Problems 1 4. Some children may be able to complete the remaining problems. Try This 10. The finished figure in Problem 9 has 2 more lines of symmetry. Draw them. Math Journal 1, p Unit 6 Geometry

4 2 Ongoing Learning & Practice Playing Angle Race (Math Masters, pp. 430 and 441; Student Reference Book, pp. 271 and 272) PARTNER Children practice measurement skills by playing Angle Race. They make angles on geoboards or on Math Masters, page 430. For detailed instructions, read the directions on Student Reference Book, pages 271 and 272 with the children. Math Boxes (Math Journal 1, p. 147) INDEPENDENT Angle Race Materials 24-pin circular geoboard or a sheet of Circular-Geoboard Paper (Math Masters, p. 430) 15 rubber bands, or a straightedge and a pencil deck of Angle Race Degree-Measure Cards (Math Masters, p. 441) Players 2 Skill Student Page Recognizing angle measures Object of the game To complete an angle exactly at the 360 mark on a circular geoboard. Directions 1. Shuffle the cards. Place the deck number-side down on the table. 2. If you have a circular geoboard, stretch a rubber band from the center peg to the 0 peg. If you do not have a circular geoboard, use a sheet of Circular-Geoboard Paper. Draw a line segment from the center dot to the 0 dot. Instead of stretching rubber bands, you will draw line segments. Games circular geoboard Circular-Geoboard Paper Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson The skill in Problem 6 previews Unit 7 content. Writing/Reasoning Have children write an answer to the following: Explain why the quadrangle you drew in Problem 3 is not a square, a rhombus, or a rectangle. Sample answer: A square and a rhombus have 4 equal sides. A square, a rhombus, and a rectangle have pairs of parallel sides. A rectangle and a square have 4 right angles. My quadrangle does not have 4 equal sides, pairs of parallel sides, or 4 right angles. Student Reference Book, p. 271 Home Link (Math Masters, p. 186) INDEPENDENT Home Connection Children fold sheets of paper to create lines of symmetry and answer questions about the shapes that they create. Date Math Boxes Student Page Time 1. 3 people share 14 pennies. Each person gets 4 pennies. There are 2 pennies left. 2. A baker packed 8 boxes of cupcakes. She packed 4 chocolate and 4 white cupcakes in each box. How many cupcakes did she pack in all? 64 cupcakes (unit) Draw a quadrangle with exactly one right angle. Label the vertices A, B, C, D. Which letter names the right angle? Angle A Sample answer: B A 4. Draw a quadrangle that is not a square, a rectangle, or a rhombus. Sample answers: C D Describe the angle. Fill in the circle for the best answer. A. greater than a 1_ 4 turn B. less than a 1_ 4 turn C. greater than a 1_ 2 turn 6. Estimate. A package of cookies costs $2.09. About how much do 3 packages cost? Show the number model for your estimate. About $6.00 Number model: $ = $6.00 Sample answer D. one full turn Math Journal 1, p. 147 Lesson 453

5 Name Date Time HOME LINK Family Note Home Link Master Symmetric Shapes Our class has been studying lines of symmetry lines that divide figures into mirror images. Help your child look for symmetric shapes in books, newspapers, and magazines, and in objects around the house, such as windows, pieces of furniture, dishes, and so on Please return this Home Link and your cutouts to school tomorrow. 1. Fold a sheet of paper in half. Cut off the folded corner, as shown. Before you unfold the cutoff piece, guess its shape. a. Unfold the cutoff piece. What shape is it? triangle b. How many sides of the cutoff piece are the same length? 2 sides c. How many angles are the same size? 2 angles d. The fold is a line of symmetry. Does the cutoff piece have any other lines of symmetry? no 2. Fold another sheet of paper in half. Fold it in half again. Make a mark on both folded edges 2 inches from the folded corner. Cut off the folded corner. Before you unfold the cutoff piece, guess its shape. a. Unfold the cutoff piece. What shape is it? b. Are there any other lines of symmetry besides the fold lines? yes c. On the back of this paper, draw a picture of the cutoff shape. Draw all of its lines of symmetry. square 2 in. 2 in. 3 Differentiation Options READINESS Reviewing Symmetry INDEPENDENT 5 15 Min To explore the concept of symmetry, have children use pattern blocks to create designs. First, children fold a blank sheet of paper in half to create a line of symmetry. They unfold the paper and lay it flat on the table. Next children make a simple design with pattern blocks on the right side of the paper. Then they use pattern blocks to create the other half of the design on the left side of the paper. Math Masters, p. 186 Folded paper provides the background for a symmetric design. One-half of design The child completes the design. 454 Unit 6 Geometry

6 ENRICHMENT Solving Pattern-Block Symmetry Riddles (Math Masters, p. 187) SMALL-GROUP Min PROBLEM SOLVING To apply children s understanding of symmetry, have them solve pattern-block puzzles involving shapes with symmetry. Children complete Math Masters, page 187. Have children describe the blocks they used to solve each riddle. For example, I used two red trapezoids and six green triangles to solve the first riddle. ELL SUPPORT SMALL-GROUP Building a Math Word Bank (Differentiation Handbook, p. 132) 5 15 Min To provide language support for symmetry, have children use the Math Word Bank template found on Differentiation Handbook, page 132. Ask children to write the term symmetry, draw a picture to represent the term, and write other related words. See the Differentiation Handbook for more information. Teaching Master Name Date Time Pattern-Block Symmetry Riddles Use your Pattern-Block Template to record your solution to each problem on another piece of paper. Check that each solution works for all the clues in the problem. Sample answers: 1. Build a symmetrical shape using these clues: Use exactly 2 red trapezoids and put them together to make a hexagon. Use exactly 6 green triangles around the outside of the hexagon. Use exactly 8 blocks. 2. Build a symmetrical shape using these clues: Use exactly 2 red trapezoids. Use exactly 5 tan rhombuses. Use exactly 7 blocks. 3. Build a symmetrical shape using these clues: Build a large triangle. Use a yellow hexagon in the center at the bottom of the large triangle. Use at least 3 different colors of blocks. Try This 4. Build a shape that has more than 1 line of symmetry using these clues: Use exactly 2 red trapezoids. Do not use yellow hexagons. The longer sides of the red trapezoids touch and line up together. Use a green triangle at the top and at the bottom of the shape. Use exactly 10 blocks. Math Masters, p. 187 Lesson 455