Line Symmetry Objective To guide exploration of the connection between reflections and line symmetry. www.everydaymathonline.com 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 polygons and describe properties of regular polygons. [Geometry Goal ] Identify and draw lines of symmetry. [Geometry Goal 3] Explore the connection between reflections and line symmetry. [Geometry Goal 3] Solve problems involving spatial visualization. [Geometry Goal 3] Describe rules for patterns and use them to solve problems. [Patterns, Functions, and Algebra Goal ] Key Activities Students use a transparent mirror to complete symmetric pictures and to find lines of symmetry in symmetric objects. They fold paper to sort polygons by the number of lines of symmetry. Ongoing Assessment: Informing Instruction See page. Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, p. 39). [Patterns, Functions, and Algebra Goal ] Key Vocabulary line of symmetry symmetric rotation (turn) symmetry Materials Math Journal, p. 79 Student Reference Book, p. (optional) Study Link 3 Math Masters, pp. 3 3; p. 39 (optional) per partnership: transparent mirror scissors slate Advance Preparation Multiplying a Fraction by a Whole Number Math Journal, pp. A and B Students practice multiplying fractions by whole numbers. Math Boxes Math Journal, p. Students practice and maintain skills through Math Box problems. Study Link Math Masters, p. 3 Students practice and maintain skills through Study Link activities. Interpreting a Cartoon Math Masters, p. 3 Students interpret a cartoon involving line symmetry. Exploring Rotation or Turn Symmetry Geometry Template pattern blocks tape Students explore turn or rotation symmetry. EXTRA PRACTICE Exploring Line Symmetry Math Masters, p. 37 Geometry Template pattern blocks Students use pattern blocks to create shapes with line symmetry. ELL SUPPORT Creating a Line Symmetry Museum magazines and newspapers scissors tape Students create a Line Symmetry Museum. Teacher s Reference Manual, Grades pp., Unit Reflections and Symmetry
Getting Started Mathematical Practices SMP, SMP, SMP, SMP, SMP7 Content Standards.NF.a,.NF.b,.NF.c,.NF.,.G.3 Mental Math and Reflexes Write fraction addition problems on the board where tenths are added to tenths, hundredths to hundredths, and tenths to hundredths. Suggestions: _ + _ = _, or + _ = 7_, or 3 + _ = _, or _, or 3 + 3_ = 9 + _ = _, or 3 + _ = _, or _, or + _ = 7_ 7_ + _ = _, or _ 9_ + _ =, or _, or 3_ + _ = _, or + 3_ =, or _ + _ = 7_, or 3_ Math Message What is symmetry? Be ready to name an object in the classroom that has line symmetry. Study Link 3 Follow-Up Have partners compare answers and describe how they know each image is a reflection of the preimage. Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Ask students to share what they know about symmetry. Tell them to indicate thumbs-up if they have a similar answer. Then ask students to explain how they know the classroom object that they chose has line symmetry. Tell students that in this lesson they will investigate how symmetry and reflections are related. Adjusting the Activity ELL English language learners may find it helpful if you use page in the Student Reference Book to summarize the discussion of line symmetry. AUDITORY KINESTHETIC TACTILE VISUAL Completing Symmetric Pictures (Math Journal, p. 79; Math Masters, p. 3) Date Ask students to turn to journal page 79. Partners share a transparent mirror while working on the activities. Tell the class that each drawing on Math Masters, page 3 is only half of a picture. Students are to figure out what each picture would look like if it were complete and then use their transparent mirrors to complete each picture. Remind them to use the recessed edge to draw the line of reflection. Bring the class together to discuss results. Ask the following questions: How are these drawings like the dog picture in Lesson -3? How are they different? As in the dog picture, there are two sides that look exactly alike (congruent) but are facing in opposite directions. Here, however, the end results are single drawings instead of pairs of drawings. Point out that here the lines of reflection are in the middle of the pictures or objects not outside, as in the dog picture. When a line of reflection is in the middle of a picture or object, it is called a line of symmetry. In this case, the pictures or objects are said to be symmetric. Line Symmetry You will need Math Masters, pages 3 3.. The drawings on Math Masters, page 3 are only half-pictures. Figure out what each whole picture would show. Then use a transparent mirror to complete each picture. Use the recessed side of the mirror to draw the line of reflection.. The pictures on Math Masters, page 3 are symmetric. a. Use the transparent mirror to draw the line of symmetry for the bat and the turtle. b. Cut out the other three pictures and find their lines of symmetry by folding. c. Which picture has two lines of symmetry? Bow 3. Cut out each polygon on Math Masters, pages 33 and 3. Find all the lines of symmetry for each polygon. Record the results below. Polygon Number of Lines A 3 B C D E Polygon Number of Lines F G H I J. Study the results in the tables above. a. How many lines of symmetry are in a regular pentagon (Polygon I)? lines b. How many lines of symmetry are in a regular hexagon (Polygon J)? lines c. How many lines of symmetry are in a regular octagon? (An octagon has sides.) lines Math Journal, p. 79 7-_EMCS_S_MJ_G_U_7.indd 79 // : PM Lesson
Half-Pictures NOTE Students may be familiar with line symmetry from previous work but may not have made a connection between line symmetry and reflections. Thinking about line symmetry in terms of reflections is a more powerful approach because it can be generalized to other kinds of symmetry. Rotation (turn) symmetry, for example, can be thought of in terms of turns. Finding Lines (Math Journal, p. 79; Math Masters, p. 3) Students use their transparent mirrors to draw lines of symmetry in the pictures of a bat and a turtle on Math Masters, page 3. Then they cut out the other three pictures on the page and find their lines of symmetry by folding. Point out that a picture may have more than one line of symmetry. Have students answer the question in Problem c on journal page 79. Bring the class together to discuss results. Ask: Which picture has more than one line of symmetry? The bow 3-3_EMCS_B_MM_G_U_79.indd 3 Math Masters, p. 3 Adjusting the Activity The symmetry activities work best if the pictures and polygons on Math Masters, pages 3 3 are carefully cut out. If there are students in your class who have difficulty with scissors, consider having a volunteer cut out their shapes for them ahead of time. Symmetric Pictures // : PM AUDITORY KINESTHETIC TACTILE VISUAL Exploring Lines of Polygons (Math Journal, p. 79; Math Masters, pp. 33 and 3) Students cut out the polygons on Math Masters, pages 33 and 3. They find all lines of symmetry for each polygon by folding, and then they record the results in the tables and answer the related questions on journal page 79. Ongoing Assessment: Informing Instruction PROBLEM SOLVING Watch for students who think that Polygon F, the parallelogram, has line symmetry. Many people think this is true because Polygon F does have symmetry; however, it is turn or rotation symmetry, rather than line symmetry. Polygon F cannot be folded (or reflected) so that the two halves match, but it can be turned to match its original shape. Bring the class together to share results. Students should have found that a regular polygon has the same number of lines of symmetry as it has sides. For example, a regular octagon has sides and lines of symmetry. Ongoing Assessment: Recognizing Student Achievement Exit Slip py g g p Use an Exit Slip (Math Masters, page 39) to assess students ability to describe a pattern and use it to solve problems. Have students describe patterns they see in Problems 3 and on journal page 79. Students are making adequate progress if they state that a regular polygon has the same number of lines of symmetry as it has sides. Some students may extend the pattern by stating the number of lines of symmetry in additional regular polygons. [Patterns, Functions, and Algebra Goal ] Math Masters, p. 3 3-3_EMCS_B_MM_G_U_79.indd 3 // : PM Unit Reflections and Symmetry
Ongoing Learning & Practice Polygons A E Multiplying a Fraction by a Whole Number (Math Journal, pp. A and B) E Students practice multiplying fractions by whole numbers. B Math Boxes (Math Journal, p. ) C Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem previews Unit content. A D Study Link (Math Masters, p. 3) 3-3_EMCS_B_MM_G_U_79.indd 33 Math Masters, p. 33 // : PM Home Connection Students complete a Venn diagram to identify capital letters of the alphabet that have horizontal and/or vertical line symmetry. They list words with horizontal or vertical line symmetry. Date Write an equation to describe each number line. Multiplying Fractions by Whole Numbers Polygons F J.. Equation: 3 _ = 3_ J I Equation: _ = _, or _, or _ 3 Use the number lines to help you solve the problems. _, or 3_ 3. = _ F. 3 _ = _, or 3_ G H py g g p Solve. You may draw a visual fraction model such as a number line if you wish.. _ 7 = 7., or =, or 3, or 3, or 7. = 3_. _ 9 = Math Journal, p. A 9 A Math Masters, p. 3 A-B_EMCS_S_MJ_G_U_7.indd A 3/3/ : PM 3-3_EMCS_B_MM_G_U_79.indd 3 // : PM Lesson 3
Date A manufacturer of dry puppy food has the following feeding guidelines. All measurements are given in cups per day. Use the information in the table to answer the questions below. Write an equation to show what you did. Weight (lb) Weeks 3 Months 7 Months Months 3 3 3 _ 3 _ 3 _ 3 3 _ 3 _ 3 3_. a. Buddy weighs 3 pounds and is 9 months old. According to the guidelines, he should eat about _ 3 cup of food per day. How much food should Buddy eat in days? _ 3 cups Equation: _ = _ 3 3, or _ 3 b. Buddy should eat between cups of food in days. Circle the best answer. and and 3 3 and. a. Cody is weeks old and weighs about pounds. How much food should he eat in days? _ 3 cups Equation: _ = 3 3, or _ 3 b. Cody should eat between cups of food in days. Circle the best answer. 3 and and and 3. a. A puppy weighs pounds and is months old. How much food should the puppy eat in one week? _ cups Equation: 7 3_ =, or _ b. The puppy should eat between cups of food in one week. Circle the best answer. 3 and and and A-B_EMCS_S_MJ_G_U_7.indd B Solving Number Stories Math Journal, p. B 3// :3 AM 3 Differentiation Options Interpreting a Cartoon (Math Masters, p. 3) Min To apply students understanding of line symmetry, have them interpret a cartoon. SMALL-GROUP Exploring Rotation or Turn Symmetry 3 Min To further explore symmetry, have students use combinations of pattern blocks to perform and analyze transformations. Ask students to tape together a trapezoid and an equilateral triangle pattern block to form a parallelogram. Date Math Boxes. Use your Geometry Template to draw the image of the figure that is shown above the line of reflection. preimage image 3. Order the fractions from least to greatest. a. _ 9, _ 9, _ 9, 9_ 9, 3_ 9 b. _, _ 9, _, _ 3, _ c. 3_ 7, _, 7_, _, 9, 3_ 9,, _ 9, _ 9, _ 9, 9_, _ 9 3,, 3_ 7, _, 7_, _. Use the following list of numbers to answer the questions. 7,,,, 9, 7, 7,,, 3, 9 a. What is the median? b. Mode? c. Maximum? d. Minimum? 7 e. Range? 7. Insert the decimal point in each product. a..7 = b. =. c. 7.3 = 3 3 d. =. 9 73 Ask the following questions: Will the parallelogram look exactly the same if it is flipped over? No. If it slanted to the right before the flip, then it will slant to the left after the flip. Does the parallelogram have line symmetry? No. Students have already tried folding a parallelogram to find a line of symmetry, and they know that it does not have one. Will the parallelogram look exactly the same if it is turned through a _ -turn? yes Have students trace the parallelogram and show that after a _ -turn, the tracing matches the original figure. Shapes that look the same after they have been turned less than a full turn have rotation or turn symmetry. Have students use pattern blocks and tape to make their own turn-symmetric shapes. Have them use their Geometry Templates to record the shapes they make. Sample answers: 3 9. Jaleel missed % of the 3 problems on his science test. How many problems did he miss? Fill in the circle next to the best answer. A. B.. What are the perimeter and area of the rectangle? Include the correct units. m m C. 3 D. 3 39 Perimeter = 7 m Area = 33 m 3 3 -turn symmetry 3 -turn symmetry -turn symmetry Math Journal, p. 7-_EMCS_S_MJ_G_U_7.indd // 9: AM Unit Reflections and Symmetry
EXTRA PRACTICE Exploring Line Symmetry (Math Masters, p. 37) 3 Min Study Link Master STUDY LINK Line Symmetry in the Alphabet Print the capital letters of the alphabet below.. The capital letter A has a vertical line of symmetry. To practice identifying lines of symmetry using a concrete model, have students use combinations of pattern blocks to create figures with a specified number of lines of symmetry. ELL SUPPORT SMALL-GROUP Creating a Line Symmetry Museum 3 Min To provide language support for symmetry, have students bring in pictures of objects with line symmetry to create a Line Symmetry Museum. Have students describe the objects in the pictures and the lines of symmetry they see. They may even draw the lines of symmetry on the pictures. If some of the pictured objects are not perfectly symmetric, consider setting up a section of the museum called Almost Symmetric. The capital letter B has a horizontal line of symmetry. Use the letters of the alphabet to complete the Venn diagram. 3. The word BED has a horizontal line of symmetry. The word HIT has a vertical line of symmetry. Use capital letters to list words that have horizontal or vertical line symmetry. Sample answers: horizontal Practice 3-3_EMCS_B_MM_G_U_79.indd 3 Capital Letters of the Alphabet Vertical Line vertical. 9 = 9R 7. = / _. 7 = 3 7. Math Masters, p. 3 Horizontal Line 7 = /7 3 // : PM Line Symmetry Use pattern blocks to create shapes with the given number of lines of symmetry. Use your Geometry Template to record the shapes and draw the lines of symmetry. Interpreting a Cartoon. yellow hexagon, orange squares. orange square, green triangles lines of symmetry lines of symmetry Sample answer: Sample answer: 3. red trapezoids. orange squares lines of symmetry line of symmetry By permission of Rick Detorie and Creators Syndicate, Inc.. What answer does Ruthie s brother expect?. Explain and draw pictures to show why both of Ruthie s answers are correct. Up and down, it s three. Across, it s zero. Try This. red trapezoids line of symmetry Show two different ways. Sample answer Interpreting a Cartoon. What answer does Ruthie s brother expect? By permission of Rick Detorie and Creators Syndicate, Inc.. Explain and draw pictures to show why both of Ruthie s answers are correct.. On the back of this page, make up a problem of your own. Give it to a partner to solve. Math Masters, p. 37 Math Masters, p. 3 3-3_EMCS_B_MM_G_U_79.indd 37 // :7 PM 3-3_EMCS_B_MM_G_U_79.indd 3 // :7 PM Lesson