Classify Quadrilaterals

Transcription

1 LESSON 10.4 Classify Quadrilaterals FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards Learning Objective 4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Sort and classify s. MATHEMATICAL PRACTICES (See ematical Practices in GO! in the Planning Guide for full text.) MP2 Reason abstractly and quantitatively. MP4 Model with mathematics. MP6 Attend to precision. Students draw s to demonstrate how you can sort and classify s. F C R Coherence: Standards Across the Grades Before Grade 4 After 3.G.A.1 4.G.A.2 5.G.B.3 5.G.B.4 F C R Rigor: Level 1: Understand Concepts...Share and Show ( Checked Items) Level 2: Procedural Skills and Fluency...On Your Own, Practice and Homework Level 3: Applications...Think Smarter and Go Deeper Language Objective Materials Board, color pencils F C R For more about how GO! fosters Coherence within the Content Standards and ematical Progressions for this chapter, see page 547J. About the Professional Development Why Teach This In this lesson, the definitions of s are formalized and the relationships among them are emphasized. First, students identify right angles in s and recognize that a cannot have exactly three right angles. Next, students examine Professional Development s by the number of pairs of parallel sides and find that some s have 1 pair, some have 2 pairs, while others have none. Students then classify s in as many ways as possible. For example, a figure can be a, a, a parallelogram, and a rectangle. Through this process, students gain a deeper understanding of the properties of s and how they relate to each other. Professional Development Videos 567A Chapter 567A Chap Ch apte terr 10 Interactive Student Edition Personal Trainer on the Spot Video Animated Models itools: Geometry HMH Mega

2 Daily Routines Common Core Problem of the Day 10.4 Simone makes a quilt square using two triangles as shown. What types of triangles are they? right Vocabulary parallelogram, rectangle, rhombus, square, Interactive Student Edition Multimedia Glossary e Vocabulary Builder Materials magazines, scissors, glue, paper, stapler Identify Quadrilaterals Have students write the name and definition of each type of at the top of separate half-sheets of paper. Then have students look through old magazines and cut out examples of each type of. Students then glue the cutout examples onto the half-sheet of paper for each. When done, have students create a booklet by folding a sheet of paper in half and inserting the half-sheets inside. Staple the pages together. Students can title their booklet Quadrilaterals and draw an example of each type on the front cover. 1 ENGAGE with the Interactive Student Edition Essential Question How can you sort and classify s? Making Connections Invite students to tell you what they know about toy kites. What is a toy kite? A kite is a toy that has a light frame with thin material stretched over it, flown in the wind at the end of a long string. How many sides does a basic kite have? 4 sides Learning Activity What is the problem the students are trying to solve? Connect the story to the problem. What problem are you trying to solve? Find the name of the figure given in the problem. What properties of the given figure do you notice? The figure has four sides and four angles. Literacy and ematics Choose one or more of the following activities. Have students write the problem as a short story. Have them predict what attributes of the figure they could use to determine the name of the figure. Have students create kites using paper and scissors. Have students compare their kites with each other and note the differences between the kites. How can you sort and classify s? 567B

3 1 LESSON EXPLORE Unlock the Problem MATHEMATICAL PRACTICES MP6 Attend to precision. Review naming a by its vertices. Discuss the s shown. Explain that tick marks on a figure indicate sides equal in length. What are some other possible names for ABCD? Possible answers: BCDA, CDAB, DABC, ADCB, DCBA, CBAD, BADC What can you tell about the sides of a rhombus? Explain. All four sides have one tick mark each, so all four sides are equal in length. ELL Strategy: Illustrate Understanding On separate index cards, have students draw and label a, a, a parallelogram, a rhombus, a rectangle, and a square. On the back of the card, have students draw a line down the center and write the book s definition on the left and their own description on the right. Activity 1 Remind students to look for the number of right angles in each. How do you know which angles are right angles? Right angles are marked with square corners. How can you describe the two sides of a that form a right angle? The sides are perpendicular. Do all parallelograms have right angles? Explain. No; possible explanation: squares and rectangles are parallelograms that have right angles, but other parallelograms do not have right angles. Talk Use Talk to help students understand that a cannot have exactly three right angles. Look at the rectangle in Activity 1. Could you have redrawn it to show a with only 3 right angles? Explain. Possible answer: no; if I changed one right angle, I would have had to change another right angle to still have 4 sides. Look at the with 2 right angles in Activity 1. Could you have redrawn it to show a with 3 right angles? Explain. Possible answer; no; if I would have changed the acute angle to a right angle, I would have had to change the obtuse angle to a right angle to still have 4 sides. 567 Chapter 10 4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Classify Quadrilaterals A is a polygon with 4 sides and 4 angles. Some s have special names: Rectangle 4 right angles 2 pairs of parallel sides Quadrilateral 4 sides 4 angles Trapezoid At least 1 pair of parallel sides Parallelogram 2 pairs of parallel sides Square 4 right angles 4 sides of equal length Rhombus 4 sides of equal length Classify each figure as many ways as possible. Write,, parallelogram, rhombus, rectangle, or square Reteach,,,,, parallelogram, parallelogram rectangle, rhombus, square Chapter Resources Classify Quadrilaterals Essential Question How can you sort and classify s? Unlock the Problem A is a polygon with four sides and four angles. You can name a by the vertices of its angles. Quadrilateral ABCD is a possible name for the figure shown at the right. Quadrilateral ACBD is not a possible name, since points A and C are not endpoints of the same side. Assume that line segments that appear to be parallel are parallel. Trapezoid at least 1 pair of parallel sides Activity 1 Identify right angles in s. Materials color pencils Use the Quadrilateral Color Guide to color the s. R Reteach Reteach Common Quadrilaterals Parallelogram Rhombus 2 pairs of parallel 2 pairs of parallel sides sides 2 pairs of sides of 4 sides of equal equal length length B No; possible explanation: if a has 3 right angles, the fourth angle must also be a right angle. O Quad Logic Read each statement carefully. Write or false. 1. Some parallelograms are rectangles. 2. All s are parallelograms. 3. All squares are rectangles. 4. Some s are s. 5. Some rectangles are rhombuses. 6. All rhombuses are squares. 7. Some parallelograms are s. 8. All rectangles are squares. Make each statement. Write All, No, or Some. All All All Some 9. rectangles are parallelograms. 10. squares are s. 11. parallelograms are s. 12. s are parallelograms. 13. Stretch Your Thinking Write three of your own quad-logic statements. Then exchange them with a classmate and complete each other s statements. Check students work. Chapter Resources A D The tick marks on the line segments show that they have the same length. Sides AD and BC have the same length. Sides AB and CD have the same length. Rectangle 2 pairs of parallel sides 2 pairs of sides of equal length 4 right angles Geometry 4.G.A.2 MATHEMATICAL PRACTICES MP1, MP2, MP6 B Differentiated Instruction false false false C Square 2 pairs of parallel sides 4 sides of equal length 4 right angles Quadrilateral Color Guide RED: exactly 4 right angles BLUE: exactly 2 right angles ORANGE: exactly 1 right angle Talk MATHEMATICAL PRACTICES 6 Can a have exactly 3 right angles? Explain. Enrich 10.4 Chapter Enrich Enrich

4 568 Activity 2 F K J E No Parallel Sides PQRS QRNZ Use a Venn diagram to sort s. Write the names of the s in the Venn diagram. G H M L B A U T Quadrilaterals V W C D Q Q R At least 1 Pair of Parallel Sides JKLM TUVW P R N Z ABCD EFGH Try This! Classify each figure as many ways as possible. Write,, parallelogram, rhombus, rectangle, or square. a. b. c. parallelogram Advanced Learners Quadrilaterals Trapezoids Parallelograms Rectangles Rhombuses Squares Visual Partners Materials Venn Diagram (see eteacher Resources) S 2 Pairs of Parallel Sides,, parallelogram, rhombus, rectangle, square Distribute a Venn diagram to each pair of students. Have partners use attributes of s to show the relationships of the following s in a Venn diagram:,, parallelogram, rhombus, rectangle, and square. Have students explain their Venn diagrams. Activity 2 Direct students to look for pairs of parallel sides. How can you determine which sides are parallel? Possible answer: I extended the sides, they would never cross. What do you notice about the side lengths of s with two pairs of parallel sides? Possible answer: the opposite sides are of equal length. If a has exactly one pair of parallel sides, do the other sides have to be of equal length? Explain. No, not necessarily; for example, JKLM has exactly one pair of parallel sides, but the other sides are not of equal length. MP8 Look for and express regularity in repeated reasoning. What names can you use to classify all of the s that you identified as having exactly 1 pair of parallel sides? and What names can you use to classify all of the s that you identified as having 2 pairs of parallel sides?,, and parallelogram Try This! Is a always a? Explain. Yes; possible explanation: a is a polygon with four sides and four angles, so it is always a. How are a square and a rectangle alike, and how are they different? Possible answer: both are s with two pairs of parallel sides and four right angles. A square always has four sides of equal length, but a rectangle does not. A rectangle always has two pairs of sides of equal length. Teacher Note: Some mathematicians define a as a with exactly one pair of parallel sides. This book does not use this definition. COMMON ERRORS Error Students may not identify all possible ways to classify a figure. Example, parallelogram, square, rhombus Springboard to Learning Have students systematically go through the properties for each type of and determine if the properties are for the figure. 568

5 3 If EXPLAIN Share and Show Quick Check MATH MATH BOARD Use the checked exercises for Quick Check. a student misses the checked exercises RtI Share and Show B A C D MATH BOARD 1. Tell whether the is also a, parallelogram, rhombus, rectangle, or square. Quadrilateral ABCD is also a parallelogram, rhombus, and a. Think: _ 2 pairs of parallel sides _ 4 sides of equal length _ 0 right angles Classify each figure as many ways as possible. Write,, parallelogram, rhombus, rectangle, or square Talk: ; possible explanation: because a parallelogram, a square, a rectangle, and a rhombus all have 2 pairs of parallel sides, and a has at least one pair of parallel sides Then Talk Differentiate Instruction with Reteach 10.4 Personal Trainer 4.G.A.2 RtI Tier 1 Activity (online) Use Talk to focus on students understanding that a without any parallel sides can only be named a. How many parallel sides does a have? at least 1 pair How many parallel sides do a parallelogram, a rhombus, a rectangle, and a square have? 2 pairs What kind of 4-sided figure has no parallel sides? a ; a can have 1 pair of parallel sides, 2 pairs of parallel sides, or no parallel sides On Your Own In Exercises 5 7, students classify s in as many ways as possible. On Your Own, parallelogram Talk Classify each figure as many ways as possible. Write,, parallelogram, rhombus, rectangle, or square parallelogram rectangle,, parallelogram, rhombus, rectangle, square, parallelogram rhombus MATHEMATICAL PRACTICES 2 Use Reasoning How would you classify a figure with 4 sides, none of which are parallel? Explain. Chapter 10 Lesson DEEPER MP7 Look for and make use of structure. Is it possible to draw a rhombus that is also a rectangle? Explain. Yes; possible explanation: draw a square. A square is a rhombus and a rectangle. 569 Chapter 10

6 MATHEMATICAL PRACTICES M 8. SMARTER Explain how a rhombus and square are alike, and how they are different Possible explanation: a rhombus and square are both s, s, and parallelograms. Both have 4 sides of equal length and 2 pairs of parallel sides. A rhombus does not always have 4 right angles, but a square does. The Louvre Museum is located in Paris, France. Architect I. M. Pei designed the glass and metal structure at the main entrance of the museum. This structure is called the Louvre Pyramid. Below is a diagram of part of the entrance to the Louvre Pyramid. MATHEMATICAL PRACTICE 1 Describe the s you see in the diagram. Possible answer: there are s with 1 pair of parallel sides. There are also s with 2 pairs of parallel sides that also look like rhombuses. If you combine the smaller shapes in different ways, you can also see other s, rhombuses, and parallelograms. DIFFERENTIATED INSTRUCTION 9. SMARTER Classify the figure. Select all that apply. parallelogram WRITE rectangle rhombus square Show Your Work 11. DEEPER How many triangles do you see in the diagram? Explain. 11 triangles; 4 small triangles, 3 triangles made of 2 triangles and 1 rhombus, 2 triangles made of 3 triangles and 3 rhombuses, 1 triangle made of 4 triangles and 6 rhombuses, and 1 large outer triangle. total triangles = 11 INDEPENDENT ACTIVITIES Image Credits: (cr) Robert Harding Picture Library Ltd/Alamy Images 4 ELABORATE Problem Solving Applications MATHEMATICAL PRACTICES SMARTER Exercise 8 requires a student to understand that a rhombus may or may not have 4 right angles. When it does, it is also a square. However, a rhombus and a square both always have 4 sides of equal length. on the Spot Video Tutor Use this video to help students model and solve this type of Think Smarter problem. on the Spot videos are in the Interactive Student Edition and at SMARTER Exercise 9 assesses students ability to classify s and identify subgroups based on their properties. Students who have difficulty explaining the relationship of a square and rectangle may not know their definitions. More likely, however, is that those students do not understand the heirarchy in the classification of s. Connect to Art MP1 Make sense of problems and persevere in solving them. What type of is formed by a rhombus and a small triangle in the diagram? a Differentiated Centers Kit 5 EVALUATE Formative Assessment Activities Connecting Vertices Students complete purple Activity Card 13 by drawing and classifying polygons. Literature A New Angle on Trains and Train Stations Students read about lines, angles, and plane figures that can be found in train stations. Essential Question Using the Language Objective Reflect Have students draw s and demonstrate to answer the Essential Question. How can you sort and classify s? Possible answer: by the number of pairs of parallel sides, number of equal length sides, and number of right angles Journal WRITE Draw and label an example of each type of :, parallelogram, rhombus, rectangle, and square. 570

7 Practice and Homework Use the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write section to determine student s understanding of content for this lesson. Encourage students to use their Journals to record their answers. Classify Quadrilaterals Classify each figure as many ways as possible. Write,, parallelogram, rhombus, rectangle, or square. 1. Think: 2 pairs of parallel sides 4 sides of equal length 0 right angles,, parallelogram, rhombus ,, parallelogram, rectangle, Practice and Homework COMMON CORE STANDARD 4.G.A.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Problem Solving 5. Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. What figure did Alan draw? Possible answers: a, rhombus, 6. Teresa drew a with 2 pairs of parallel sides and 4 right angles. What could she have drawn? Possible answers: a square, rectangle, 7. WRITE Draw and label an example of each type of :, parallelogram, rhombus, rectangle, and square. Check students drawings. Chapter PROFESSIONAL DEVELOPMENT ematical Practices in Your Classroom CCSS..Practice.MP7 Look for and make use of structure. In order to classify s, students must understand the structure of geometric figures. How many parallel lines does it have? Does it have right angles? How many sides of equal length does it have? By analyzing the structure of the figure, students can describe and classify it. This analysis deepens students understanding of properties of two-dimensional figures and how they are related. Ask questions such as the following to help students focus on the structure of geometric figures in order to classify them: How can identifying pairs of parallel lines help you classify s? Possible answer: I can check if the figure has 2 pairs, exactly 1 pair, or no pair of parallel lines. How can identifying the number of right angles help you classify s? Answers will vary. Possible answer: if the has 4 right angles, it is a rectangle, a square, a parallelogram, and a and sometimes it is a rhombus. How can identifying the number of sides of equal length help you classify s? Answers will vary. Possible answer: if the has 4 sides of equal length, it is a rhombus, a square, a rectangle, a parallelogram, and a. But not all rectangles, parallelograms, and s are rhombuses or squares. 571 Chapter 10

8 Lesson Check (4.G.A.2) 1. Joey is asked to name a that is also a rhombus and has 2 pairs of parallel sides. What should be his answer? square TEST PREP 2. What has at least one pair of parallel sides, but cannot be called a parallelogram? Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section. Spiral Review (4.OA.B.4, 4.OA.C.5, 4.NF.B.3d, 4.G.A.1) 3. Terrence has 24 eggs to divide into equal groups. What are all the possible numbers of eggs that Terence could put in each group? 4. In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7. What number should Jenna say? 1, 2, 3, 4, 6, 8, 12, Lou eats 6 of a pizza. What fraction of the 8 pizza, in simplest form, is left over? 6. a capital letter that appears to have parallel lines Possible answer: N FOR MORE PRACTICE GO TO THE Personal Trainer Monitoring Common Core Success Maintaining Focus on the Major Work In Lessons 10.2 and 10.4, students classify shapes (triangles and s) by the presence or absence of their lines and angles (4.G.A). Through doing this, they expand their knowledge of shapes learned in Grade 3 and establish a base understanding of shapes they can apply to geometric measurement in Grade 5. Students will be better prepared to comprehend concepts of volume and be able to relate volume to multiplication and addition (5.MD.C). Connecting Content Across Domains and Clusters In Lessons , students work within Cluster 4.G.A. Students learn to draw and identify points, lines, rays, angles, and perpendicular and parallel lines. Students learn to classify angles as right, straight, acute, or obtuse by informally assessing their measurements. Students also learn to classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specific size. Focus on ematical Practices In Lessons , students must attend to precision, MP6. Students learn the definitions of points, lines, and angles and apply their understanding to classify categories of shapes. Students must be able to recognize the visual properties of right, straight, acute, and obtuse angles and refer to these in order to choose the correct classification. Students make similar determinations regarding parallel, intersecting, and perpendicular lines. Students tie these skills together when classifying triangles by their angles and s by their angles and sides. GO! author Juli Dixon brings the mathematical practices to life by modeling the integration of ematical Practice 6 (attend to precision) in ematical Practices Professional Development Videos, Segment