Describe Plane Shapes

Transcription

1 LESSON 12.1 Describe Plane Shapes FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards Learning Objective 3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Identify and describe attributes of plane shapes. MATHEMATICAL PRACTICES (See ematical Practices in GO! in the Planning Guide for full text.) MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. Student pairs brainstorm then check the textbook to list some ways to describe two-dimensional shapes. F C R Coherence: Standards Across the Grades Before Grade 3 After 2.G.A.1 3.G.A.1 4.G.A.2 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 F C R For more about how GO! fosters Coherence within the Content Standards and ematical Progressions for this chapter, see page 695J. About the Professional Development Why Teach This Plane geometry is the study of figures in a plane or flat surface. Students need to understand the following geometric terms because other geometric concepts and terms are built upon them. A plane is a flat, continuous, unending surface. Planes can contain s (exact locations in space), lines (straight, continuous, unending collections of s), line segments (parts of lines with two ends), and s (parts of lines with one end that continues in one direction without end). Plane shapes are two-dimensional. A shape, such as a circle or square, starts and ends at the same. An shape does not start and end at the same. Professional Development Videos 697A Chapter 12 Interactive Student Edition Personal Trainer on the Spot Video Animated Models itools: Geometry

2 Problem of the Day X.X 12.1 Basic Frank Facts made Use a fruit counters. salad. He Add. used 1_ 4 cup of 1. NumList grapes, 3_ cup of strawberries, and 1_ 4 2 cup of 2. NumList melon. List the fractions 1_ 4, 3_, and 1_ 4 2 in order from least to greatest. 3. NumList Vocabulary Daily Routines Common Core 1 4, 1_ 2, 3_ 4 Vocabulary shape, end, line, line segment, shape, plane shape,,, two-dimensional shape Interactive Student Edition Multimedia Glossary e Vocabulary Builder Word Pictures List the vocabulary words on the board with a number next to each word. Randomly draw pictures to illustrate each word. Have students hold up fingers to match the number next to the word that you have illustrated. 1 ENGAGE with the Digital Interactive Lesson Student Edition Essential Question TE_BdyTxt What are some ways to describe two-dimensional shapes? Making Connections TE_BdyTxt Ask students to tell what they know about shapes. zte_bold Look around the room. some shapes you see. Answers will vary. Learning What is different Task between a triangle and a square? TE_BdyTxtTE_BdyTxtTE_BdyTxt A triangle has 3 sides. A square has 4 sides. TE_BdyTxt How are a square and a rectangle alike? Both have 4 sides. How are they different? A square has all sides the same length. TE_BullLst Literacy Learning and Activity ematics What is the problem the students are trying to solve? Connect the TE_BdyTxt story to the problem. Ask the following questions. What shape is Lucia wondering about? the stop sign What does she want to know about the shape? how many line segments it would take to draw it Literacy and ematics View the lesson er with the students. Then, choose one or more of the following activities: Have students draw a shape on grid paper. Have them use math terms to describe their shape. Have students write about the shapes they see in the classroom or in a photo. Have students use math terms to describe what they see. What are some ways to describe How do two-dimensional you make a ten to shapes? help you subtract? 697B

3 LESSON EXPLORE Unlock the Problem MATHEMATICAL PRACTICES Have students read the introduction to make connections between mathematics and the real world. Discuss that the architect uses plane shapes to represent what will become the roof, walls, windows, and doors of the building. MP6 Attend to precision. Review the highlighted math words with students. Look at the picture of the line. What do the arrows mean? that the line continues in both directions and does not end How are a line and line segment alike? How are they different? Alike: both are straight. Different: a line segment has two ends, but a line continues forever in both directions. Why does a only have one arrow? It continues in only one direction. of a line. 697 Chapter 12 Use to check students understanding of the definition Could you measure a? a line segment? Explain. Possible answers: You could not measure a since it goes on forever in one direction, but you could measure a line segment because it has two end s. ELL Strategy: Frontload Frontload essential vocabulary including, line, ends, line segment and to build understanding of the properties of plane shapes. Explain the definitions of, line, ends, line segment, and with words and pictures. Have students rephrase the definitions in their own words. Prompt students by asking questions. What do you know about a line segment? A line segment is part of a line. A line segment does not go on forever. Have students record the vocabulary with a drawing and labels in their Journal. MP2 Reason abstractly and quantitatively. What plane shape can be formed with three line segments? triangle 3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Describe Plane Shapes Essential Question What are some ways to describe two-dimensional shapes? Unlock the Problem An architect draws plans for houses, stores, offices, and other buildings. Look at the shapes in the drawing at the right. A plane shape is a shape on a flat surface. It is formed by s that make curved paths, line segments, or both. is an exact position or location ends s that are used to show segments of lines ends Some plane shapes are made by connecting line segments at their ends. One example is a square. Describe a square using math words. A square has _ 4 line segments. The line segments meet only at their. ends 3 Differentiated 2 1 line is a straight path continues in both directions does not end line segment is straight is part of a line has 2 ends Geometry 3.G.A.1 MATHEMATICAL PRACTICES MP1, MP3, MP6 is straight is part of a line has 1 end continues in one direction Describe Plane Shapes You can use math words to describe plane shapes. an exact position or location line ends line segment Circle all the words that describe the shape line line segment Write whether the shape is or. a straight path that goes in two directions without end s that are used to show segments of lines part of a line and has 2 ends part of a line that has 1 end and continues in one direction A plane shape is a shape on a flat surface. It is formed by s that make curved paths, line segments, or both. Plane shapes can be or. A shape starts and An shape does not start ends at the same. and end at the same. Look at this plane shape called a triangle. It is a shape. It has 3 line segments. The line segments meet at the ends. shape shape Chapter Resources Reteach Reteach shape shape 12-5 Reteach Think: How many line segments and ends does a square have? Possible explanation: because a line goes on forever in both directions Shape Up! MATHEMATICAL PRACTICES 3 Apply Why can you not measure the length of a line? Chapter Read the description. Then draw the shape. If the shape cannot be drawn, write the word impossible. Check students drawings. Possible shapes are given. 1. a with two ends 2. a shape with 6 line segments impossible 3. a part of a line with two ends 4. an triangle 5. an shape with 7 line segments Enrich impossible 6. a shape with 3 line segments and a curved path 7. Nick says we cannot see any true lines in the real world. He thinks everything we call a line is really a line segment. Do you agree or disagree? Explain. I agree; Possible explanation: all the straight lines we see have a beginning and an end. They do not go on without ending. Chapter Resources Enrich 12.1 Instruction 12-6 Enrich

4 Plane shapes have length and width but no thickness, so they are also called two-dimensional shapes. Try This! Draw plane shapes. Plane shapes can be or. A shape starts and ends at the same. An shape does not start and end at the same. Is the plane shape at the right a shape or an shape? Explain how you know. 698 length width Hands In the space below, draw more examples of shapes. Check students drawings. In the space below, draw more examples of shapes. Check students drawings. Possible explanation: it can be either or. The letter B above is a shape with a curved path that is. The letter S is a shape with a curved path that is. Possible explanation: it is a shape because it starts and ends at the same. On MATHEMATICAL PRACTICES 6 Explain whether a shape with a curved path must be a shape, an shape, or can be either. Try This! Read about the two types of plane shapes shapes and shapes. How can you tell if a shape is? It starts and ends at the same ; the lines or curved paths are connected, with no ing. Is a three-sided shape always? Explain. No; possible explanation: because two sides may not be connected How could you change an shape so that it is a shape? Connect the starting and ending s. Is a cardboard box a two-dimensional shape? Why or why not? No, because it has 3 dimensions length, width, and height or thickness The answer to this question is yes: Is a a shape? What could go in the blank? Answers will vary. Possible answers: a circle or any polygon students name such as a triangle, rectangle, square, pentagon. How can you describe the paths in the shapes on this page? Some are straight and others are curved. Which shapes have both kinds of paths? the B and the pie with a missing piece Tell students that their books describe some shapes having straight paths or curved paths. That is because in geometry, a shape can be made up of one, the other, or both. Point out that when we talk about shapes we may use line to mean something different. We may use it to mean a line segment or even a curved path. Hands On Use to focus on students understanding of shapes with curved paths. Advanced Learners Visual Individual COMMON ERRORS Draw the following shapes on the board. Which plane shape is formed by only line segments? triangle by only curved paths? circle by both? letter D Then have students print uppercase letters in their name and describe each with respect to whether it has line segments or curved paths. Error Students might confuse lines, line segments, and s. Example Students may name a line segment as a line when describing the square on page 697. Springboard to Learning Draw a line and remind students that it continues in both directions. Then draw two s on the line. Explain that a segment is part of the line, so it has ends. Then to and explain that a has only one end. 698

5 3 EXPLAIN MATH Share and Show MATH BOARD The first problem connects to the learning model. Have students use the Board to explain their thinking. Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the Board. Use to focus on students understanding of the definition of and shapes. two letters of the alphabet that represent a shape with a curved path and two letters that represent an shape with a curved path. Possible answers: : B, D, O, : S, C, U, J Share and Show On Your Own MATH BOARD 1. Write how many line segments the shape has. 3 line segments Circle all the words that describe the shape shape shape Write whether the shape is or. Write how many line segments the shape has. shape shape Possible explanation: An shape does not begin and end at the same. A shape does line line segment MATHEMATICAL PRACTICES 1 Describe How do you know whether a shape is or? If Then Quick Check a student misses the checked exercises RtI Differentiate Instruction with Reteach 12.1 Personal Trainer 3.G.A.1 RtI Tier 1 Activity (online) line segments 8 line segments Write whether the shape is or. 4 line segments line segments 4 6 Chapter 12 Lesson On Your Own If students complete the checked exercises correctly, they may continue with the On Your Own section. Then ask: How are a and a line segment alike? Possible answer: they are both straight and are part of a line. 699 Chapter 12

6 MATHEMATICAL PRACTICES M 18. What s the Error? Brittany says there are two ends in the shape shown at the right. Is she correct? Explain. 19. MATHEMATICAL PRACTICE 700 No; possible explanation: the shape is a. So, there is 1 end and the continues in the other direction. 6 Explain how you can make the shape at the right a shape. Change the shape so it is a shape. Check students drawings. Possible explanation: draw a sixth line segment, so the shape starts and ends at the same. 20. DEEPER Look at Carly s drawing at the right. What did she draw? How is it like a line? How is it different? Change the drawing so that it is a line. Check students drawings. Ray; possible answer: a is like a line because they are both straight. While a line continues in both directions, a continues in only one direction. 21. SMARTER Draw a shape in the workspace by connecting 5 line segments at their ends. Check students drawings. Possible drawing is shown. 22. SMARTER Draw each shape where it belongs in the table. Closed Shape Open Shape DIFFERENTIATED INSTRUCTION Activities Classification Act Students complete orange Activity Card 18 by classifying two-dimensional shapes based on their attributes. Differentiated Centers Kit INDEPENDENT ACTIVITIES Activities Figure It Out Students complete blue Activity Card 18 by identifying two-dimensional shapes by their attributes. 4 5 ELABORATE Problem Solving Applications MATHEMATICAL PRACTICES MP6 Attend to precision. Exercise 19 assesses students understanding of and shapes. Guide students to understand that shapes start and end at the same. Have pairs brainstorm ways to create a shape from the shape given. SMARTER For Exercise 21, students need to visualize a five-sided shape with no sides crossing. To extend their thinking about Exercise 21, show students a concave pentagon and have them compare and contrast the drawing to theirs. 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 This item assesses a student s ability to identify whether a two-dimensional shape is or. Students who draw the semicircle with the shapes might be confusing the or property with whether a shape is a polygon instead. EVALUATE Formative Assessment Essential Question Using the Language Objective Reflect Have student pairs brainstorm then check the textbook to answer the Essential Question. What are some ways to describe two-dimensional shapes? Two-dimensional shapes have length and width but no thickness. Journal WRITE Draw an shape and a shape. Label your shapes. 700

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. Describe Plane Shapes Write how many line segments the shape has Write whether the shape is or. 3. _ 4 line segments 4. Practice and Homework _ 6 line segments COMMON CORE STANDARD 3.G.A.1 Reason with shapes and their attributes. Problem Solving 5. Carl wants to show a shape in his drawing. Show and explain how to make the drawing a shape. 6. The shape of a fish pond at a park is shown below. Is the shape or? Add a fourth line segment, so the shape starts and ends at the same. 7. WRITE Draw an shape and a shape. Label your shapes. Check students work. Chapter Extend the Activity Materials large paper clip, 2 pencils, ruler Discuss these vocabulary words with students. A circle is a plane shape made of s that are the same distance from the center. The center is the in the middle of the circle. A radius is a line segment. One end is always the center of the circle. The other end is on the circle. A diameter is a line segment that passes through the center of the circle and has its ends on the circle. Investigate Students will draw a circle and label its parts. Draw a on a sheet of paper. Place a pencil in each end of a paper clip. Place one pencil on the you drew. Move the first pencil around to draw a circle. Use a ruler. Draw a radius and a radius diameter. center Label the parts of your circle. diameter Why does the paper clip represent the radius of your circle? It is the distance from the center of the circle to the outside of the circle. Summarize Can a square have a in the center so that all the s on the sides of the square are the same distance from it? No; if you draw a shape so that all the s are the same distance from one, it is a circle. So, it will not be a square. 701 Chapter 12

8 Lesson Check (3.G.A.1) 1. How many line segments does this shape have? 5 line segments 2. What is part of a line, has one end, and continues in one direction? 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 (3.OA.A.3, 3.OA.C.7, 3.NF.A.3a) 3. What multiplication sentence does the ar show? 4. What is the unknown factor and quotient? 9 = = 4 8 = 32 or 8 4 = What fraction is equivalent to 4_ 8? 702 Possible answers: 1_ or 2_ Mr. MacTavish has 30 students from his class going on a field trip to the zoo. He puts 6 students in each group. How many groups of students will he make? 5 groups of students FOR MORE PRACTICE GO TO THE Personal Trainer Connecting and Science Planning and Building In Chapter 12, students extend their understanding of two-dimensional shapes by identifying polygons. These same topics are used often in the development of various science concepts and process skills. The team decided the best solution would be to build another bridge across the Ohio River. Active Reading As you read these two pages, underline the sentences that describe steps in the design process. The next steps in the design process are to develop, test, and improve a prototype. The engineers gather data about important features of the bridge design, such as how stable it is and how much weight it can support. The team may modify minor aspects of the design based on this data. If the data show that the prototype has significant flaws, the team must start over again. They redesign the bridge by making major changes to their initial plan. 60 (bkgd) Corbis S.T.E.M. Activity Chapter 12 Planning and Building Use with ScienceFusion pages Develop Vocabulary 1. Write the definition using your own words. prototype: A prototype is the first model of something that is built. New forms or versions of this prototype are copied and built later. Do the! 5. Look at the bridge in the picture. What geometric shapes do you see? Develop Concepts Possible answer: There are rectangles in the bridge that make up the road and 2. If a team of engineers is planning on building a new bridge, what will help them towers. There are triangles formed where the cords, road, and tower meet. know what kind of bridge to build? A prototype will be most helpful to the engineers. 6. Are the angles at the top of the bridge greater than or less than a right angle? Are there any right angles on the bridge? The angles at the top of the bridge are less than right angles. There are right angles at the 3. What are some objects around your house that might use a prototype when where they are road connects with the tower structure in the middle. being designed and created? Possible answers: a toaster, a freezer, a bicycle, and a television 7. In the space below, use geometric shapes such as triangles and rectangles to draw a bridge. Label the shapes and angles in your design. 4. Read the process for designing a bridge. What is the last step in the design process? What is the purpose of this step? Students should use this space to draw a bridge that is similar to the one shown in The engineers communicate the results of their solution. Engineers in other places could the activity. It should include geometric shapes such as triangles and rectangles. All use their results to build similar bridges or improve on the design. shapes should be labeled and all angles should be identified. S.T.E.M. Activity 119 Summarize 8. What is the main idea of the S.T.E.M. activity on pages 60 61? The main idea of the activity is to describe steps in the design process, including prototyping and communicating results. 120 Help students make the connection between math, science, and engineering through the S.T.E.M. activities and activity worksheets found at In Chapter 12, students connect math, science, and engineering with the S.T.E.M. Activity Planning and Building and the accompanying worksheets (pages 119 and 120). Through this S.T.E.M. Activity, students will connect the GO! Chapter 12 concepts and skills with various applications of geometry, including designing a bridge. Students will also discover the overall role that math plays in science. It is recommended that this S.T.E.M. Activity be used after Lesson