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Relate Figures, Fractions, and Area

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Relate Figures, Fractions, and Area 16.4 Relate Figures, Fractions, and Area ? Essential Question How can you divide figures into parts with equal areas and INVESTIGATE write the area as a unit fraction of the whole? Texas Essential Knowledge and Skills Geometry and Measurement—3.6.E Decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape MATHEMATICAL PROCESSES 3.1.C Select tools, technology, and techniques 3.1.E Create and use representations How can you divide figures into parts with equal areas and write the area as a unit fraction of the whole? Are You Ready? Access Prior Knowledge Use the Are You Ready? 16.4 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson. Vocabulary Lesson Opener Go to Multimedia eGlossary at Making Connections thinkcentral.com Invite students to tell you what they know about kites. Materials Have you ever flown a kite? What shape was your kite? Where did you fly it? Pattern blocks, color pencils, ruler Using the Digital Lesson Model the shape of the kite with different colored pattern blocks, as in the problem. Have students make observations about the different shapes and parts of the kite shape. Learning Task What is the problem the students are trying to solve? Connect the story to the problem. • What are you being asked to find? (How much of the kite is green) Resources • What figures can you see in the kite? (Triangles and parallelograms) • What does Doc want to use to describe the figures in the kite? (Fractions) For the student For the teacher Interactive Digital Management Literacy and Mathematics Student Edition Center organizes program Choose one or more of the following activities. provides students resources by TEKS! with an interactive learning • Have students design a kite and write three reasons why their design is creative, environment! eTeacher original, and interesting. Edition • Have students work in pairs to clarify information by asking and answering Math on the Spot questions about the problem. Video Tutor Online Assessment System iTools Virtual Manipulatives Soar to Success Math Online Intervention Lesson 16.4 531A Name Geometry and Relate Figures, Fractions, Measurement—3.6.E 16.4 MATHEMATICAL PROCESSES and Area 3.1.C, 3.1.E ? Essential Question Investigate How can you divide figures into parts with equal areas Be sure students have partitioned the hexagon and write the area as a unit fraction of the whole? tracing into equal parts. Hands InvestigateInvestigate On Point out that since the denominator of the fraction should show the total number of equal parts, and Materials ■ pattern blocks ■ color pencils ■ ruler there are 2 parts in all, the fraction named in Part D Connect Use what you know about combining and should be _2 . separating pattern blocks to explore the relationship 2 between fractions and area. • How do you know the two figures have the same A. Trace a hexagon pattern block. area? Possible answer: I can cover the area with two trapezoid pattern blocks. The blocks are the same size and B. Divide your hexagon into two parts with equal area. shape. What new figures have you drawn? • What is another way you can be sure the figures trapezoids________ or pentagons Math Idea have the same area? Possible answer: cut out the figure C. Write the fraction that names each part of the and fold it in half; if the sides match, they are the same Equal parts of a whole _1 have equal area. size. whole you divided. _2 _1 Each part is 2 of the whole figure’s area. Go Deeper _2 D. Write the fraction that names the whole area. _2 To extend students’ thinking, ask what would happen if they divided the hexagon into three figures with equal area. Have them tell what fraction Make ConnectionsConnections names the area of each part of the divided hexagon The rectangle at the right is divided into four parts with equal area. 1 and what fraction names the whole area. _ • Write the unit fraction that names each part of the divided whole. _4 Make Connections • What is the area of each part? ___5 square units • How many equal shares does it take to make one whole? _4 Math Talk Remind students that a unit fraction will always have Mathematical Processes a numerator of 1. • Does each equal share of the whole have the same shape? _No • What unit fraction names 1 part of the divided • Is the area of each equal share the same? Explain how you know. 1 whole? _ 4 Yes; possible explanation: I can count the unit squares. There are 5 unit squares in each _1 part, so the area of each _1 part is the same. Guide students to see how counting the squares in 4 4 each part has the same effect as covering each part Module 16 531 © Houghton Mifflin Harcourt Publishing Company with pattern blocks to determine whether the areas are equal, even though the shapes are different. Visual English Language Learners ELL Language Support Small Group Leveled Activities ELPS ELPS 1.B.1, 2.E.3, 3.F.2 Beginning: Activity 20 1.A.1, 3.G.2, 4.C.3 Intermediate: Activity 3 2.D.2, 2.E.3, 3.F.2 Strategy: Model Language Materials: pattern blocks Advanced: Activity 58 2.C.2, 4.C.3, 4.F.9 Advanced High: Activity 59 1.F, 3.E, 3.H.3, 4.C.3 • Teachers model language to teach pronunciation. thinkcentral.com for the ELL Activity • Show each pattern block and tell students its proper name. Guide containing these leveled activities. • Have students repeat the name for each block. • Trace a pattern block and divide it into equal parts. Have students name the shape of each part. 531 Module 16 Share and Show 1. Divide the trapezoid into 3 parts with equal area. Write the names of the new shapes. Then write the fraction Share and Show that names the area of each part of the whole. The first problem connects to the learning model. 1 Math Talk 3 triangles; _ 3 Mathematical Processes Have students use the MathBoard to explain their Possible explanation: I can cover the area with 3 triangle Explain how you know thinking. pattern blocks. The blocks are the same size and shape, the areas of all the parts so the areas of the parts are equal. are equal. • How do you know that your figures in Exercise 1 Draw lines to divide the figure into equal parts that show the fraction given. Possible drawings are shown. have the same area? Possible answer: I can cover the area with 3 triangle pattern blocks. 2. 3. 4. 1 1 1 6 2 8 Math Talk Mathematical Processes Use Math Talk to focus on students’ understanding of partitioning a figure into parts with equal areas. Draw lines to divide the figure into parts with equal area. Write the area of each part as a unit fraction. Possible drawings are shown. Use the checked exercises for Quick Check. Students 5. 6. 7. should show their answers for the Quick Check on the MathBoard. 3 2 1 Quick Check _1 _1 1 _ 3 equal parts 3 6 equal parts 6 4 equal parts 4 IF a student misses the checked exercises Problem SolvingSolving Differentiate Instruction with Write Math THEN 8. If the area of three is equal RtI Tier 1 Lesson 81 to the area of one , the area of how many equals four ? Explain your answer. × = 12 blue rhombuses; Possible explanation: I can multiply 3 4 12. Problem Solving 9. Apply Show how you can divide the hexagon into four shapes with equal area. Check students’ drawings. 1 Problems _ Each part is _4 of the whole shape’s area. Problem 8 requires students to use proportional 532 © Houghton Mifflin Harcourt Publishing Company reasoning using given relationships between objects. Students can use drawings to represent the relationship. For each yellow hexagon, students should draw three blue rhombuses. Problem 9 requires students to partition the hexagon into four equal parts. Emphasize that all parts should be equal when they draw the lines to divide the Visual / Kinesthetic figure. Enrich Partners Materials: pattern blocks, paper, scissors • Have students trace a pattern block and cut it into equal parts. Then have them label each piece with the unit fraction that names each part of the divided whole. • Ask students to trade their pieces with a partner. Partners should use the pieces 1 to reassemble the whole and name the 1 6 1 original figure. 6 6 • Challenge students to divide the figures 1 1 into as many equal parts as possible 6 6 before trading. 1 6 Hexagon Go to Go to thinkcentral.com for additional enrichment activities in the Enrich Activity Guide. Lesson 16.4 532 Name 10. Multi-Step Sense or Nonsense? Problem Check students’ drawings. For Problem 10, ask students to compare the figures that result from dividing the hexagon into 6 equal parts with the figures that result from dividing the Divide the hexagon into six Divide the trapezoid into three trapezoid into 3 equal parts. equal parts. equal parts. • Are any of the triangles larger than the others? no • Why can the triangle areas be described with different fractions if they are the same size? Possible answer: the fractions compare the area of one part to the area of the whole. The original shapes of the wholes Which pattern block represents Which pattern block represents were different, so the denominators will be different.
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