16.4 INVESTIGATE. Relate Figures, Fractions, and Area. Are You Ready? Lesson Opener Making Connections. Resources. Essential Question

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1 . INVESTIGTE Relate Figures, Fractions, and rea? Essential Question How can you divide figures into parts with equal areas and write the area as a unit fraction of the whole? How can you divide figures into parts with equal areas and write the area as a unit fraction of the whole? Lesson Opener Making onnections Invite students to tell you what they know about kites. Have you ever flown a kite? What shape was your kite? Where did you fly it? Using the igital 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. Texas Essential Knowledge and Skills Geometry and Measurement..E ecompose 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 MTHEMTIL PROESSES.. Select tools, technology, and techniques..e reate and use representations re You Ready? ccess Prior Knowledge Use the re You Ready?. in the ssessment Guide to assess students understanding of the prerequisite skills for this lesson. Vocabulary Go to Multimedia eglossary at thinkcentral.com Materials Pattern blocks, color pencils, ruler Learning Task What is the problem the students are trying to solve? onnect the story to the problem. What are you being asked to find? (How much of the kite is green) What figures can you see in the kite? (Triangles and parallelograms) What does oc want to use to describe the figures in the kite? (Fractions) For the student Resources For the teacher Literacy and Mathematics hoose one or more of the following activities. Have students design a kite and write three reasons why their design is creative, original, and interesting. Have students work in pairs to clarify information by asking and answering questions about the problem. Interactive Student Edition provides students with an interactive learning environment! Math on the Spot Video Tutor itools Virtual Manipulatives igital Management enter organizes program resources by TEKS! eteacher Edition Online ssessment System Soar to Success Math Online Intervention Lesson. 5

2 Investigate e sure students have partitioned the hexagon tracing into equal parts. Point out that since the denominator of the fraction should show the total number of equal parts, and there are parts in all, the fraction named in Part should be _. How do you know the two figures have the same area? Possible answer: I can cover the area with two trapezoid pattern blocks. The blocks are the same size and shape. What is another way you can be sure the figures have the same area? Possible answer: cut out the figure and fold it in half; if the sides match, they are the same size. Go eeper To extend students thinking, ask what would happen if they divided the hexagon into three figures with equal area. Have them tell what fraction names the area of each part of the divided hexagon and what fraction names the whole area. Make onnections Remind students that a unit fraction will always have a numerator of. What unit fraction names part of the divided whole? Guide students to see how counting the squares in each part has the same effect as covering each part with pattern blocks to determine whether the areas are equal, even though the shapes are different. Houghton Mifflin Harcourt Publishing ompany?. Essential Question Investigate Materials pattern blocks color pencils ruler onnect Use what you know about combining and separating pattern blocks to explore the relationship between fractions and area.. Trace a hexagon pattern block.. ivide your hexagon into two parts with equal area. What new figures have you drawn? trapezoids or pentagons. Write the fraction that names each part of the whole you divided. _ Each part is of the whole figure s area. _. Write the fraction that names the whole area. _ Make onnections Relate Figures, Fractions, and rea How can you divide figures into parts with equal areas and write the area as a unit fraction of the whole? The rectangle at the right is divided into four parts with equal area. Geometry and Measurement..E MTHEMTIL PROESSES..,..E Math Idea Equal parts of a whole have equal area. Write the unit fraction that names each part of the divided whole. _ What is the area of each part? 5 square units How many equal shares does it take to make one whole? _ oes each equal share of the whole have the same shape? _ No Is the area of each equal share the same? Explain how you know. Math Talk Mathematical Processes Yes; possible explanation: I can count the unit squares. There are 5 unit squares in each part, so the area of each part is the same. Module 5 Hands On English Language Learners Leveled ctivities eginning: ctivity 0 Intermediate: ctivity dvanced: ctivity 5 dvanced High: ctivity 59 ELPS..,.G.,....,.E.,.F...,..,.F.9.F,.E,.H.,.. thinkcentral.com for the ELL ctivity Guide containing these leveled activities. ELL Language Support ELPS..,.E.,.F. Strategy: Model Language Materials: pattern blocks Teachers model language to teach pronunciation. Show each pattern block and tell students its proper name. Have students repeat the name for each block. Visual Small Group Trace a pattern block and divide it into equal parts. Have students name the shape of each part. 5 Module

3 Share and Show. ivide the trapezoid into parts with equal area. Write the names of the new shapes. Then write the fraction that names the area of each part of the whole. Possible explanation: I can cover the area with triangle pattern blocks. The blocks are the same size and shape, so the areas of the parts are equal. raw lines to divide the figure into equal parts that show the fraction given. Possible drawings are shown.... triangles; Math Talk Mathematical Processes Explain how you know the areas of all the parts are equal. raw lines to divide the figure into parts with equal area. Write the area of each part as a unit fraction. Possible drawings are shown Share and Show The first problem connects to the learning model. Have students use the Mathoard to explain their thinking. How do you know that your figures in Exercise have the same area? Possible answer: I can cover the area with triangle pattern blocks. Math Talk Mathematical Processes Use Math Talk to focus on students understanding of partitioning a figure into parts with equal areas. Use the checked exercises for Quick heck. Students should show their answers for the Quick heck on the Mathoard. equal parts equal parts equal parts Problem Solving. Write Math If the area of three is equal to the area of one, the area of how many equals four? Explain your answer. 9. pply Show how you can divide the hexagon into four shapes with equal area. heck students drawings. 5 Enrich Each part is _ of the whole shape s area. blue rhombuses; Possible explanation: I can multiply =. Materials: pattern blocks, paper, scissors Visual / Kinesthetic Partners Houghton Mifflin Harcourt Publishing ompany IF THEN Quick heck a student misses the checked exercises ifferentiate Instruction with RtI Tier Lesson Problem Solving Problems Problem requires students to use proportional 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 figure. 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. sk students to trade their pieces with a partner. Partners should use the pieces to reassemble the whole and name the original figure. hallenge students to divide the figures into as many equal parts as possible before trading. Go to Go to thinkcentral.com for additional enrichment activities in the Enrich ctivity Guide. Hexagon Lesson. 5

4 Houghton Mifflin Harcourt Publishing ompany OMMON ERRORS Error Students may draw lines of division that do not result in equal parts. Example Problem For Problem 0, ask students to compare the figures that result from dividing the hexagon into equal parts with the figures that result from dividing the trapezoid into equal parts. re 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 were different, so the denominators will be different. 0. Multi-Step Sense or Nonsense? heck students drawings. ivide the hexagon into six equal parts. Which pattern block represents of the whole area? triangle lexis said the area of of the trapezoid is greater than the area of of the hexagon because >. oes her statement make sense? Explain your answer. No; possible explanation: lexis just looked at the fractional parts ivide the trapezoid into three equal parts. Which pattern block represents of the whole area? triangle and. ll the triangle parts have the same area, but since the wholes are not the same size, you cannot compare the fractions. Write a statement that makes sense. Possible answer: the area of of the trapezoid is equal to the area of of the hexagon. Springboard to Learning Use pattern blocks to show that the hexagon cannot be covered using the figure created by the partition. Remind students that unless the parts are equal, you cannot write a unit fraction to represent the area of a part. Houghton Mifflin Harcourt Publishing ompany. What if you divide the hexagon into equal parts? Use Math Language to write a sentence that compares the area of each equal part of the hexagon to each equal part of the trapezoid. Possible answer: the area of of the hexagon is greater than the area of of the trapezoid. Module Lesson 5 Math on the Spot Video Tutor Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and the H.O.T. problems, students will build skills needed in the TEXS assessment. LESSON RtI Tier Lesson Relate Figures, Fractions, and rea OJETIVE Partition figures into parts with equal areas and express the area as a unit fraction of the whole. You can separate a plane figure into equal parts to explore the relationship between fractions and area. ivide the rectangle into parts with equal area. Write the fraction that names the area of each part of the whole. Step raw lines to divide the rectangle into parts with equal area. Use the grid to help you...e Enrich 77 Secret Message Enrich 77 raw lines to divide the figure into the given number of parts of equal area. Write the fraction that names each part of the whole. Possible drawings are shown. 0 equal parts F equal parts H equal parts Math on the Spot videos are in the Interactive Student Edition and at thinkcentral.com. 5 Module Houghton Mifflin Harcourt Publishing ompany Step Write the fraction that names each part of the divided whole. Think: Each part is part out of equal parts. Each part is _ of the whole figure s area. Step Write the fraction that names the whole area. Think: There are equal parts. The fraction that names the whole area is. raw lines to divide the figure into parts with equal area. Write the area of each part as a unit fraction.. equal parts _ Each part is of the whole figure s area. Possible drawings are shown.. equal parts _ Each part is of the whole figure s area. Geometry and Measurement Enrich I equal parts M equal parts N equal parts S 5 equal parts T 9 equal parts U equal parts Write the fractions in order from least to greatest. Use the letter for each fraction to write the secret message. M _ T H I S F U N E77 _ 9

5 Mathematical Processes aily ssessment Task Fill in the bubble for the correct answer choice.. Inez made a stained glass design with the rectangles shown at the right. Which rectangles have the same shape and the same area? and and and and aily ssessment Task an students divide figures into parts with equal areas and write the area as a unit fraction of the whole? IF THEN. Paulo buys a mirror. The frame is made of same-size trapezoids. What unit fraction of the frame is each trapezoid? TEXS Test Prep 5. Rav divided the rectangle at the right into six parts with equal area. What is the area of each part? square units square units square units 0 square units. Multi-Step nastasia is painting one wall of her room. She divides the wall into squares with the same area. She paints half of the squares light green and half of the squares dark green. What fraction of the wall is one dark green square? 5 ifferentiated enters Kit Houghton Mifflin Harcourt Publishing ompany NO YES TEXS Test Prep oach Test Prep oach helps teachers to identify common errors that students can make. In the Test Prep exercise, if students selected: They counted the number of equal parts. They multiplied the number of equal parts by the number of unit squares in each part. They added the number of equal parts and the number of unit squares in each part.? Essential Question Soar to Success Math Warm-Up 5.0 Enrich 77 Homework and Practice Lesson. Write Math How can you divide figures into parts with equal areas and write the area as a unit fraction of the whole? Possible answer: I can trace pattern blocks and then draw lines that divide the figure into equal parts. Then I can write the area of each part as a fraction by using as the numerator and the number of equal parts as the denominator. ctivities Fish for Fractions Students complete orange ctivity ard by playing a Go Fish game in which they match fraction symbols, words, and pictures. Literature The Whole Picture Students read the book and model fractional parts. ctivities lassification ct Students complete orange ctivity ard by classifying two-dimensional shapes based on their attributes. Lesson. 5

6 5 Houghton Mifflin Harcourt Publishing ompany Homework and Practice. Problem Solving raw lines to divide the figure into equal parts that show the fraction given. Possible drawings are shown.... raw lines to divide the figure into parts with equal area. Write the area of each part as a unit fraction.. equal parts Relate Figures, Fractions, and rea. Sanchez puts a window in his house made of same-size triangles. What unit fraction of the window is each triangle? 5. Geometry and Measurement..E MTHEMTIL PROESSES..,..E Possible drawings are shown. equal parts Module Lesson 55 Lesson heck Fill in the bubble completely to show your answer. 7. Georgie has a rectangular window that is divided into same-size squares. What fraction of the window is square? 9. Rory divides the rectangle into 7 parts with equal area. What is the area of each part? square units 5 square units 7 square units square units 0. Multi-Step Perry makes a quilt with same-size squares. He makes red squares, blue squares, yellow squares, and green squares. What fraction of the quilt are the red squares? 5 TEXS Test Prep. Marcy has a square window that is divided into same-size squares. What fraction of the window is square?. Multi-Step oreen makes a painting with same-size squares. She has painted one-half of the squares with a design. How many squares has oreen painted? Houghton Mifflin Harcourt Publishing ompany Homework and Practice Use the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson Module