16.2. Use Area Models. Are You Ready? Lesson Opener Making Connections. Resources. Texas Essential Knowledge and Skills.

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1 6.? Essential Question Why can you multiply to find the area of a rectangle? Why can you multiply to find the area of a rectangle? Lesson Opener Making Connections Invite students to tell you what they know about painting a space. Ask students if they have ever helped paint an area or room. For students who answer yes, ask what they painted and about how much paint they used. Texas Essential Knowledge and Skills Geometry and Measurement.6.C Determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row MATHEMATICAL PROCESSES..A Apply mathematics to problems..d Communicate mathematical ideas and reasoning..e Create and use representations Are You Ready? Access Prior Knowledge Use the Are You Ready? 6. in the Assessment Guide to assess students understanding of the prerequisite skills for this lesson. Vocabulary Go to Multimedia eglossary at thinkcentral.com Using the Digital Lesson It may help to draw the parking space as a rectangle for students to understand the concepts of length and width. Label the length and width with the stated dimensions from the problem. Learning Task What is the problem the students are trying to solve? Connect the story to the problem. How long is the parking space? (7 meters) How wide is the parking space? ( meters) What is the problem asking you to find? (The area of the parking space) Literacy and Mathematics Choose one or more of the following activities. Point out to students that equa- in equation is similar to the word equal. Have students explain how the words equal and equation are related. Have students evaluate whether or not they think the problem provides enough information to be solved, explaining why. For the student Resources Interactive Student Edition provides students with an interactive learning environment! Math on the Spot Video Tutor itools Virtual Manipulatives For the teacher Digital Management Center organizes program resources by TEKS! eteacher Edition Online Assessment System Soar to Success Math Online Intervention Lesson 6. 59A

2 Unlock the Problem Students have learned to find the area of figures by counting unit squares. Tell them there is an easier way, using multiplication. Relate the multiplication strategies students have previously learned to the area problems on this page. One Way What do you notice about the number of unit squares in each row of Melissa s garden? The same number of unit squares are in each row. How can you use addition to find a total amount for a problem involving equal groups? I can use repeated addition to add equal groups. Another Way How is this figure like an array? The figure has rows with the same number of unit squares in each row. How can you use multiplication to find the total number of unit squares in an array? I can multiply the number of unit squares in each row by the number of rows. It is important for students to understand that they can use multiplication in this example because the shape is a rectangle. Rectangles are like arrays and involve rows with the same number of unit squares in each row. Use to deepen students understandings that each method gives the same result and why they can use the methods to find the area of rectangles.? 6. Essential Question You can count the number of square units to find the area of a figure. This rectangle has an area of 6 square units. You can also use multiplication. Unlock the Problem Why can you multiply to find the area of a rectangle? Melissa has a garden that is shaped like the rectangle below. Each unit square represents square meter. What is the area of her garden? One Way Use repeated addition. Count the number of rows. Count the number of unit squares in each row. _ rows of _ 6 = Write an addition equation. So, the area is _ 8 square meters. Another Way Use multiplication. Count the number of rows. Count the number of unit squares in each row. _ rows of _ 6 = Remember Geometry and Measurement.6.C MATHEMATICAL PROCESSES..A,..D,..E A unit square can be different sizes: square meter, square foot, square centimeter, and so on. _ 6 unit squares _ 6 unit squares _ 6 unit squares _ 6 + _ 6 + _ 6 = _ 8 _ rows _ 6 unit squares in each row This figure is like an array. How do you find the total number of squares in an array? You can multiply the number in each row by _ _ 6 = _ 8 the number of rows. Write a multiplication equation. So, the area is _ 8 square meters. Explain when you can Possible explanation: if the figure is shaped like a rectangle, use different methods to you can count the number of unit squares in all or multiply the find the same area. number of unit squares in each row by the number of rows. Module 6 59 English Language Learners Leveled Activities Beginning: Activity 44 Intermediate: Activity Advanced: Activity 46 Advanced High: Activity 5 ELPS.D,.C.4, 4.C..D.,.E.,.F..F,.I.4, 4.G..B.,.F,.C.4,.G. thinkcentral.com for the ELL Activity Guide containing these leveled activities. 59 Module 6 ELL Language Support ELPS.C.,.D.,.I.5 Strategy: Draw Materials: -Centimeter Grid Paper (see eteacher Resources) Interpersonal / Social Small Group Have students draw a rectangle on a sheet of centimeter grid paper. What is the area of unit square? square centimeter Have students count rows. You may point to the rows in the drawing to illustrate the word row. Ask how many rows students have. Answers will vary. Have students shade unit squares in each row, one by one. Slide your finger along a row if necessary. Ask how many unit squares there are in each row. Answers will vary. Have students find the area of their rectangles. Ask how they found the area. Answers will vary.

3 Share and Show. Find the area of the rectangle in two ways. _ rows of _ 4 = Add. _ 4 + _ 4 + _ 4 = _ Multiply. _ _ 4 = _ What is the area of the rectangle? _ square units Each unit square is square foot... Which method do you prefer using? Explain. Possible explanation: I prefer using multiplication because it is quicker than counting or using repeated addition. Share and Show The first problem connects to the learning model. Have students use the MathBoard to explain their thinking. Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard. Quick Check 4 square feet 5 square feet IF THEN a student misses the checked exercises Differentiate Instruction with RtI Tier Lesson 76 square meters square meters Use to continue the discussion about which methods students prefer. If students are having difficulty solving with one method, suggest that they try using a different method square meters 5 square meters COMMON ERRORS Error Students use the incorrect unit when writing the area. Example Students write square units or square feet when the measurement should be square meters. Springboard to Learning Tell students that they should circle the unit given in the problem. Enrich Visual / Spatial Individuals Materials: ruler or measuring tape Have students estimate the area of several objects in the classroom using two different units of measurement. Suggest the following: computer screen: square inches, square centimeters doorway: square feet, square meters Have students measure the object to the nearest whole unit using a ruler or measuring tape. Then have students find the area using multiplication. Have students repeat the activity using an object of their own. Go to Go to thinkcentral.com for additional enrichment activities in the Enrich Activity Guide. Lesson 6. 50

4 Problem Solving Problems In Problem 9, students write their own problems. Then, students must solve their problems using the content of the lesson. Be sure that students explain the method they used in their solution. Problem 0 requires students to understand the concept of area in order to draw three different rectangles with the same area, 4 square units. The problem requires students to start with the area to find appropriate side lengths. Since students have not learned multiplication facts for or 4, encourage them to write an addition equation if they draw a rectangle that is units by units or unit by 4 units. Problem Solving 8. Write Math Use Math Language Multi-Step Compare the areas of the two rugs at the right. Each unit square represents square foot. Which rug has the greater area? Explain. Areas are the same. Possible explanation: the green rug has 4 rows of or 4 = square feet; the purple rug has rows of 4 or 4 = square feet. 9. Pose a Problem A tile company tiled a wall using square tiles. A mural is painted in the center. The drawing shows the design. The area of each tile used is square foot. Write a problem that can be solved by using the drawing. Then solve your problem. 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 TEXAS assessment. Math on the Spot videos are in the Interactive Student Edition and at thinkcentral.com. Possible problem: A wall is tiled using yellow tiles and hand-painted tiles. How many more square feet of yellow tiles were used than square feet of hand-painted tiles?; more square feet 0. Draw and shade three different rectangles with an area of 4 square units. Then write an addition or multiplication equation for each area. Possible equations: + = 4 square units; 8 = 4 square units; 4 6 = 4 square units Module 6 Lesson 5 RtI Tier Lesson 76 Enrich 75 Enrich 75 LESSON 76 OBJECTIVE Relate area to addition and multiplication by using area models..6.c Area Riddles Use multiplication to find the area of the rectangle. Use the clues to solve the riddle. You may use grid paper to draw the figure. Step Count the number of rows. There are 6 rows Step Count the number of unit squares in each row. There are 0 unit squares My sides are all the same length.. I am a square. One of my sides is My area is 9 square meters. What is 9 feet long. What is my area? the length of one of my sides? meters 8 square feet. I am a rectangle. One of my sides is 4. I am a rectangle. Two of my sides 8 centimeters long. Another side is are each 7 inches long. My area is 6 centimeters long. What is my area? 8 square inches. What is the length of each of my other two sides? 48 square centimeters 4 inches Step Multiply the number in each row by the number of rows to find the area. number of rows number in each row = area 6 0 = 60 So, the area of the rectangle is 60 square meters. 5. I am a rectangle. Each of my shorter 6. I am a square. My area is 64 square sides measure 5 meters. My area is feet. What is the length of one of my 45 square meters. What is the length sides? of each of my longer sides? 9 meters 8 feet.. 7 square meters 5 square meters 7. How did you find the 8. Stretch Your Thinking Suppose answer in Exercise 4? you know that a figure is a rectangle and its area is 8 square meters. What are all the different wholenumber side lengths the rectangle Possible answer: I found could have? what number, when and 8 meters or and multiplied by 7, equals 8: 4 meters 4 5 Module 6 Geometry and Measurement 5 Enrich E75

5 Daily Assessment Task Fill in the bubble for the correct answer choice.. Brianna is coloring a bookmark. Each unit square is square inch. Which multiplication equation can be used to find the area of the bookmark? A = 4 C 7 = 4 B 7 7 = 49 D = 4. Maria is painting a tile design for her porch. Each square tile is square foot. What is the area of the design? A 9 square feet C 6 square feet B 8 square feet D 0 square feet. Multi-Step Tom and Bill are painting a fence. Tom paints the yellow area. Bill paints the white area. Each unit square is square foot. How many more square feet does Bill paint than Tom? A 0 square feet C 5 square feet B 40 square feet D 5 square feet Daily Assessment Task Can students understand why they multiply to find the area of a rectangle? IF NO YES THEN Soar to Success Math Warm-Up 48.8 Enrich 76 Homework and Practice Lesson 6. TEXAS Test Prep Coach Test Prep Coach helps teachers to identify common errors that students can make. In the Test Prep exercise, if students selected: TEXAS Test Prep 4. Heather drew this rectangle. Which equation can be used to find the area of the rectangle? 5 A 5 8 = 40 B 8 8 = 64 C = D 5 5 = 5 B They multiplied the number in each row by itself. C They used an addition equation and counted only 4 rows. D They multiplied the number of rows by itself.? Essential Question Write Math Why can you multiply to find the area of a rectangle? A rectangle is like an array involving rows with an equal number of unit squares, so I can use multiplication to find the area of a rectangle just like I can use an array to solve a multiplication problem. Differentiated Centers Kit Activities Jump to 9 Students complete blue Activity Card 6 by measuring and then adding lengths. Activities Hurray for Arrays! Students complete blue Activity Card 5 by using arrays to model multiplication facts. Lesson 6. 5

6 5 Homework and Practice 6... square meters. 4. Geometry and Measurement.6.C MATHEMATICAL PROCESSES..A,..D,..E 4 square meters Lesson Check Fill in the bubble completely to show your answer. 6. Nolan draws this diagram for a rug. Which equation can be used to find the area? A = 40 B 5 5 = 5 C 8 5 = 40 D 8 8 = 64 TEXAS Test Prep 7. Marisol puts together a floor puzzle. Each puzzle piece is square foot. What is the area of the puzzle? A 7 square feet B 8 square feet C square feet D 5 square feet 8. Multi-Step Lu Chen draws this diagram of his patio. Each square is square meter. He wants to add square meters to the patio. What will be the size of the new patio? 6 square meters 5 square meters A B 40 square meters 6 square meters Problem Solving C D 4 square meters 48 square meters 5. Shoshauna is using one-inch tiles to cover a table. She wants to put a green border around the edge of the table. She wants to make the center of the table yellow. How many more yellow tiles does she need than green tiles? Explain. 8 more yellow tiles; Possible explanation: The area of the center of the table is 6 square inches; the area of the border is 8 square inches. 6 8 = 8 Module 6 Lesson 5 9. Multi-Step Aliki and Deke are covering a wall with panels. Aliki covers the yellow area. Deke covers the white area. Each panel is square foot. How many more square feet does Aliki cover than Deke? A 6 square feet C 9 square feet B 8 square feet D 7 square feet 54 Homework and Practice Use the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson Module 6