9.1 PROBLEM SOLVING Use the Distributive Property? Essential Question How can you use the strategy draw a diagram to multiply with multiples of? How can you use the strategy draw a diagram to multiply with multiples of? Lesson Opener Making Connections Invite students to tell you what they know about multiples of. What is a multiple of? (A number that has as a factor.) What pattern do you see in multiples of? (Possible answer: They end in 0.) What digit does 0 end in? (0) Using the Digital Lesson You may want to discuss how multiples of ten can be represented by tens bars, tens cubes, or tens lines. Learning Task What is the problem the students are trying to solve? Connect the story to the problem. How many boxes are there? ( boxes) How many golf balls are in each box? (0 golf balls) What operations could you use to find the total number of golf balls? (multiplication, addition) What equations could you use to find the total number of golf balls? ( 0, 0 + 0 + 0) Literacy and Mathematics Choose one or more of the following activities. Ask students to clarify the story and the problem by asking them to pick out the important information from the lesson opener. Have students think of reasons a golfer might hit so many golf balls. Why did he want to practice? Texas Essential Knowledge and Skills Number and Operations.4.G Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties Also.4.E,.4.K MATHEMATICAL PROCESSES.1.A Apply mathematics to problems.1.b Use a problem-solving model.1.e Create and use representations Are You Ready? Access Prior Knowledge Use the Are You Ready? 9.1 in the Assessment Guide to assess students understanding of the prerequisite skills for this lesson. Vocabulary Go to Multimedia eglossary at thinkcentral.com For the student Resources Interactive Student Edition provides students with an interactive learning environment! Math on the Spot Video Tutor itools Virtual Manipulatives Soar to Success Math Online Intervention For the teacher Digital Management Center organizes program resources by TEKS! eteacher Edition Online Assessment System Lesson 9.1 25A
Unlock the Problem An area model helps students visualize multiplication and how the Distributive Property can be used to multiply with greater numbers. Make sure students understand that they need to find the number of third graders at the assembly. Discuss with students how the graphic organizer helps to organize their problem solving. Why are you using the Distributive Property? Possible answer: if I break apart the factor 20 into smaller numbers, I can multiply using facts I know. Discuss with students that drawing a model on grid paper is like making an array. It shows rows and columns but there is no space between the rows and columns. This model is called an area model. How does the diagram show the Distributive Property? Possible answer: it shows rows of added to another rows of. Help students work through the steps of finding and adding the products of the smaller rectangles to solve. Why do you add the products of the smaller rectangles to find the total product? Possible answer: the products of the two smaller rectangles combined equal the total number of third graders at the assembly. Why is it helpful to break apart 20 into +? Possible answer: It is easy to multiply with. Could you break apart the factors in a different way? Explain. Yes; possible explanation: I could break apart the into a 1 and a 2. Multiply 2 20 = 40 and 1 20 = 20. Add 40 + 20 =.? 9.1 PROBLEM SOLVING Use the Distributive Property Essential Question Unlock the Problem The school assembly room has rows of chairs with 20 chairs in each row. If the third-grade classes fill rows of chairs, how many third graders are at the assembly? Read What do I need to find? I need to find how many third graders are at the assembly. What information am I given? There are _ 20 chairs in each row. The third graders fill _ rows of chairs. Plan What is my plan or strategy? The Distributive Property tells me I can break apart the factor 20 to multiply. 20 = ( + _) How can you use the strategy draw a diagram to multiply with multiples of? Draw a diagram. Finish the shading to show rows of 20 chairs. 1 0 Solve 0 I can use the sum of the products of the smaller rectangles to find how many third graders are at the assembly. = _ 0 = _ 0 _ 0 + _ 0 = _ 20 = _ Number and Operations.4.G Also.4.E,.4.K MATHEMATICAL PROCESSES.1.A,.1.B,.1.E So, _ third graders are at the assembly. 1. Explain how breaking apart the factor 20 makes finding the product easier. Possible explanation: I can use facts I know to find the product. Module 9 25 English Language Learners Leveled Activities Beginning: Activity 8 Intermediate: Activity 40 ELPS 2.1.4,.G.1,.H. 4.F.6, 4.G.2, 4.G.4 Advanced: Activity 5 2.C.4,.D.2,.E Advanced High: Activity 0 1.F, 2.I.,.H. Go to thinkcentral.com for the ELL Activity Guide containing these leveled activities. ELL Language Support ELPS 1.A.2, 1.D,.H. Strategy: Draw Materials: Base-Ten Grid Paper (see eteacher Resources) Have students draw to break apart a larger rectangle into smaller ones. Students can use their drawings to help explain how to use the Distributive Property. Have students use their models to explain how they arrived at their answers. 4 4 x 0 = 4 x ( + + ) Visual Small Group 0 + + 25 Module 9
Try Another Problem Megan is watching a marching band practice. The band marches by with 4 rows of people playing instruments. She counts 0 people in each row. How many people are marching in the band? Read What do I need to find? What information am I given? Plan What is my plan or strategy? 2. Explain how you can use the Distributive Property to help you find a product. 26 Enrich I need to find how many people are marching in the band. The band has 4 rows of people playing instruments. There are 0 people in each row. I will draw a diagram and break apart the factor 0 into + + to use facts I know. 4 40 Solve Record the steps you used to solve the problem. 1 1 Possible explanation: I can break apart the greater factor to use facts I know. Then I can add the products to find the total product. 40 First, I shade 4 rows of 0, or + +. Next, I find the products of the three smaller rectangles. 4 = 40 4 = 40 4 = 40 Then, I find the sum of the three products. 40 + 40 + 40 = 120 4 0 = 120 So, 120 people are marching in the band. Possible explanation: there are 4 rows with 0 people in each row; 0 + 0 + 0 + 0 = 120. So, my answer of 120 people is reasonable. Visual / Kinesthetic Individual / Partners Materials: Base-Ten Grid Paper (see eteacher Resources) Have students find all the possible ways to break apart a factor into multiples of for 4 =. Students should break apart into 4 40 Math Talk Mathematical Processes Explain how you can check to see if your answer is reasonable. + + + + + 40 40 40 40 40 40 4 x = 4 x ( + + + + + ) addends that are multiples of. Let students know that they may use any number of addends. Have students show each example on grid paper with an equation that shows the Distributive Property. One possible way is shown. Have students write an explanation for how they found all the ways to break apart the factor. Try Another Problem For this problem, make sure students understand that they need to find the number of people marching in the band. Have students answer the questions in the graphic organizer and solve the problem. Invite students to share their diagrams by sketching them on the board. Ask them to communicate the steps they used. What strategy and steps did you use to solve the problem? Possible answer: I broke apart the factor 0 into + +. I shaded 4 rows of three times. I used the diagram to find the products of the smaller rectangles. Then I added the products. Why do you add the products of the smaller rectangles to find the total product? Possible answer: each smaller product is part of the total product. I add the parts together to find the whole product. How could you break apart the factor 0 into three addends? Possible answer: I could break apart 0 into + +. What is another way you can break apart the factor 0? Possible answer: + 20 Math Talk Mathematical Processes Use Math Talk to help students understand the reasonableness of their answer. COMMON ERRORS Error Students may use addition instead of multiplication when using an area model to solve a problem. Example Students write: 4 + = 14 4 + = 14 4 + = 14 14 + 14 + 14 = 42 4 0 = 42 Springboard to Learning Remind students that an area model shows equal groups. Help students recognize that these groups are shown by rows, which each have the same number of squares. Point out that the number of rows and the number of squares in each row represent factors. Go to Go to thinkcentral.com for additional enrichment activities in the Enrich Activity Guide. Lesson 9.1 26
Share and Show The first problem connects to the learning model. Have students use the MathBoard to explain their thinking. Problem 2 requires students to reinterpret Problem 1 given different information. Go Deeper Have students compare their models in Problems 1 and 2 and discuss different ways to break apart the factors. Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard. 2 1 IF THEN Quick Check a student misses the checked exercises Differentiate Instruction with RtI Tier 1 Lesson 41 Problem Solving Problem In Problem, students need to multiply to find the lengths of the blue ribbons and the red ribbons and then compare the two products. Math on the Spot Video Tutor Share and Show 1. The front section of a theater has 6 rows with 40 seats in each row. In the front section, 24 seats are reserved. How many seats in the front section of the theater are not reserved? Step 1, Write the problem you need to solve. 6 40 Draw and label a diagram to break apart the problem. 1 1 1 6 Problem Solving Find the products of the smaller rectangles. 6 = 6 _ = _ Tips Unlock the Problem Use the Problem Solving MathBoard. Underline important facts. Choose a strategy you know. _ 6 _ = 6 _ = _ Find the sum of the products. _ + _ + _ + _ = 240 There are 240 seats in the front section of the theater. Step 2, Find the difference. 240 _ 24 = 216 So, there are 216 seats in the front section that are not reserved. 2. What if seats are added to the front section of the theater so that there are 6 rows with 50 seats in each row? How many seats are in the front section? 00 seats. Multi-Step Tova sewed pieces of blue ribbon together to make a costume. Each piece of ribbon was 2 meters long. She also sewed 40 pieces of red ribbon together that were each meters long. Did Tova use more blue ribbon or red ribbon? Explain. She used the same amount. 2 = 120; 40 = 120 Module 9 Lesson 1 2 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. 2 1 LESSON Problem Solving Use the 41 Distributive Property OBJECTIVE Solve multiplication problems by using the strategy draw a diagram. There are 6 rows of singers in a performance. There are 20 singers in each row. How many singers are in the performance? Read What do I need to find? RtI Tier 1 Lesson 41 I need to find how many singers are in the performance What information am I given? There are 6 rows of singers. Each row has 20 singers. Solve 1.4.G Record the steps you used to solve the problem. 6 + First, I draw and label a diagram to 6 20 show rows of singers. Enrich 42 Enrich 42 Apply the Distributive Property Use the Distributive Property to help solve each problem. Use this problem for 1. Use this problem for 4 6. An artist sells 4 paintings for Lee has 6 sheets of stickers with $20 each, 4 sculptures for 0 stickers on each sheet. She has $ each, and 4 photographs for 8 sheets with 20 stickers each and $ each at her art show. 9 sheets with stickers each. 1. How much money does the artist 4. How many stickers does Lee have in make on these sales in all? all? $ 40 stickers 2. The artist sells 2 more paintings 5. Lee gives 4 sheets with 20 stickers and 4 more sculptures at the same and sheets with stickers to her prices. What is the total amount of sister. How many stickers does Lee money the artist has made so far? have left? Plan What is my plan or strategy? I can draw a diagram and use the Distributive Property to break apart the factor 20 into + to use facts I know. 1. Eight teams play in a Little League series. Each team has 20 players. How many players are in the series? Next, I break apart 20 into + and find the products of the two smaller rectangles. 6 = 6 = Then, I find the sum of the two products. + = 6 20 = So, there are 120 120 120 singers. 2. The assembly room has 6 rows with 0 chairs in each row. If third graders fill rows, how many third graders are in the room? 1 players 90 third graders $640 20 stickers. How many more paintings, 6. Now Lee gives some stickers to sculptures, and photographs would her friend Myla. What sheets does the artist need to sell to make Lee give to Myla if she has 200 another $500? stickers left? Possible answer: 5 paintings, Possible answer: 2 sheets with 5 sculptures, photographs 0 stickers and sheets with 20 stickers. How did the Distributive Property help you solve the problems? Possible answer: I used the Distributive Property to break apart greater numbers into lesser numbers that are easier to work with. 2 Module 9 Number and Operations 81 Enrich E42
Daily Assessment Task Fill in the bubble for the correct answer choice. 4. Apply A zoo gives 8 tubs of food to the male gorillas. Each tub has 40 pounds of food. How much food do the male gorillas eat each day? A B C D 20 pounds 180 pounds 20 pounds 90 pounds 5. Marcus will make 20 omelets. Each omelet takes eggs. How many eggs will Marcus use? A 2 C B 1 D 50 6. Multi-Step Shania makes a scrapbook about her trip to the state capitol. She makes 2 sections about the history and 4 sections about what she saw. Each history section has 0 pages and each section about what she saw has 20 pages. How many pages does Shania s scrapbook have? A 140 C 80 B 00 D Mathematical Processes 2 Daily Assessment Task 1 Can students use the strategy draw a diagram to multiply with multiples of? IF NO YES THEN Soar to Success Math Warm-Up 12.51 Enrich 42 Homework and Practice Lesson 9.1 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: 28 TEXAS Test Prep. Stefan orders theater tickets for each of the 5 members in his family. If each ticket costs $20, what is the total cost for the tickets? A $0 B $0 C $25 D $0 A They may have added 5 to the tens place. B They may have broken $20 into $ + $ and added $5 to each $. C They added $5 to $20.? Essential Question Write Math How can you use the strategy draw a diagram to multiply with multiples of? Possible answer: I can draw and shade a rectangle on grid paper to show the problem. Then I can break apart a factor to make smaller rectangles for facts I know. Differentiated Centers Kit Games Games Multiplication Bingo Students practice multiplication facts through. Literature Party Plans by the Numbers! Students read the book and use multiplication facts and strategies to plan a party. Activities Multiplication Dash Students complete orange Activity Card 1 by using models to apply multiplication facts through 12 by 12. Lesson 9.1 28
5 Homework and Practice 9.1 PROBLEM SOLVING Use the Distributive Property Draw and label the diagram to solve. 1. The Morgan family buys booklets of tickets at the carnival. Each booklet has 0 tickets. Of all the tickets bought, 21 tickets are for rides. How many tickets are not for rides? Step 1 + + 1 1 Number and Operations.4.G Also.4.E,.4.K MATHEMATICAL PROCESSES.1.A,.1.B,.1.E Lesson Check Fill in the bubble completely to show your answer. 4. Ari has a rock collection. He puts 20 rocks into each of 8 boxes. How many rocks does Ari have in his collection? A 1 B 28 C 16 D 140 TEXAS Test Prep 5. At the town picnic, there are stacks of paper cups on a shelf. Each stack holds cups. How many cups are on the shelf? A 490 B 420 C D 6 Find the products of the smaller rectangles. = 0 = = 0 Find the sum of the products. 0 + 0 + 0 = 2 0 6. Mr. Franz buys 4 bags of forks. There are 0 forks in each bag. Which number sentence shows how many forks are there in all? A 4 + 0 = 4 B 4 0 = 120 C 4 + 0 = 120 D 40 + 0 = 0. Valerie buys 5 sticker books. Each book has 80 stickers. Which number sentence shows how many stickers Valerie buys? A 5 80 = 40 B 8 + 50 = 58 C 5 80 = 400 D 5 80 = 450 0 = They have 2 tickets. Step 2 Find the difference. 2 21 = 189 So, there are 189 tickets that are not for rides. Problem Solving 2 2. The roller coaster ride costs 8 tickets. If 0 people ride the roller coaster, how many tickets are collected?. The giant swing ride costs 6 tickets. If 50 people ride the giant swing ride, how many tickets are collected? 0 8 = 240 50 6 = 00 Module 9 Lesson 1 29 8. Multi-Step A farm stand has 4 bushels of apples. Each bushel has 40 red apples. There are also bushels of 0 green apples. How many apples are there in all? A 490 280 B 0 C 280 D 1 9. Multi-Step Marcel buys large boxes of cherries. Each box holds 40 cherries. He also buys 8 small boxes. Each small box holds 20 cherries. How many cherries does Marcel buy? A 280 B 120 C 480 D 1 Homework and Practice Use the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson. 29-280 Module 9