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LESSON 2.3 Multiply Tens, Hundreds, and Thousands FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. MATHEMATICAL PRACTICES MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. F C R Coherence: Standards Across the Grades Before Grade 4 After 3.OA.A.3 4.NBT.B.5 5.NBT.B.5 F C R Rigor: Level 1: Understand Concepts....................Share and Show ( Checked Items) Level 2: Procedural Skills and Fluency.......On Your Own Level 3: Applications..................................Think Smarter and Go Deeper Learning Objective Multiply tens, hundreds, and thousands by whole numbers through 10. Language Objective Students complete the sentence frame, Place value helps you to multiply tens, hundreds, and thousands by __________. Materials MathBoard F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 61J. About the Math Professional Development Teaching for Depth In this lesson, students are shown different ways to multiply tens, hundreds, and thousands by a whole number through 10. The first strategy involves students’ understanding of place value. In One Way, students draw a quick picture of the problem using a square for one hundred and a square with a T inside for one thousand. Students regroup as needed to find the answer. In Another Way, students rewrite the problem using place value. For example, 8 × 200 can be rewritten as 8 × 2 hundreds. Then students use the basic fact, 8 × 2, to write the answer as 16 hundreds, or 1,600. In the second strategy, students use patterns to find products. Students visualize patterns using number lines and patterns in multiplication problems. As the number of zeros in a factor increases, the number of zeros in the product increases. Professional Development Videos 75A Chapter 2 Interactive Student Edition Personal Math Trainer Math on the Spot Animated Math Models iTools: Base-Ten Blocks iTools: Number Charts iTools: Number Lines Daily Routines Common Core Problem of the Day 2.3 1 ENGAGE with the Interactive Student Edition Essential Question For Field Day, the students were grouped into 20 teams of 10 students each. How many is 20 tens? 200 How does understanding place value help you multiply tens, hundreds, and thousands? Vocabulary Invite students to tell you what they know about place value. Interactive Student Edition Multimedia eGlossary Making Connections What happens to place value as you move from tens to hundreds? The value is 10 times larger. What happens to place value as you move from hundreds to thousands? The value is 10 times larger. Learning Activity Connect the story to the problem. Fluency Builder Materials Digit Cards 0-9 (see eTeacher Resource) Mental Math Have pairs practice their multiplication facts. Give partners two sets of digit cards (0-9). Have students shuffle the cards and place them facedown in a single pile on the table. One student turns over two cards and makes a 2-digit number with them. The other student states a multiplication fact with the 2-digit number as the product or states that it is not possible. Partners switch roles and continue until all cards have been played. • What are you trying to find? how much money the gas station owner collects in one day • How much does one gallon of gas cost? $4 • How many gallons of gas were sold? 200 • What does the 2 represent in 200? hundreds • What expression will you use? 200 × 4 Literacy and Mathematics Choose one or more of the following activities. • Ask students to identify the full word that gas is an abbreviation for. gasoline Have them think of other words that use abbreviations in that way. bike/bicycle; mic/microphone; phone/ telephone • Have students work in pairs and explain how they might solve the problem if only 6 gallons of gas were sold that day, at $4 a gallon. How does understanding place value help you multiply tens, hundreds, and thousands? Lesson 2.3 75B LESSON 2.3 2 EXPLORE 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, DO NOT EDIT--Changes made "File info" using strategies based onmust placebevalue andthrough the properties of operations. Illustrate and explain the calculation by using equations, CorrectionKey=B rectangular arrays, and/or area models. Lesson 2.3 Name Unlock the Problem Multiply Tens, Hundreds, and Thousands Number and Operations in Base Ten—4.NBT.B.5 Also 4.NBT.A.1 MATHEMATICAL PRACTICES MP2, MP5, MP7 Essential Question How does understanding place value help you multiply tens, hundreds, and thousands? MATHEMATICAL PRACTICES Read and discuss the problem. Make sure students understand that a “car” is one section of a train. • How many cars long is the train? 8 cars • How many seats are in each car? 200 seats Unlock Unlock the the Problem Problem Each car on a train has 200 seats. How many seats are on a train with 8 cars? Find 8 × 200. One Way One Way Draw a quick picture. MP4 Model with mathematics. Point out that drawing quick pictures can help students represent a problem. • What does each square on the left represent? Each square represents 1 hundred. • How do the squares on the left show 8 × 200? Possible answer: there are 8 rows of T Think: 10 hundreds = 1,000 2 squares. This shows 8 groups of 200 or 8 × 200. • What does the picture to the right show? Possible answer: it shows a group of 10 hundreds regrouped as 1 thousand plus 6 hundreds. Explain that students can use place value as another way to solve the problem. • How can you rename 200 using place value? 2 hundreds • What basic fact can you use to help you solve this problem? 8 × 2 = 16 • How can you rename 16 hundreds in standard form? Write 2 zeros after 16 to get 1,600. Think: 6 hundreds = 600 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Corbis Another Way 1,600 1,000 + 600 = _ Another Way Use place value. 2 hundreds 8 × 200 = 8 × _ Possible explanation: I can solve the basic fact 8 × 2 and then write the number of zeros in the greater factor, 200. 16 hundreds =_ 1,600 Think: 16 hundreds is 1 thousand, 6 hundreds. =_ Math Talk 1,600 seats on a train with 8 cars. So, there are _ MATHEMATICAL PRACTICES 7 Look for a Pattern How can finding 8 × 2 help you find 8 × 200? Chapter 2 75 Math Talk Use Math Talk to focus on students’ understanding of how to use place value and the basic fact to solve the problem. ELL Strategy: Scaffold Language Draw a picture of a multiplication problem with tens, hundreds, and thousands by a whole number through 10. •Have students describe the picture. •Next prompt them to say it using place value and write a multiplication sentence to match. •Use leveled questions to help students use math language: Beginning: Yes/no–Is this 2 × 400? Intermediate: How many hundreds are there? Advanced: Explain how your model works. 75 Chapter 2 4_MNLESE342194_C02L03.indd 75 10/7/14 7:07 PM Reteach 2.3 2 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A 1 Lesson 2.3 Reteach Name Multiplication Inequalities Write ,, ., or 5 for each You can use a pattern to multiply with tens, hundreds, and thousands. Count the number of zeros in the factors. ← basic fact 4 3 60 5 240 ← When you multiply by tens, the last digit in the product is 0. 4 3 600 5 2,400 ← When you multiply by hundreds, the last two digits in the product are 0. Lesson 2.3 Enrich Name Multiply Tens, Hundreds, and Thousands 4 3 6 5 24 Differentiated Instruction Enrich 2.3 3 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A 4 × 6,000 = 24,000 ← When you multiply by thousands, the last three digits in the product are 0. When the basic fact has a zero in the product, there will be an extra zero in the final product: . 1. 7 3 60 . 400 2. 700 , 90 3 8 3. 3 3 800 , 2,500 4. 2,000 5 400 3 5 5. 8 3 6,000 . 40,000 6. 3 3 9,000 , 39,000 7. 6 3 900 , 700 3 8 8. 8 3 3,000 5 6,000 3 4 9. 9 3 4,000 5 6,000 3 6 5 3 4 5 20, so 5 3 4,000 5 20,000 Complete the pattern. 1. 9 3 2 5 18 2. 8 3 4 5 32 3 20 5 8 3 40 5 8 3 400 5 180 1,800 9 3 200 5 18,000 9 3 2,000 5 9 3. 6 3 6 5 36 360 6 3 60 5 3,600 6 3 600 5 36,000 6 3 6,000 5 Find the product. 5. 7 3 300 5 7 3 5 5 © Houghton Mifflin Harcourt Publishing Company 4_MNLEAN343078_C02R03.indd 9 4. 4 3 7 5 28 3 70 5 800 3 9 , 3,000 3 3 Explain how you found the answer in Exercise 10. 11. 280 2,800 4 3 700 5 28,000 4 3 7,000 5 4 10. Possible answer: I used the basic fact 8 3 9 5 72 and a pattern to find 800 3 9 5 7,200. I used the basic fact 3 3 3 5 9 and a pattern to find 3,000 3 3 5 9,000. Then I compared 7,200 and 9,000. Since 9,000 has the greater digit in the thousands place, 7,200 is less than 9,000. 3 21 2,100 Chapter Resources 320 3,200 32,000 8 3 4,000 5 hundreds hundreds 6. 5 3 8,000 5 5 3 5 5 2-9 8 thousands 40 thousands 40,000 Reteach Chapter Resources © Houghton Mifflin Harcourt Publishing Company 2/12/14 2:22 PM 4_MNLEAN343078_C02E03.indd 10 2-10 Enrich 2/12/14 2:21 PM Other Ways A Use a number line. Example A Lead a discussion with students about why they would use multiplication to solve this problem. I am combining the number of sleds rented Bob’s Sled Shop rents 4,000 sleds each month. How many sleds does the store rent in 6 months? each month. When I combine equal groups, I can multiply to find the total. Other Ways • How do the numbers on the number lines change from one number line to the next? Find 6 × 4,000. Multiplication can be thought of as repeated addition. Draw jumps to show the product. 14 14 14 14 14 Possible answer: each number line is 10 times greater than the number line above it. 14 6 × 4 = 24 0 4 8 12 16 20 24 0 40 80 120 160 200 240 0 400 800 1,200 1,600 2,000 2,400 ← basic fact • How do the products 24, 240, 2,400, and 24,000 change from one product to the next? Possible answer: each product is 10 times 6 × 40 = 240 0 4,000 8,000 12,000 16,000 20,000 greater than the product before it. 24,000 • How does the last number line show 6 × 4,000? Possible answer: the number line shows 6 × 400 = 2,400 6 jumps of 4,000. 6 × 4,000 = 24,000 Example B • Explain the pattern that you see. Possible B Use patterns. Basic fact with a zero: Basic fact: 3 × 7 = 21 ← basic fact 3 × 70 = 210 ← basic fact 8 × 5 = 40 8 × 50 = 400 2,100 3 × 700 = ___ 4,000 8 × 500 = ___ 21,000 3 × 7,000 = ___ 40,000 8 × 5,000 = ___ t How does the number of zeros in the product of 8 and 5,000 compare to the number of zeros in the factors? Explain. Possible explanation: there are 4 zeros in the product and only 3 zeros in the factors because there is a zero in the basic fact, 8 × 5 = 40. Possible description: as the number of zeros in a factor increases, the number of zeros in the product increases. Math Talk MATHEMATICAL PRACTICES 5 Use Patterns to tell how the number of zeros in the factors and products changes in Example B. 76 Advanced Learners Logical Individual © Houghton Mifflin Harcourt Publishing Companyt*NBHF$SFEJUTUS ª"SJFM4LFMMFZ#MFOE*NBHFT$PSCJT 24,000 So, Bob’s Sled Shop rents __ sleds in 6 months. explanation: when you increase the number of zeros in one of the factors, there will be an equal increase in the number of zeros in the product. Math Talk Use Math Talk to help students recognize patterns in the number of zeros in factors and products. • As the number of zeros in a factor changes each time, how does the size of the factor change? Possible answer: It becomes 10 times greater. MP8 Look for and express regularity in repeated reasoning. • When a tens, hundreds, or thousands number is multiplied by a one-digit number, how does the number of zeros in the product compare to the number of zeros in the tens, hundreds, or thousands number? Possible answer: There will be as many zeros in the product as in the tens, hundreds, or thousands number. There will be an additional zero if the basic fact has a zero. • What is the Associative Property of Multiplication? The property that says you may group factors anyway you like and the product will remain the same. Show students this problem: 9 × 80. • How can you write 80 as a product of a number and 10? 80 = 8 × 10 This means we can rewrite the problem as 9 × (8 × 10) or, using the Associative Property of Multiplication, (9 × 8) × 10. • Which expression shows a basic fact? (9 × 8) • Rewrite the expression using the product from the basic fact. 72 × 10 • So, what is the product of 9 × 80? the same as the product COMMON ERRORS Error Students may not include the correct number of zeros in the product. Example 8 × 5,000 = 4,000 Springboard to Learning Have the students write the basic fact first and then circle it before they write the zeros. 8 × 5,000 = 40,000 of 72 × 10, or 720 Lesson 2.3 76 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A Name 3 EXPLAIN Share Share and and Show Show MATH BOARD Math Talk 1. Use the drawing to find 2 × 500. Share and Show MATH T Hands On BOARD Math Talk Complete the pattern. 2. 3 × 8 = 24 • How can you restate 2 ∙ 500 using place value? 2 × 5 hundreds • How can you use place value to write the product of 2 ∙ 5 hundreds in standard form? 10 hundreds can be renamed as 1 thousand, 240 3 × 80 = __ 120 6 × 20 = __ 200 4 × 50 = __ 2,400 3 × 800 = __ 1,200 6 × 200 = __ 2,000 4 × 500 = __ 24,000 3 × 8,000 = __ 12,000 6 × 2,000 = __ 20,000 4 × 5,000 = __ 5 5. 6 × 500 = 6 × __ hundreds Then a student misses the checked exercises Differentiate Instruction with • Reteach 2.3 • Personal Math Trainer 4.NBT.B.5 • RtI Tier 1 Activity (online) On Your Own If students complete the checked exercises correctly, they may continue with the remaining exercises. MP2 Reason abstractly and quantitatively. • How can you use inverse operations to find the missing factor for Exercise 11? I can think 56 divided by 7 equals what number? Since 7 × 8 = 56, then 56 ÷ 7 = 8. So, 7 × 8,000 = 56,000. MP5 Use appropriate tools strategically. Exercise 13 provides students an opportunity to communicate verbally, not just demonstrate, how the product of a basic fact that ends in zero affects the number of zeros in a product. 77 Chapter 2 5 6. 9 × 5,000 = 9 × __ thousands 30 = __ hundreds 45 = __ thousands 3,000 = __ 45,000 = __ On On Your Your Own Own Find the product. 42,000 7. 7 × 6,000 = __ MATHEMATICAL PRACTICE © Houghton Mifflin Harcourt Publishing Company If If Rt II Rt © Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©Ariel Skelley/Blend Images/Corbis Use the checked exercises for Quick Check. 3 3 2 2 1 1 20 4. 4 × 5 = __ 3. 6 × 2 = 12 Find the product. which can be written in standard form. Quick Check Check Quick Possible explanation: I can think of 2 × 500 as 2 times 5 hundreds, which equals 10 hundreds. 10 hundreds equal 1,000. 1,000 2 × 500 = ___ Use Math Talk to focus on students’ understanding of how to use place value to find the product. MATHEMATICAL PRACTICES 7 Look for Structure to tell how you would use place value to find 2 × 500. 2 320 8. 4 × 80 = __ 1,500 9. 3 × 500 = __ Use Reasoning Algebra Find the missing factor. 10. 7 × 9,000 = 63,000 _ 8,000 = 56,000 11. 7 × _ 400 = 3,200 12. 8 × _ 13. MATHEMATICAL 5 Communicate How does the number of zeros in the product PRACTICE of 8 and 5,000 compare to the number of zeros in the factors? Explain. Possible explanation: there are 4 zeros in the product and only 3 zeros in the factors because there is a zero in the basic fact, 8 × 5 = 40. Chapter 2 • Lesson 3 4_MNLESE342194_C02L03.indd 77 77 2/26/14 12:12 PM MATHEMATICAL PRACTICES ANALYZEt-00,'034536$563&t13&$*4*0/ 4 ELABORATE Unlock Unlock the the Problem Problem 14. SMARTER Joe’s Fun and Sun rents beach chairs. The store rented 300 beach chairs each month in April and in May. The store rented 600 beach chairs each month from June through September. How many beach chairs did the store rent during the 6 months? Unlock the Problem MATHEMATICAL PRACTICES a. What do you need to know? the total number of beach chairs rented during SMARTER the 6 months Have students read Exercise 14 and discuss the important information. Students can make a list of the steps necessary to solve this multistep problem. b. How will you find the number of beach chairs? I will multiply 2 times 300 and 4 times 600. Then I will add the products. c. Show the steps you use to solve the problem. d. Complete the sentences. 600 For April and May, a total of __ beach chairs were rented. 2 × 300 = 600 4 × 600 = 2,400 600 + 2,400 = 3,000 Math on the Spot Video Tutor For June through September, a total of Use this video to help students model and solve this type of Think Smarter problem. 2,400 WRITE Math twere Showrented. Your Work __ beach chairs 3,000 Joe’s Fun and Sun rented __ beach chairs during the 6 months. DEEPER Mariah makes bead necklaces. Beads are packaged in bags of 50 and bags of 200. Mariah bought 4 bags of 50 beads and 3 bags of 200 beads. How many beads did Mariah buy? 16. SMARTER 800 beads SMARTER Carmen has three books of 20 stamps and five books of 10 stamps. How many stamps does Carmen have? Complete the equation using the numbers on the tiles. 3 5 110 50 60 100 © Houghton Mifflin Harcourt Publishing Company 15. Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com. 3 5 110 _ × 20 + _ × 10 = _ 78 Exercise 16 assesses students' ability to use place value as well as their knowledge of the order of operations. If students choose the correct numbers as "3" and "5" but get an answer of "650," they are working out the problem from left to right. Students will need to review the order of operations. 5 EVALUATE Formative Assessment Essential Question DIFFERENTIATED INSTRUCTION D INDEPENDENT ACTIVITIES Differentiated Centers Kit Literature Putting the World on a Page Students read about how Julia uses multiplication to decide how to arrange the stamps in a collection. Games Triangle Products (BNFT gameboard. Students practice multiplying by tens to win spaces on the Using the Language Objective Reflect Have students complete the sentence frame, Place value helps you to multiply tens, hundreds, and thousands by __________, to answer the Essential Question. How does understanding place value help you multiply tens, hundreds, and thousands? Possible answer: I can rewrite the problem using place value. For example, to find 4 × 300, I can rewrite it as 4 × 3 hundreds. Then I can solve 4 × 3 hundreds = 12 hundreds, using the basic fact 4 × 3. Then I rename 12 hundreds as 1,200 by writing 2 zeros after the basic fact. Math Journal WRITE Math Explain how finding 7 × 20 is similar to finding 7 × 2,000. Then find each product. Lesson 2.3 78 Practice and Homework Name Multiply Tens, Hundreds, and Thousands Lesson 2.3 COMMON CORE STANDARD—4.NBT.B.5 Use place value understanding and properties of operations to perform multi-digit arithmetic. Find the product. Practice and Homework 28,000 1. 4 × 7,000 = ___ 540 2. 9 × 60 = ___ Think: 4 × 7 = 28 So, 4 × 7,000 = 28,000 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 Math section to determine student’s understanding of content for this lesson. Encourage students to use their Math Journals to record their answers. 1,600 3. 8 × 200 = ___ 30,000 4. 5 × 6,000 = ___ 5,600 5. 7 × 800 = ___ 720 6. 8 × 90 = ___ 18,000 7. 6 × 3,000 = ___ 24,000 8. 3 × 8,000 = ___ 2,500 9. 5 × 500 = ___ 36,000 10. 9 × 4,000 = ___ Problem Problem Solving Solving 11. A bank teller has 7 rolls of coins. Each roll has 40 coins. How many coins does the bank teller have? 12. Theo buys 5 packages of paper. There are 500 sheets of paper in each package. How many sheets of paper does Theo buy? © Houghton Mifflin Harcourt Publishing Company 280 coins 13. 2,500 sheets Math Explain how finding 7 × 20 is similar to WRITE finding 7 × 2,000. Then find each product. Check students’ work. Chapter 2 79 COMMON COMM ON CORE CORE PROFESSIONAL DEVELOPMENT 79 Math Talk in Action Teacher: Explain how you found the answer to Exercise 10. Mattie: I found the answer a different way. I thought of 9 3 4,000 as 9 3 4 thousands. Then I found 4 3 9 5 36, so the answer is 36 thousands, or 36,000. Eli: I made a quick picture of the problem. I drew 9 rows of 4 thousands blocks. That was 36 thousands blocks, or 36,000. Teacher: How did you know what to draw? Teacher: Did anyone use a number line to find the product? Eli: 9 3 4,000 means 9 groups of 4,000. Roland: Teacher: Did anyone use a different strategy? Jessika: I looked for a pattern. I knew 4 3 9 5 36, so 4 3 90 5 360, 4 3 900 5 3,600, and 4 3 9,000 5 36,000. I did. I thought of the problem as repeated addition. So, I made a number line that started at 0. I marked 4,000; 8,000; 12,000; and so on. It increased by 4,000 each time. Then I made 9 jumps of 4,000 and ended on 36,000. Teacher: You all used good strategies to find the product! Well done. Teacher: Explain the pattern you used. Jessika: Each time I wrote a zero in a factor, I wrote a zero in the product. Chapter 2 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=B Lesson Check (4.NBT.B.5) 1. A plane is traveling at a speed of 400 miles per hour. How far will the plane travel in 5 hours? 2,000 miles 2. One week, a clothing factory made 2,000 shirts in each of 6 different colors. How many shirts did the factory make in all? 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. 12,000 shirts Spiral Review (4.OA.A.1, 4.OA.A.2, 4.OA.A.3, 4.NBT.A.2) 3. Write a comparison sentence to represent this equation. 6 × 7 = 42 Possible answer: 42 is 6 times as 4. The population of Middleton is six thousand, fifty-four people. Write this number in standard form. 6,054 many as 7. voted for Carl Green and 67,952 people voted for Maria Lewis. By how many votes did Carl Green win the election? 17,082 votes 6. Meredith picked 4 times as many green peppers as red peppers. If she picked a total of 20 peppers, how many green peppers did she pick? 16 green peppers © Houghton Mifflin Harcourt Publishing Company 5. In an election for mayor, 85,034 people FOR MORE PRACTICE GO TO THE 80 4_MNLESE342194_C02P03.indd 80 Personal Math Trainer 10/7/14 7:11 PM Lesson 2.3 80