Unit 5. Landmarks and Large Numbers. How Much Is 1,000? Common Core

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1 Unit 5 Landmarks and Large Numbers Common Core Mathematical Practices (MP) Domains Number and Operations in Base Ten (NBT) Measurement and Data (MD) INVESTIG ATION 1 How Much Is 1,000? Day Session Common Core Adaptation Common Core Standards How Much Is 1,000? MP7.NBT.1,.NBT.2,.NBT Finding Numbers to 1,000 MP5, MP7.NBT.2,.NBT. DISCUSSION Finding Numbers Teaching Note Greater Than, Less Than Signs Reintroduce greater than (>) and less than (<) signs. After students share how they located 51 on the 1,000 chart ask: Is 51 greater or less than 500? Is it greater or less than 600? Write 51 > 500 and 51 < 600 on the board. Throughout the unit, continue to use greater than and less than signs to compare numbers Changing Places MP5, MP7.NBT.2,.NBT. TEN-MINUTE MATH Have students also write the number in expanded form after Practicing Place Value they have practiced writing or saying the number. ACTIVITY Introducing Practicing Place Value Teaching Note Expanded Form Include expanded form in this activity. Explain that when students use expanded form, they will break a number apart by place. Write 35 = under How Many Miles to 1,000? MP5, MP7.NBT.2,.NBT.,.MD.2 TEN-MINUTE MATH Have students also write the number in expanded form after Practicing Place Value they have practiced writing or saying the number A Place-Value Understanding Assessment: Numbers to 1, Adding and Subtracting to 1,000 See p. CC30. MP5, MP7.NBT.2,.NBT.3 MP5, MP7.NBT.2,.NBT.,.MD.2 MP5.NBT.2,.NBT.,.MD.2 CC26 UNIT 5 Landmarks and Large Numbers

2 INVESTIG ATION 2 Adding It Up Day Session Common Core Adaptation Common Core Standards Solving Addition Problems TEN-MINUTE MATH Practicing Place Value Have students also write the number in expanded form after they have practiced writing or saying the number. MP3, MP6, MP8.NBT.2,.NBT.,.MD Addition Strategies MP3, MP6, MP8.NBT.,.MD Starter Problems MP3, MP6, MP8.NBT.,.MD Studying the U.S. Algorithm for Addition TEN-MINUTE MATH Practicing Place Value Have students also write the number in expanded form after they have practiced writing or saying the number. MP6, MP8.NBT.2,.NBT Close to 1,000 MP2.NBT.2,.NBT. TEN-MINUTE MATH Have students also write the number in expanded form after Practicing Place Value they have practiced writing or saying the number. SESSION FOLLOW-UP Daily Practice and Homework Assessment: Solving an Addition Problem in Two Ways Daily Practice: In addition to Student Activity Book page 32, students complete Student Activity Book page 3 or C20 (School Enrollments) for reinforcement of the content of this unit. MP2, MP6.NBT.2,.NBT. Instructional Plan CC27

3 INVESTIG ATION 3 Working with Numbers to 10,000 Day Session Common Core Adaptation Common Core Standards Making a 10,000 Chart MP1, MP7.NBT.1,.NBT.2,.NBT How Much Is 10,000? MP1.NBT.1,.NBT.2,.NBT Working with the 10,000 Chart Thousands of Miles MP1 TEN-MINUTE MATH Practicing Place Value Adding Numbers in the Thousands TEN-MINUTE MATH Practicing Place Value Have students also write the number in expanded form after they have practiced writing or saying the number. Have students also write the number in expanded form after they have practiced writing or saying the number. MP1.NBT.2,.NBT..NBT.2,.NBT.,.MD.2 MP1.NBT.2,.NBT.,.MD A Larger Place Values See p. CC35. MP1.NBT.1,.NBT.2,.NBT.3 CC28 UNIT 5 Landmarks and Large Numbers

4 INVESTIG ATION Subtraction Day Session Common Core Adaptation Common Core Standards 20.1 Representing Subtraction Problems MP.NBT.2,.NBT Strategies for Subtraction MP.NBT.2,.NBT. Session Follow-up Daily Practice: In addition to Student Activity Book page 58, Daily Practice and Homework students complete Student Activity Book page 60 or C2 (Areas of Countries) for reinforcement of the content of this unit Assessment: Numbers to 10,000 TEN-MINUTE MATH Practicing Place Value 23.A Studying the U.S. Algorithm for Subtraction Have students also write the number in expanded form after they have practiced writing or saying the number. See p. CC0. MP.NBT.2,.NBT. MP8.NBT.2,.NBT. 2. Do I Add or Subtract? MP1.NBT.2,.NBT. TEN-MINUTE MATH Have students also write the number in expanded form after Practicing Place Value they have practiced writing or saying the number Solving Addition and Subtraction Problems TEN-MINUTE MATH Practicing Place Value Session Follow-up Daily Practice and Homework 26.6 Solving Addition and Subtraction Problems, continued Have students also write the number in expanded form after they have practiced writing or saying the number. Daily Practice: In addition to Student Activity Book page 69, students complete Student Activity Book page 70B or C28 (Subtraction Practice) for reinforcement of the content of this unit. MP1.NBT.2,.NBT.,.MD.2 MP1.NBT.2,.NBT.,.MD End-of-Unit Assessment MP1, MP2, MP8.NBT. Instructional Plan CC29

5 s e s s i o n 1. 5 A Place-Value Understanding Math Focus Points Rounding numbers to the nearest ten and the nearest hundred Writing numbers to 1,000 in expanded form Using >, =, and < to compare numbers to 1,000 Today s Plan activity Rounding Numbers ACTIVITY Expanded Form Activity Comparing Numbers Using >, =, and < Session Follow-Up Daily Practice 20 Min Groups 20 Min Class 20 Min Pairs Vocabulary expanded form less than greater than Materials Students 1,000 books (from Session 1.1) Student Activity Book, p. 13A or C17, Using Place Value Make copies. (as needed) Students 1,000 books Student Activity Book, p. 13B or C18, Comparing Numbers Make copies. (as needed) Students 1,000 books Student Activity Book, p. 13C or C19, River Lengths Make copies. (as needed) Student Math Handbook, p. 6 Ten-Minute Math Practicing Place Value Say six hundred eighty-three and have students practice writing the number. Make sure that all students can read, write, and say this number correctly. Have students write 683 in expanded form. Ask students to solve these problems mentally, if possible: What is ? ? ? ? ? Write each answer on the board. Have students compare each sum or difference with 683. Ask students: Which places have the same digits? Which do not? Why? If time permits, pose additional similar problems using these numbers: 318 and 857. CC30 Investigation 1 How Much Is 1,000?

6 1 Activity 2 Activity 3 Activity Session Follow-Up A C T I V I T Y Rounding Numbers On the board, write the following three numbers: Min groups One of the largest animals ever found was a blue whale that weighed 183 tons. Is 183 tons closer to 100 tons or to 200 tons? Talk in your group to figure this out. Then convince the rest of us that your answer is right. Students might say: 183 is closer to 200. Here, look at my 1,000 book. 183 is on the page that goes from 101 to 200. It s pretty close to 200. We made a number line. First we put an X on 150 because that s halfway between 100 and 200. Then we could see that 183 is way past that. So, it s closer to We say that 183 rounded to the nearest hundred is 200. When you round a number, you get another number that can be used to tell about how big the original number is. The blue whale weighed about 200 tons. Now I want you to work in your groups and figure out which two tens 183 is between. Which ten is it closer to? Ask students to share their reasoning. We say that 183 rounded to the nearest ten is 180. Explain that numbers halfway between two tens or two hundreds are rounded up. Provide students a variety of numbers through 1,000 (such as 85, 732, 9, 223, 785, 127, 288, 369, 83, 958) and have them round the numbers to the nearest ten or the nearest hundred. Session 1.5A Place-Value Understanding CC31

7 1 Activity 2 Activity 3 Activity Session Follow-Up Name Date Landmarks and Large Numbers Ongoing Assessment: Observing Students at Work Using Place Value In Problems 1, round each number to the nearest ten Students round numbers to the nearest ten and the nearest hundred. Can students round 2- or 3-digit numbers to the nearest In Problems 5 8, round each number to the nearest hundred ten or nearest hundred? Do they remember to round up for halfway numbers? 9. The base of the Statue of Liberty is 15 feet tall. Is this number closer to 100 or 200? Explain. In Problems 10 13, write each number in expanded form Ac tivit y Pearson Education Session 1.5A Unit 5 13A Student Activity Book, Unit 5, p. 13A; Resource Masters, C17 INV12_SE0_U5.indd 1 20 Min Expanded Form //11 class Write 72 on the board. 1:53 PM How many hundreds are in this number? How many tens? How many ones? You can use your 1,000 books for help. Record students responses on the board. Here s a way to show the number of hundreds, tens, and ones. It s called expanded form. It clearly shows the value of each digit in 72. Write 72 = on the board hundreds, 2 tens, ones 72 = Discuss several other examples, such as 517, 8, 602, and 390. Then have students complete Student Activity Book page 13A or C17. CC32 Investigation 1 How Much Is 1,000? INV12_TE0_U05_S1.5A.indd 32 6/16/11 9:13 AM

8 1 Activity 2 Activity 3 Activity Session Follow-Up Name Date Landmarks and Large Numbers Ac tivit y 20 Min PAIRS Comparing Numbers Using >, =, and < Write 35 and 61 on the board. Comparing Numbers 1. How many hundreds are in 755? How many hundreds are in 680? Which number is greater, 755 or 680? 2. How many hundreds are in 266? Students might say: We figured 35 has 3 hundreds, and 61 has 6 hundreds, so 61 is way bigger because it has more hundreds. We looked in our 1,000 books. 61 is a lot closer to 1,000, which is the biggest number in the book. So 61 has got to be greater. How many hundreds are in 281? How many tens are in 266? How many tens are in 281? Which number is greater, 266 or 281? In Problems 3 8, compare the numbers. Write <, >, or = Abdul has 30 coins, and Luke has 03 coins. Who has more coins? Pearson Education Which number is greater? Talk with a partner to figure this out. Then explain your thinking. 13B Unit 5 Session 1.5A Student Activity Book, Unit 5, p. 13B; Resource Masters, C18 INV12_SE0_U5.indd 2 6/1/11 9:15 AM Model writing a comparison using both words and the < symbol. Explain that the symbol < means is less than. Then discuss how to write the comparison in words and with the symbol. Explain that this symbol > means is greater than. 35 is less than is greater than < 61 > 35 What if both numbers have the same number of hundreds? How can you compare 781 and 79? Students might say: You can t tell from the hundreds. So move to the tens and compare those. 8 tens is more than tens, so 781 is greater than 79. Have students complete Student Activity Book page 13B or C18. Session 1.5A Place-Value Understanding CC33 INV12_TE0_U05_S1.5A.indd 33 6/1/11 2:05 PM

9 Pearson Education INV12_SE0_U5.indd 3 6/1/11 9:16 AM 1 Activity 2 Activity 3 Activity Session Follow-Up Name Date Landmarks and Large Numbers Daily Practice River Lengths Use the data about U.S. rivers. Pecos River 926 miles long Yellowstone River 692 miles long 1. Write the length of each river in expanded form. Pecos River: Yellowstone River: 2. Round the length of each river to the nearest hundred. Pecos River: Yellowstone River: 3. Round the length of each river to the nearest ten. Pecos River: note Students use placevalue understanding to write numbers in expanded form, round numbers, and compare numbers through 1,000. differentiation: Supporting the Range of Learners Some students may confuse the < and > symbols. Point out that the pointy, smaller part of the arrow points to the smaller number. Students who can easily compare numbers can be challenged to order lists of 3-digit numbers. Yellowstone River:. Compare the lengths of the rivers. Write <, >, or = Session 1.5A Unit 5 Student Activity Book, Unit 5, p. 13C; Resource Masters, C19 13C S E S S I O N F O L L O W - U P Daily Practice Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page 13C or C19. Student Math Handbook: Students and families may use Student Math Handbook page 6 for reference and review. See pages in the back of Unit 5. CC3 Investigation 1 How Much Is 1,000?

10 s e s s i o n 3. 6 A Larger Place Values Math Focus Points Understanding place-value concepts to 1,000,000 Using >, =, and < to compare numbers to 1,000,000 Writing numbers to 1,000,000 in expanded form Rounding numbers to 1,000,000 Today s Plan Discussion Place Value to 1,000, Min Groups Materials Chart paper (Prepare the place-value chart pictured on the next page.) activity Expanded Form 20 Min Class Activity Rounding Large Numbers 25 Min Pairs Session Follow-Up Daily Practice Student Activity Book, p. 51A or C21, Place Value to 1,000,000 Make copies. (as needed) Place-value chart (from discussion) Student Activity Book, p. 51B or C22, Rounding Large Numbers Make copies. (as needed) 10,000 chart (from Session 3.1) Student Activity Book, p. 51C or C23, Concert Tickets Make copies. (as needed) Student Math Handbook, pp. 6 7 Ten-Minute Math Practicing Place Value Say five thousand two hundred eleven and have students practice writing the number. Make sure all students can read, write, and say this number correctly. Have students write 5,211 in expanded form. Ask students to solve these problems mentally, if possible: What is 5, ? 5, ? 5,211 10? 5, ? 5,211 1,000? Write each answer on the board. Have students compare each sum or difference to 5,211. Ask students: Which places have the same digits? Which do not? Why? If time permits, pose additional similar problems using these numbers: 2,17 and 6,831. Session 3.6A Larger Place Values CC35

11 1 Discussion 2 Activity 3 Activity Session Follow-Up Differentiation 1 English Language Learners Some students might come from a country in which periods, not commas, are used to separate groups of three digits in large numbers. In these countries, commas are used in decimals instead of periods. D i s c u s s i o n Place Value to 1,000,000 Math Focus Points for Discussion 15 Min Understanding place-value concepts through 1,000,000 Groups On the board, write 566,11. Recently this number was the population of Portland, Oregon. Does anyone know how to read such a large number? Talk it over in your groups. Give students a chance to consider the number and share their ideas. Then display the place-value chart you prepared for this session. Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones A place-value chart can help you understand and read large numbers. This number is read five hundred sixty-six thousand, one hundred forty-one. In large numbers, commas are used to separate the digits into groups of three, starting at the right. 1 Two of the digits in this number are 6s. Do both 6s have the same value? Students might say: The 6 in the ten thousands place means 60,000, but the 6 in the thousands place means only 6,000. The same digit in different places can never stand for the same amount. The value of the digit on the left is always 10 times the value of the digit on the right. CC36 Investigation 3 Working with Numbers to 10,000

12 1 Discussion 2 Activity 3 Activity Session Follow-Up Write 560,332 in the place-value chart. Name Date Landmarks and Large Numbers Recently the population of Oklahoma City, Oklahoma, was five hundred sixty thousand, three hundred thirty-two. Is its population greater than or less than the population of Portland? How can the place-value chart help you figure this out? Place Value to 1,000,000 Use the place-value chart to help you complete the problems. Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones In Problems 1, write each number in expanded form ,956 Students might say: Portland is bigger. I could tell from the chart that both populations have the same number of hundred thousands and ten thousands. But Portland has more thousands. 2. 7, , , Do all 6-digit numbers have 6 addends in their expanded form? Explain. Pearson Education 6. In the number at the right, circle the that has 10 times the value of the underlined. Ask a volunteer to write a comparison statement about the two populations using the < or > symbol., In Problems 7 and 8, write <, >, or =. 7. 2,551 Session 3.6A 0, ,726 1,000,000 Unit 5 51A Student Activity Book, Unit 5, p. 51A; Resource Masters, C21 INV12_SE0_U5.indd 1 5//11 1:5 PM Save the place-value chart for use during the next activity. Ac tivit y Expanded Form 20 Min class Direct the class attention to the place-value chart. Let s look at the first number, 566,11. How many hundred thousands are in this number? How many ten thousands? Thousands? Hundreds? Tens? Ones? We can show this using expanded form. Write the expanded form for 566, ,11 = 500, , , Ask students to write the expanded form for the second number in the chart, 560,332. Then have students complete Student Activity Book page 51A or C21. Session 3.6A Larger Place Values CC37 INV12_TE0_U05_S3.6A.indd 37 6/3/11 1: PM

13 1 Discussion 2 Activity 3 Activity Session Follow-Up Ongoing Assessment: Observing Students at Work Students write the expanded form of a large number. Do students write the correct value for each digit? Do students skip an addend when the digit is 0? differentiation: Supporting the Range of Learners Some students may lose track of which digit has which value. Provide these students with additional place-value charts so they can record each number before they write its expanded form. A c t i v i t y Rounding Large Numbers 25 Min Review rounding numbers to the nearest ten and the nearest hundred. Then write 6,271 on the board. PAirs How would you round this number to the nearest thousand? Talk with your partner and then explain your reasoning. Students might say: It rounds to 6,000. We pictured where the number would go on the 10,000 chart and we figured it s closer to 6,000 than to 7,000. Next, write 258,91 on the board. How would you round this number to the nearest ten thousand? It s too big for the 10,000 chart. Can you and your partner figure out a way to round any large number, even if it doesn t fit on the 10,000 chart? Students might say: It rounds to 260,000. Check the digit to the right of where you re rounding. It s an 8, so that means the number is closer to 260,000 than to 250,000. CC38 Investigation 3 Working with Numbers to 10,000

14 1 Discussion 2 Activity 3 Activity Session Follow-Up Ask students to round 96,225 to the nearest ten thousand. In this problem they should notice that when they round the 9 up to the next ten thousand, the result is 100,000. Have students complete Student Activity Book page 51B or C22. Name Date Landmarks and Large Numbers Rounding Large Numbers In Problems 1 and 2, round each number to the nearest thousand. 2. 8, ,716 In Problems 3 and, round each number to the nearest ten thousand.. 97, ,07 In Problems 5 and 6, round each number to the nearest hundred thousand. Daily Practice Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page 51C or C23. Student Math Handbook: Students and families may use Student Math Handbook pages 6 and 7 for reference and review. See pages in the back of Unit , , Round each population to the nearest ten thousand. City Population Austin, TX 786,382 Cleveland, OH 31,363 Oakland, CA 09,18 Nearest Ten Thousand 8. Suppose a number is rounded to the nearest hundred thousand. What is a number less than 700,000 that rounds to 700,000? What is a number greater than 700,000 that rounds to 700,000? 51B Unit 5 Pearson Education Session Follow-Up Session 3.6A S tudent Activity Book, Unit 5, p. 51B; Resource Masters, C22 INV12_SE0_U5.indd 2 6/2/11 :08 PM Name Date Landmarks and Large Numbers Daily Practice Concert Tickets Use the data about the number of concert tickets sold. Holiday Rock Concert 13,125 tickets Summer Jazz Concert 18,832 tickets note Students use placevalue understanding to write numbers in expanded form, round numbers, and compare numbers through 1,000, Write the number of tickets sold in expanded form. Holiday Rock Concert: Summer Jazz Concert: 2. Round the number of tickets sold to the nearest ten thousand. Holiday Rock Concert: Summer Jazz Concert: 3. Round the number of tickets sold to the nearest hundred thousand. Holiday Rock Concert: Summer Jazz Concert:. Compare the number of tickets sold. Write <, >, or =. 13,125 18,832 Pearson Education Session 3.6A Unit 5 51C S tudent Activity Book, Unit 5, p. 51C; Resource Masters, C23 INV12_SE0_U5.indd 3 Session 3.6A Larger Place Values INV12_TE0_U05_S3.6A.indd 39 5//11 1:5 PM CC39 6/3/11 1:6 PM

15 s e s s i o n. A Studying the U.S. Algorithm for Subtraction Math Focus Points Understanding the meaning of the steps and notation of the U.S. algorithm for subtraction Using clear and concise notation for recording addition and subtraction strategies Today s Plan activity Examining the U.S. Algorithm for Subtraction activity The U.S. Algorithm for Subtraction Discussion Solving Problems with the U.S. Algorithm Session Follow-Up Daily Practice 30 Min Class 20 Min Individuals 10 Min Class Materials Student Activity Book, pp. 62A 62B or C25 C26, The U.S. Algorithm Make copies. (as needed) Students completed copies of Student Activity Book, pp. 62A 62B or C25 C26 (from Activity 2) Student Activity Book, p. 62D or C27, Using the U.S. Algorithm Make copies. (as needed) Ten-Minute Math Practicing Place Value Write 7,72 on the board and have students practice saying it. Make sure all students can read, write, and say this number correctly. Ask students to write this number in expanded form. Then ask students to solve these problems mentally, if possible. What is 7,72 50? 7,72 60? 7, ? 7, ? 7, ? Write each answer on the board. Have students compare each sum or difference with 7,72. Ask students: Which places have the same digits? Which do not? Why? CC0 Investigation Subtraction

16 1 Activity 2 Activity 3 Discussion Session Follow-Up A c t i v i t y Examining the U.S. Algorithm for Subtraction 30 Min Tell students that today they are going to examine a subtraction strategy and notation that a number of people use the U.S. algorithm for subtraction. 1 2 Write this problem on the board: class In this strategy, each place is subtracted separately. The people who invented this algorithm wanted to use only positive numbers. They figured out a way to rewrite the top number so they could subtract each place and get all positive numbers. Let s look at how we could rewrite the top number to solve this problem. When people use this U.S. algorithm, they start from the ones place. To help us understand this strategy better, first let s write each number in expanded form. Ask students how to write the numbers in expanded form, and write the following on the board: ( ) I wrote the bottom number in parentheses to show that we are subtracting all the parts. We start with the ones place, but we don t want to subtract 7 from 3. We want to change the way we re breaking up the number so that we get only positive differences. 3 We re going to break up the 80 and combine part of it with the 3. Write on the board next to the other problems, and ask students what number goes on the blank to still have the sum of ( ) Professional Development 1 Teacher Note: Why Study the U.S. Conventional Algorithms?, Curriculum Unit 5, p. 177 Math Note 2 The U.S. Algorithm The U.S. algorithm for subtraction, sometimes called borrowing or regrouping, is a procedure that was devised for compactness and efficiency. One advantage of the algorithm is that it requires only subtraction of single digits from numbers less than 20. However, its efficiency of steps and notation obscures the place value of the numbers. By examining the numbers in expanded form (e.g., ) and the equivalent notation that results from regrouping the numbers (e.g., ), students study the meaning of the algorithm. As with other strategies, studying this one and thinking through why these steps make sense allows students to deepen their knowledge about the operation of subtraction. Students who have developed good, efficient subtraction methods that they understand and can carry out easily (e.g., subtracting in parts, adding up, or subtracting back) may also benefit from practicing and becoming fluent in the U.S. algorithm. However, students are not expected to switch to using this algorithm. Continuing to use the methods they have developed will serve them well for their computation needs now and in the future. 3 Using Positive Numbers Only A student may say (or you may choose to bring up) that you can subtract 7 from 3 and get (negative four). Acknowledge that this is correct but that the U.S. algorithm for subtraction uses only positive numbers. Session.A Studying the U.S. Algorithm for Subtraction CC1

17 1 Activity 2 Activity 3 Discussion Session Follow-Up Give students a moment to discuss this, and call on students to explain their thinking. Write 13 on the blank. Rewrite the rest of the problem. Then ask students what 13 7 is and write 6 under ( ) ( ) 6 This is what is sometimes called borrowing or regrouping. We didn t have enough ones to subtract from to get a positive number, so we used one of the 8 tens and added it to 3. Then instead of , we had , which is the same amount that is just broken up differently. Ask students to subtract the tens and then the hundreds and record the results: ( ) If needed, spend a few more minutes discussing how breaking up 283 in a different way allowed subtraction by place with a positive result in each place. Then move on to examining the standard notation for this algorithm. When people use this algorithm they use a shorthand notation instead of writing out the new way to break the number apart like we did. Let s look at the notation ( ) ( ) = As you write the algorithm on the board, talk through the procedure. I don t want to subtract 7 from 3, so I take a ten from the tens place and give it to the ones place. I show this by crossing out the 8, making it a 7, and writing a 1 next to the 3 to make it minus 7 is 6. Then 7 minus 3 is ; that s 7 tens minus 3 tens. Then 2 minus 1 is 1. What do the 2 and the 1 mean? CC2 Investigation Subtraction

18 INV12_SE0_U5.indd 1 6/1/11 9:20 AM Pearson Education 1 Activity 2 Activity 3 Discussion Session Follow-Up Spend a few more minutes talking through this notation. Then work through another example in which both the tens and hundreds places must be changed ( ) ( ) ( ) = 277 Name Landmarks and Large Numbers Date The U.S. Algorithm (page 1 of 2) Use the U.S. algorithm for subtraction to solve the following problems. (Then solve the problems using a different strategy to make sure your final answer is correct.) In Problems 1 and 2, the steps of the U.S. algorithm are shown. Fill in the blanks with the correct numbers ( ) ( ) Give students a few minutes to discuss these steps, and then discuss the shorthand notation ( ) + + ( ) A Unit 5 Session.A Student Activity Book, Unit 5, p. 62A; Resource Masters, C25 Name Landmarks and Large Numbers Date The U.S. Algorithm (page 2 of 2) For Problems 3 and, use the U.S. algorithm for subtraction to solve each problem. Also, write the correct numbers in the blanks, showing how you broke apart the original numbers. A c t i v i t y The U.S. Algorithm for Subtraction 20 Min Individuals Students complete Student Activity Book pages 62A 62B or C25 C26. They practice the U.S. algorithm for subtraction by breaking apart the numbers by place and then regrouping in order to use only positive numbers. They also practice the shorthand notation for this algorithm. As students work, ask them to explain what they are doing for each step and why particularly when they are regrouping and when they are recording using shorthand notation. Pay attention to whether they are able to use the algorithm to solve Problems 2 and in which both the tens and hundreds places need to be changed. Pearson Education ( ) + + ( + + ) ( ) + + ( + + ) Session.A Unit 5 INV12_SE0_U5.indd 2 6/1/11 9:20 AM Student Activity Book, Unit 5, p. 62B; Resource Masters, C26 62B Ongoing Assessment: Observing Students at Work Do students understand how the numbers are broken apart to show regrouping? Can students use this algorithm to solve subtraction problems? Do they understand the shorthand notation of the algorithm? Session.A Studying the U.S. Algorithm for Subtraction CC3

19 Pearson Education 1 Activity 2 Activity 3 Discussion Session Follow-Up Name Date Landmarks and Large Numbers Daily Practice Using the U.S. Algorithm Use the U.S. algorithm for subtraction to solve each problem. Also, write the correct numbers in the blanks, showing how you broke apart the original numbers. note Students practice using the U.S. algorithm for subtraction by breaking apart the numbers by place and regrouping when necessary. They also practice the standard notation for this algorithm ( ) differentiation: Supporting the Range of Learners For students who have been using (or trying to use) this algorithm, these problems should provide support in helping them understand the mathematics behind the algorithm ( + + ) ( ) + + ( + + ) Students who have difficulty regrouping tens or hundreds from one place to another may benefit from practice breaking apart a number in different ways. For example, 863 can be broken apart as or or , and so on. Session.A Unit 5 INV12_SE0_U5.indd 6/1/11 9:21 AM Student Activity Book, Unit 5, p. 62D; Resource Masters, C27 62D Students who can explain and use the U.S. algorithm for the problems on these pages can be challenged to solve problems that include zeros in the first number (e.g., ). D i s c u s s i o n Solving Problems with the U.S. Algorithm Math Focus Points for Discussion 10 Min class Understanding the meaning of the steps and notation of the U.S. algorithm for subtraction Have students look at their completed Student Activity Book pages 62A 62B or C25 C26. What questions do you have after solving problems using the U.S. algorithm? How is this strategy different from other strategies we have discussed? How is it similar? Refer students to the charts of subtraction strategies posted in Session.3. S e s s i o n F o l l o w - U p Daily Practice Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page 62D or C27. CC Investigation Subtraction

20 Name Landmarks and Large Numbers Date Using Place Value In Problems 1, round each number to the nearest ten In Problems 5 8, round each number to the nearest hundred The base of the Statue of Liberty is 15 feet tall. Is this number closer to 100 or 200? Explain. In Problems 10 13, write each number in expanded form Unit 5 Session 1.5A C17 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

21 Name Landmarks and Large Numbers Date Comparing Numbers 1. How many hundreds are in 755? How many hundreds are in 680? Which number is greater, 755 or 680? 2. How many hundreds are in 266? How many hundreds are in 281? How many tens are in 266? How many tens are in 281? Which number is greater, 266 or 281? In Problems 3 8, compare the numbers. Write <, >, or = Abdul has 30 coins, and Luke has 03 coins. Who has more coins? Unit 5 Session 1.5A C18 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

22 Name Landmarks and Large Numbers River Lengths Use the data about U.S. rivers. Date Daily Practice note Students use place-value understanding to write numbers in expanded form, round numbers, and compare numbers through 1,000. Pecos River Yellowstone River 926 miles long 692 miles long 1. Write the length of each river in expanded form. Pecos River: Yellowstone River: 2. Round the length of each river to the nearest hundred. Pecos River: Yellowstone River: 3. Round the length of each river to the nearest ten. Pecos River: Yellowstone River:. Compare the lengths of the rivers. Write <, >, or = Unit 5 Session 1.5A C19 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

23 Name Landmarks and Large Numbers School Enrollments Use the data about school enrollments. Date Daily Practice note Students use place-value understanding to write numbers in expanded form, round numbers, and compare numbers through 1,000. Bryant School Holmes School 03 students 38 students 1. Write each school s enrollment in expanded form. Bryant School: Holmes School: 2. Round each school s enrollment to the nearest ten. Bryant School: Holmes School: 3. Round each school s enrollment to the nearest hundred. Bryant School: Holmes School:. Compare the school enrollments. Write <, >, or = Unit 5 Session 2.5 C20 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

24 Name Landmarks and Large Numbers Date Place Value to 1,000,000 Use the place-value chart to help you complete the problems. Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones In Problems 1, write each number in expanded form , , , , Do all 6-digit numbers have 6 addends in their expanded form? Explain. 6. In the number at the right, circle the that has 10 times the value, of the underlined. In Problems 7 and 8, write,,., or ,551 0, ,726 1,000,000 Unit 5 Session 3.6A C21 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

25 Name Landmarks and Large Numbers Date Rounding Large Numbers In Problems 1 and 2, round each number to the nearest thousand. 1. 2, ,325 In Problems 3 and, round each number to the nearest ten thousand ,07. 97,300 In Problems 5 and 6, round each number to the nearest hundred thousand , , Round each population to the nearest ten thousand. City Population Nearest Ten Thousand Austin, TX 786,382 Cleveland, OH 31,363 Oakland, CA 09,18 8. Suppose a number is rounded to the nearest hundred thousand. What is a number less than 700,000 that rounds to 700,000? What is a number greater than 700,000 that rounds to 700,000? Unit 5 Session 3.6A C22 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

26 Name Landmarks and Large Numbers Concert Tickets Use the data about the number of concert tickets sold. Date Daily Practice note Students use place-value understanding to write numbers in expanded form, round numbers, and compare numbers through 1,000,000. Holiday Rock Concert Summer Jazz Concert 13,125 tickets 18,832 tickets 1. Write the number of tickets sold in expanded form. Holiday Rock Concert: Summer Jazz Concert: 2. Round the number of tickets sold to the nearest ten thousand. Holiday Rock Concert: Summer Jazz Concert: 3. Round the number of tickets sold to the nearest hundred thousand. Holiday Rock Concert: Summer Jazz Concert:. Compare the number of tickets sold. Write <, >, or =. 13,125 18,832 Unit 5 Session 3.6A C23 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

27 Name Landmarks and Large Numbers Areas of Countries In Problems 1, use the data about the areas of some countries. Date Daily Practice note Students use place-value understanding to write numbers in expanded form and round numbers through 1,000,000. Austria Indonesia Chile 32,382 square miles 71,096 square miles 292,258 square miles 1. Write each country s area in expanded form. Austria: Indonesia: Chile: 2. Round Austria s area to the nearest ten thousand. 3. Round Indonesia s area to the nearest thousand.. Round Chile s area to the nearest hundred thousand. 5. Write three numbers that would round to 520,000 when rounded to the nearest ten thousand. Unit 5 Session.2 C2 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

28 Name Landmarks and Large Numbers Date The U.S. Algorithm (page 1 of 2) Use the U.S. algorithm for subtraction to solve the following problems. (Then solve the problems using a different strategy to make sure your final answer is correct.) In Problems 1 and 2, the steps of the U.S. algorithm are shown. Fill in the blanks with the correct numbers ( ) ( ) ( ) ( ) 1 1 Unit 5 Session.A C25 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

29 Name Landmarks and Large Numbers Date The U.S. Algorithm (page 2 of 2) For Problems 3 and, use the U.S. algorithm for subtraction to solve each problem. Also, write the correct numbers in the blanks, showing how you broke apart the original numbers ( ) ( 1 1 ) ( ) ( 1 1 ) Unit 5 Session.A C26 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

30 Name Landmarks and Large Numbers Date Daily Practice Using the U.S. Algorithm Use the U.S. algorithm for subtraction to solve each problem. Also, write the correct numbers in the blanks, showing how you broke apart the original numbers. note Students practice using the U.S. algorithm for subtraction by breaking apart the numbers by place and regrouping when necessary. They also practice the standard notation for this algorithm ( ) ( + + ) ( ) ( + + ) Unit 5 Session.A C27 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

31 Name Landmarks and Large Numbers Date Daily Practice Subtraction Practice Use the U.S. algorithm for subtraction to solve each problem. Also, write the correct numbers in the blanks, showing how you broke apart the original numbers. note Students practice using the U.S. algorithm for subtraction by breaking apart the numbers by place and regrouping when necessary. They also practice the standard notation for this algorithm ( ) ( + + ) ( ) ( + + ) Unit 5 Session.5 C28 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

32 Nombre Números de referencia y números grandes Fecha Usar el valor posicional En los Problemas 1 a, redondea cada número a la decena más cercana En los Problemas 5 a 8, redondea cada número a la centena más cercana La base de la Estatua de la Libertad mide 15 pies de alto. Se acerca este número más a 100 o a 200? Explica tu respuesta. En los Problemas 10 a 13, escribe cada número en forma desarrollada Unidad 5 Sesión 1.5A C17 Pearson Education, Inc., or its affiliates. All Rights Reserved.

33 Nombre Números de referencia y números grandes Fecha Comparar números 1. Cuántas centenas hay en 755? Cuántas centenas hay en 680? Qué número es mayor, 755 o 680? 2. Cuántas centenas hay en 266? Cuántas centenas hay en 281? Cuántas decenas hay en 266? Cuántas decenas hay en 281? Qué número es mayor, 266 o 281? En los Problemas 3 a 8, compara los números. Escribe <, > o = Abdul tiene 30 monedas y Luke tiene 03 monedas. Quién tiene más monedas? Unidad 5 Sesión 1.5A C18 Pearson Education, Inc., or its affiliates. All Rights Reserved.

34 Nombre Números de referencia y números grandes Fecha Práctica diaria Longitudes de ríos Usa los datos sobre ríos en los Estados Unidos. río Pecos río Yellowstone 926 millas de largo 692 millas de largo nota Los estudiantes usan la comprensión del valor posicional para escribir números en forma desarrollada, redondear números y comparar números hasta 1, Escribe la longitud de cada río en forma desarrollada. río Pecos: río Yellowstone: 2. Redondea la longitud de cada río a la centena más cercana. río Pecos: río Yellowstone: 3. Redondea la longitud de cada río a la decena más cercana. río Pecos: río Yellowstone:. Compara las longitudes de los ríos. Escribe <, > o = Unidad 5 Sesión 1.5A C19 Pearson Education, Inc., or its affiliates. All Rights Reserved.

35 Nombre Números de referencia y números grandes Fecha Práctica diaria Inscripciones escolares Usa los datos sobre las inscripciones escolares. Escuela Bryant Escuela Holmes 03 estudiantes 38 estudiantes nota Los estudiantes usan la comprensión del valor posicional para escribir números en forma desarrollada, redondear números y comparar números hasta 1, Escribe las inscripciones de cada escuela en forma desarrollada. Escuela Bryant: Escuela Holmes: 2. Redondea las inscripciones de cada escuela a la decena más cercana. Escuela Bryant: Escuela Holmes: 3. Redondea las inscripciones de cada escuela a la centena más cercana. Escuela Bryant: Escuela Holmes:. Compara las inscripciones escolares. Escribe <, > o = Unidad 5 Sesión 2.5 C20 Pearson Education, Inc., or its affiliates. All Rights Reserved.

36 Nombre Números de referencia y números grandes Fecha Valor posicional hasta 1,000,000 Usa la tabla de valor posicional como ayuda para completar los problemas. Millones Centenas de millar Decenas de millar Millares Centenas Decenas Unidades En los Problemas 1 a, escribe cada número en forma desarrollada , , , , Todos los números de 6 dígitos tienen 6 sumandos en su forma desarrollada? Explica tu respuesta. 6. En el número de la derecha, encierra en un círculo el que tiene 10 veces el valor del subrayado. En los Problemas 7 y 8, escribe <, > o =. 7. 2,551 0, ,726 1,000,000 Unidad 5 Sesión 3.6A C21 Pearson Education, Inc., or its affiliates. All Rights Reserved.

37 Nombre Números de referencia y números grandes Fecha Redondear números grandes En los Problemas 1 y 2, redondea cada número al millar más cercano. 1. 2, ,325 En los Problemas 3 y, redondea cada número a la decena de millar más cercana ,07. 97,300 En los Problemas 5 y 6, redondea cada número a la centena de millar más cercana , , Redondea cada población a la decena de millar más cercana. Ciudad Población Decena de millar más cercana Austin, TX 786,382 Cleveland, OH 31,363 Oakland, CA 09,18 8. Supón que un número se redondea a la centena de millar más cercana. Qué número menor que 700,000 se redondea a 700,000? Qué número mayor que 700,000 se redondea a 700,000? Unidad 5 Sesión 3.6A C22 Pearson Education, Inc., or its affiliates. All Rights Reserved.

38 Nombre Números de referencia y números grandes Fecha Práctica diaria Boletos para conciertos Usa los datos sobre el número de boletos vendidos para los conciertos. nota Los estudiantes usan la comprensión del valor posicional para escribir números en forma desarrollada, redondear números y comparar números hasta 1,000,000. Concierto de rock de Navidad Concierto de jazz de verano 13,125 boletos 18,832 boletos 1. Escribe el número de boletos vendidos en forma desarrollada. Concierto de rock de Navidad: Concierto de jazz de verano: 2. Redondea el número de boletos vendidos a la decena de millar más cercana. Concierto de rock de Navidad: Concierto de jazz de verano: 3. Redondea el número de boletos vendidos a la centena de millar más cercana. Concierto de rock de Navidad: Concierto de jazz de verano:. Compara el número de boletos vendidos. Escribe <, > o =. 13,125 18,832 Unidad 5 Sesión 3.6A C23 Pearson Education, Inc., or its affiliates. All Rights Reserved.

39 Nombre Números de referencia y números grandes Fecha Práctica diaria Áreas de países En los Problemas 1 a, usa los datos sobre las áreas de algunos países. nota Los estudiantes usan la comprensión del valor posicional para escribir números en forma desarrollada y redondear números hasta 1,000,000. Austria Indonesia Chile 32,382 millas cuadradas 71,096 millas cuadradas 292,258 millas cuadradas 1. Escribe el área de cada país en forma desarrollada. Austria: Indonesia: Chile: 2. Redondea el área de Austria a la decena de millar más cercana. 3. Redondea el área de Indonesia al millar más cercano.. Redondea el área de Chile a la centena de millar más cercana. 5. Escribe tres números que podrían redondearse a 520,000 si tuvieras que redondearlos a la decena de millar más cercana. Unidad 5 Sesión.2 C2 Pearson Education, Inc., or its affiliates. All Rights Reserved.

40 Nombre Números de referencia y números grandes Fecha El algoritmo usual (página 1 de 2) Usa el algoritmo usual de la resta para resolver los siguientes problemas. (Luego resuelve los problemas usando una estrategia diferente para asegurarte de que tu respuesta final sea correcta). En los Problemas 1 y 2 se muestran los pasos del algoritmo usual. Completa los espacios en blanco con los números correctos ( ) ( ) ( ) ( ) + + Unidad 5 Sesión.A C25 Pearson Education, Inc., or its affiliates. All Rights Reserved.

41 Nombre Números de referencia y números grandes Fecha El algoritmo usual (página 2 de 2) En los Problemas 3 y, usa el algoritmo usual de la resta para resolver cada problema. También, escribe los números correctos en los espacios en blanco, mostrando cómo descompusiste los números originales ( ) ( + + ) ( ) ( + + ) Unidad 5 Sesión.A C26 Pearson Education, Inc., or its affiliates. All Rights Reserved.

42 Nombre Números de referencia y números grandes Fecha Práctica diaria Usar el algoritmo usual Usa el algoritmo usual de la resta para resolver cada problema. También, escribe los números correctos en los espacios en blanco, mostrando cómo descompusiste los números originales. nota Los estudiantes practican el uso del algoritmo usual de la resta al descomponer los números por lugar y reagruparlos cuando es necesario. También practican la notación estándar para este algoritmo ( ) ( + + ) ( ) ( + + ) Unidad 5 Sesión.A C27 Pearson Education, Inc., or its affiliates. All Rights Reserved.

43 Nombre Números de referencia y números grandes Práctica de resta Usa el algoritmo usual de la resta para resolver cada problema. También, escribe los números correctos en los espacios en blanco, mostrando cómo descompusiste los números originales. Fecha Práctica diaria nota Los estudiantes practican el uso del algoritmo usual de la resta al descomponer los números por lugar y reagruparlos cuando es necesario. También practican la notación estándar para este algoritmo ( ) ( + + ) ( ) ( + + ) Unidad 5 Sesión.5 C28 Pearson Education, Inc., or its affiliates. All Rights Reserved.

44 Unit 6 Fraction Cards and Decimal Squares Common Core Mathematical Practices (MP) Domains Number and Operations in Base Ten (NBT) Number and Operations Fractions (NF) Measurement and Data (MD) INVESTIG ATION 1 Parts of Rectangles Day Session Common Core Adaptation Common Core Standards Fractions of an Area: Halves, Fourths, and Eighths Fractions of an Area: Thirds and Sixths Fractions of Groups of Things 1. Same Parts, Different Wholes Assessment: Identifying and Comparing Fractions Combinations That Equal 1 MP1, MP2.NBT.2,.NF.1,.NF.3.a,.NF.3.b MP1, MP2.NBT.2,.NF.3.a,.NF.3.b MP.NBT.2,.NF.3.d MP.NBT.2,.NF.3.d MP1, MP2, MP.NBT.2,.NF.1,.NF.3.a MP2.NBT.2,.NF.3.a,.NF.3.b Adding Fractions MP2.NBT.2,.NF.2,.NF.3.a 8 1.8A Subtracting Fractions See p. CC8. MP1, MP, MP5.NF.3.a,.NF.3.d Instructional Plan CC5

45 INVESTIG ATION 2 Ordering Fractions Day Session Common Core Adaptation Common Core Standards Fraction Cards MP3.NF.1,.NF.2 SESSION FOLLOW-UP Daily Practice: In addition to Student Activity Book page 28, Daily Practice and Homework students complete Student Activity Book page 30 or C31 (Fraction Subtraction) for reinforcement of the content of this unit Fraction Cards, continued MP3.NF Capture Fractions MP3.NF.1,.NF Comparing Fractions to Landmarks Fractions on a Number Line Assessment: Comparing Fractions A Adding and Subtracting Mixed Numbers See p. CC52. MP7.NF.2 MP5.NF.1,.NF.2,.NF.3.a MP5.NF.1,.NF.2 MP5.NF.3.c,.MD. INVESTIG ATION 3A Multiplying Fractions Day Session Common Core Adaptation Common Core Standards 16 3A.1 Multiplying Whole See p. CC57. MP Numbers and Fractions.NF..a,.NF..b,.NF..c 17 3A.2 Multiplying Whole Numbers and Fractions, continued 18 3A.3 Assessment: Multiplying with Fractions See p. CC62. See p. CC66. MP.NF..a,.NF..b,.NF..c MP.NF..a,.NF..b,.NF..c CC6 UNIT 6 Fraction Cards and Decimal Squares