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

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 1 1.1 How Much Is 1,000? MP7.NBT.1,.NBT.2,.NBT. 2 1.2 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. 3 1.3 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 = 00 + 30 + 5 under 35. 1. 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. 5 1.5A Place-Value Understanding 6 1.5 Assessment: Numbers to 1,000 7 1.6 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

INVESTIG ATION 2 Adding It Up Day Session Common Core Adaptation Common Core Standards 8 2.1 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.2 9 2.2 Addition Strategies MP3, MP6, MP8.NBT.,.MD.2 10 2.3 Starter Problems MP3, MP6, MP8.NBT.,.MD.2 11 2. 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. 12 2.5 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 13 2.6 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

INVESTIG ATION 3 Working with Numbers to 10,000 Day Session Common Core Adaptation Common Core Standards 1 3.1 Making a 10,000 Chart MP1, MP7.NBT.1,.NBT.2,.NBT. 15 3.2 How Much Is 10,000? MP1.NBT.1,.NBT.2,.NBT. 16 3.3 Working with the 10,000 Chart 17 3. Thousands of Miles MP1 TEN-MINUTE MATH Practicing Place Value 18 3.5 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.2 19 3.6A Larger Place Values See p. CC35. MP1.NBT.1,.NBT.2,.NBT.3 CC28 UNIT 5 Landmarks and Large Numbers

INVESTIG ATION Subtraction Day Session Common Core Adaptation Common Core Standards 20.1 Representing Subtraction Problems MP.NBT.2,.NBT. 21.2 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. 22.3 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. 25.5 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.2 27.7 End-of-Unit Assessment MP1, MP2, MP8.NBT. Instructional Plan CC29

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 683 + 10? 683 + 20? 683 + 100? 683 + 200? 683 100? 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?

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: 100 183 200 20 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 200. 183 100 150 200 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

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. 1. 312 2. 78 3. 235. 97 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. 5. 60 6. 807 7. 650 8. 539 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. 10. 173 Ac tivit y Pearson Education 11. 620 13. 308 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 12. 5 5//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 = 700 + 20 + on the board. 72 7 hundreds, 2 tens, ones 72 = 700 + 20 + 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

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 =. 3. 571 277. 62 5. 813 813 6. 152 7. 91 930 8. 1 26 55 1 9. 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 61. 61 is greater than 35. 35 61 < 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

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 =. 926 692 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 203 206 in the back of Unit 5. CC3 Investigation 1 How Much Is 1,000?

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 1,000,000 15 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 5,211 + 30? 5,211 + 300? 5,211 10? 5,211 100? 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

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

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. 1. 38,956 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. 7,10 3. 68,713. 305,501 5. 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 0,725 8. 712,726 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. 566,11 = 500,000 + 60,000 + 6,000 + 100 + 0 + 1 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

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

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. 8,325 1. 2,716 In Problems 3 and, round each number to the nearest ten thousand.. 97,300 3. 781,07 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 203 206 in the back of Unit 5. 5. 570,003 6. 116,325 7. 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 1,000,000. 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 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

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, 72 + 300? 7,72 + 00? 7,72 + 500? 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

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: 283 137 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: 283 200 + 80 + 3 137 (100 + 30 + 7) 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 200 + 70 + on the board next to the other problems, and ask students what number goes on the blank to still have the sum of 283. 283 200 + 80 + 3 200 + 70 + 137 (100 + 30 + 7) 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., 00 + 60 + 3) and the equivalent notation that results from regrouping the numbers (e.g., 00 + 50 + 13), 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

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 13 7. 283 200 + 80 + 3 200 + 70 + 13 137 (100 + 30 + 7) (100 + 30 + 7) 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 200 + 80 + 3, we had 200 + 70 + 13, 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: 200 + 70 + 13 (100 + 30 + 7) 100 + 0 + 6 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. 283 200 + 80 + 3 200 + 70 + 13 137 (100 + 30 + 7) (100 + 30 + 7) 100 + 0 + 6 = 16 7 2 8 1 3 137 16 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 13. 13 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

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. 55 500 + 0 + 5 500 + 30 + 15 00 + 130 + 15 268 (200 + 60 + 8) (200 + 60 + 8) (200 + 60 + 8) 200 + 70 + 7 = 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. 1. 7 5 7 2 8 1 7 5 7 2 8 700 + 50 + 7 (00 + 20 + 8) 700 + + (00 + 20 + 8) Give students a few minutes to discuss these steps, and then discuss the shorthand notation. 2. 5 2 6 1 8 8 1 1 1 5 2 6 1 8 8 + + 500 + 20 + 6 (100 + 80 + 8) + + (100 + 80 + 8) + + 1 3 1 55 268 277 62A 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 3. 3 6 1 1 3 3 6 1 1 3. 8 7 5 7 8 7 5 7 300 + 60 + 1 (100 + 0 + 3) + + ( + + ) 800 + 0 + (700 + 50 + 7) + + ( + + ) 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

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. 1. 9 8 00 + 90 + 8 27 9 (200 + 70 + 9) 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. 9 8 27 9 2. 5 2 5 16 5 2 5 16 + + ( + + ) 500 + + 20 5 (100 + 60 + ) + + ( + + ) 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 800 + 60 + 3 or 800 + 50 + 13 or 700 + 160 + 3, 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., 903 26). 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

Name Landmarks and Large Numbers Date Using Place Value In Problems 1, round each number to the nearest ten. 1. 312 2. 78 3. 235. 97 In Problems 5 8, round each number to the nearest hundred. 5. 60 6. 807 7. 650 8. 539 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. 10. 173 11. 620 12. 5 13. 308 Unit 5 Session 1.5A C17 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 =. 3. 571 277. 62 26 5. 813 813 6. 152 55 7. 91 930 8. 1 1 9. 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.

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 =. 926 692 Unit 5 Session 1.5A C19 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 =. 03 38 Unit 5 Session 2.5 C20 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 1. 38,956 2. 7,10 3. 68,713. 305,501 5. 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 5. 7. 2,551 0,725 8. 712,726 1,000,000 Unit 5 Session 3.6A C21 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Landmarks and Large Numbers Date Rounding Large Numbers In Problems 1 and 2, round each number to the nearest thousand. 1. 2,716 2. 8,325 In Problems 3 and, round each number to the nearest ten thousand. 3. 781,07. 97,300 In Problems 5 and 6, round each number to the nearest hundred thousand. 5. 570,003 6. 116,325 7. 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.

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.

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.

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. 7 5 7 2 8 700 1 50 1 7 2 (00 1 20 1 8) 1 7 5 7 2 8 700 1 1 2 (00 1 20 1 8) + + 2. 5 2 6 1 8 8 500 1 20 1 6 2 (100 1 80 1 8) 1 1 1 5 2 6 1 8 8 1 1 2 (100 1 80 1 8) 1 1 Unit 5 Session.A C25 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 3. 3 6 1 1 3 300 1 60 1 1 2 (100 1 0 1 3) 3 6 1 1 3 1 1 2 ( 1 1 ). 8 7 5 7 800 1 0 1 2 (700 1 50 1 7) 8 7 5 7 1 1 2 ( 1 1 ) Unit 5 Session.A C26 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 1. 9 8 2 7 9 00 + 90 + 8 (200 + 70 + 9) 9 8 2 7 9 + + ( + + ) 2. 5 2 5 1 6 500 + 20 + 5 (100 + 60 + ) 5 2 5 1 6 + + ( + + ) Unit 5 Session.A C27 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 1. 7 8 1 5 9 3 700 + 80 + 1 (500 + 90 + 3) 7 8 1 5 9 3 + + ( + + ) 2. 9 3 3 6 7 900 + 30 + 3 (600 + 0 + 7) 9 3 3 6 7 + + ( + + ) Unit 5 Session.5 C28 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 1. 312 2. 78 3. 235. 97 En los Problemas 5 a 8, redondea cada número a la centena más cercana. 5. 60 6. 807 7. 650 8. 539 9. 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. 10. 173 11. 620 12. 5 13. 308 Unidad 5 Sesión 1.5A C17 Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 =. 3. 571 277. 62 26 5. 813 813 6. 152 55 7. 91 930 8. 1 1 9. 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.

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 1,000. 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 =. 926 692 Unidad 5 Sesión 1.5A C19 Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 1,000. 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 =. 03 38 Unidad 5 Sesión 2.5 C20 Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 1. 38,956 2. 7,10 3. 68,713. 305,501 5. 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 0,725 8. 712,726 1,000,000 Unidad 5 Sesión 3.6A C21 Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 2,716 2. 8,325 En los Problemas 3 y, redondea cada número a la decena de millar más cercana. 3. 781,07. 97,300 En los Problemas 5 y 6, redondea cada número a la centena de millar más cercana. 5. 570,003 6. 116,325 7. 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.

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.

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.

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. 1. 7 5 7 2 8 700 + 50 + 7 (00 + 20 + 8) 1 7 5 7 2 8 700 + + (00 + 20 + 8) + + 2. 5 2 6 1 8 8 500 + 20 + 6 (100 + 80 + 8) 1 1 1 5 2 6 1 8 8 + + (100 + 80 + 8) + + Unidad 5 Sesión.A C25 Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 3. 3 6 1 1 3 300 + 60 + 1 (100 + 0 + 3) 3 6 1 1 3 + + ( + + ). 8 7 5 7 800 + 0 + (700 + 50 + 7) 8 7 5 7 + + ( + + ) Unidad 5 Sesión.A C26 Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 1. 9 8 2 7 9 00 + 90 + 8 (200 + 70 + 9) 9 8 2 7 9 + + ( + + ) 2. 5 2 5 1 6 500 + 20 + 5 (100 + 60 + ) 5 2 5 1 6 + + ( + + ) Unidad 5 Sesión.A C27 Pearson Education, Inc., or its affiliates. All Rights Reserved.

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. 1. 7 8 1 5 9 3 700 + 80 + 1 (500 + 90 + 3) 7 8 1 5 9 3 + + ( + + ) 2. 9 3 3 6 7 900 + 30 + 3 (600 + 0 + 7) 9 3 3 6 7 + + ( + + ) Unidad 5 Sesión.5 C28 Pearson Education, Inc., or its affiliates. All Rights Reserved.

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 1 1.1 Fractions of an Area: Halves, Fourths, and Eighths 2 1.2 Fractions of an Area: Thirds and Sixths 3 1.3 Fractions of Groups of Things 1. Same Parts, Different Wholes 5 1.5 Assessment: Identifying and Comparing Fractions 6 1.6 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 7 1.7 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

INVESTIG ATION 2 Ordering Fractions Day Session Common Core Adaptation Common Core Standards 9 2.1 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. 10 2.2 Fraction Cards, continued MP3.NF.2 11 2.3 Capture Fractions MP3.NF.1,.NF.2 12 2. Comparing Fractions to Landmarks 13 2.5 Fractions on a Number Line 1 2.6 Assessment: Comparing Fractions 15 2.7A 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

INVESTIG ATION 3 Working with Decimals Day Session Common Core Adaptation Common Core Standards 19 3.1 Representing Decimals MP5, MP6 SESSION FOLLOW-UP Daily Practice and Homework Daily Practice: In addition to Student Activity Book page 6, students complete Student Activity Book page 8 or C3 (Bug Collections) for reinforcement of the content of this unit..nf.5,.nf.6,.nf.7,.md.2 20 3.2 Comparing Decimals MP5, MP6.NF.6,.NF.7 21 3.3 Representing and Combining Decimals 22 3. Estimating and Adding Miles and Tenths of a Mile SESSION FOLLOW-UP Daily Practice and Homework 23 3.5 Comparing and Combining Decimals SESSION FOLLOW-UP Daily Practice 2 3.6 Comparing and Combining Decimals, continued SESSION FOLLOW-UP Daily Practice Daily Practice: In addition to Student Activity Book page 5, students complete Student Activity Book page 56 or C (Buying Fabric) for reinforcement of the content of this unit. Daily Practice: In addition to Student Activity Book page 59, students complete Student Activity Book page 60A or C5 (Multiplying with Fractions) for reinforcement of the content of this unit. Daily Practice: In addition to Student Activity Book page 60, students complete Student Activity Book page 60B or C6 (Working Hard) for reinforcement of the content of this unit. MP5, MP7.NF.5,.NF.6,.NF.7 MP, MP5.NF.7,.MD.2 MP.NF.7,.MD.2 MP.NF.7,.MD.2 25 3.7 End-of-Unit Assessment MP1, MP2.NF.2,.NF.7 Instructional Plan CC7

s e s s i o n 1. 8 A Subtracting Fractions Math Focus Points Using visual representations to subtract fractions with like denominators Subtracting fractions with like denominators Today s Plan activity Subtracting Fractions Discussion Subtracting Fractions Session Follow-Up Daily Practice 5 Min Class 15 Min Class Materials Student Activity Book, p. 26A or C29, Subtracting Fractions Make copies. (as needed) Students completed copies of Student Activity Book, p. 26A or C29 (from Activity 1) Student Activity Book, p. 26B or C30, More Subtracting Fractions Make copies. (as needed) Ten-Minute Math Practicing Place Value Write 3,850 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 3,850 300? 3,850 00? 3,850 + 300? 3,850 + 00? 3,850 + 500? Write each answer on the board. Have students compare each sum or difference with 3,850. Ask students: Which places have the same digits? Which do not? Why? CC8 Investigation 1 Parts of Rectangles

INV12_SE0_U6.indd 1 Pearson Education 6/1/11 3:03 PM 1 Activity 2 Discussion 3 Session Follow-Up A C T I V I T Y Subtracting Fractions 5 Min Ask students to draw a rectangle, shade 3_, and check with a neighbor to make certain they have correctly shaded 3_ of the rectangle. class We ve been adding fractions, and today we re going to work on subtracting fractions. Let s solve this problem: Helena had 3_ of a bag of marbles and she gave 1_ of the bag of marbles to her little brother. How much of the bag did she have left? Look at your rectangle. How could you show the 1_ Helena gave to her brother? What s the answer to the problem? Students might say: Name Fraction Cards and Decimal Squares Subtracting Fractions Date Solve each problem and show your work. For the word problems, write an equation. 1. There was 7_ of a pan of brownies on the table. Some friends 8 came over and ate _ of the pan of brownies. What fraction of 8 the pan of brownies is left? 2. Marisol walks to school. The school is 6 of a mile from her 10 house. She has already walked of a mile. How much farther 10 does Marisol have to walk? 3. There was 7 of a gallon of milk in the refrigerator. The Jones 12 family used 3 of the gallon during breakfast. How much milk 12 remains?. 5 2 5 = 5. 9 12 5 12 = 26A Unit 6 Session 1.8A Student Activity Book, Unit 6, p. 26A; Resource Masters, C29 I just crossed out the 1_ of the marbles Helena gave away. That left me with 2_. What equation would you write to represent the problem? Write the equation on the board: 3_ 1_ 2_. [Damian] says he wrote 3_ 1_ 1_ Are these answers equal? 2 Is 1_ also correct? 2 Students should agree that 2_ and 1_ are equivalent fractions and that 2 both answers are correct. Students solve problems involving subtraction of fractions on Student Activity Book page 26A or C29. As you work on these problems, think about what you know about fractions and about subtraction. Session 1.8A Subtracting Fractions CC9

1 Activity 2 Discussion 3 Session Follow-Up Ongoing Assessment: Observing Students at Work Students use representations to solve subtraction problems involving fractions with like denominators. How are students using representations to subtract fractions? Are they using rectangles or making drawings that match the context of the problem? Are they maintaining equalsized parts? Are answers reasonable? Are students continuing to reason about the size of fractions? differentiation: Supporting the Range of Learners Some students are still developing their ideas about the meaning of fractions and may be unable to draw representations for each of the fractions. Help these students divide a rectangle into equal parts, and then shade in the appropriate fraction. Some students will quickly recognize they only need to subtract the numerator, and the denominator stays the same. Give these students problems with unlike, but related fractions, such as 7_ 8 1_ or 10 9 3_ 5, and ask them to use representations and reasoning to solve these problems. D i s c u s s i o n Subtracting Fractions Math Focus Points for Discussion Subtracting fractions with like denominators 15 Min class Ask one or two students for solutions, including drawings, to Problem 1 on Student Activity Book page 26A or C29. After each student explains his or her solution, ask the class: Where is each of the fractions in the drawing? The 7_? _? 3_ 8 8 8? CC50 Investigation 1 Parts of Rectangles

1 Activity 2 Discussion 3 Session Follow-Up Write down the equations for Problems 1 3, and ask students to provide the answer for each. 1. 2. 3. 7_8 _8 = 3_8 6 = 2 (or 10 10 10 7 3 = (or 12 12 12 Name Date Fraction Cards and Decimal Squares Daily Practice More Subtracting Fractions Solve each problem and show your work. For the word problems, write an equation. 1. There is _78 of a carton of juice in the refrigerator. The Ortega family drank _58 of the carton with their breakfast. What fraction of the carton remains? _15 ) 1_3 ) 2. Venetta was walking to the library, which is _3 of a mile away. She has walked _1 of a mile. How much farther does Venetta have to walk? As you were solving these problems, and now looking at the solutions, is there anything you noticed about these fractions? Which numbers changed and which stayed the same? [Yuki] noticed that the denominator stays the same, unless we use an equivalent fraction for the answer. Why do you think this is true? Turn and discuss with a neighbor. 3. Richard had _5 of a bag of carrots. He fed _25 of the bag to his rabbit. What fraction of the bag did Richard have left? 7. = 10 Pearson Education Collect a few responses, and focus on the idea of like denominators. note Students solve subtraction problems involving fractions with like denominators. 10 6 1 5. = 8 8 Session 1.8A Unit 6 26B Student Activity Book, Unit 6, p. 26B; Resource Masters, C30 INV12_SE0_U6.indd 2 6/1/11 3:05 PM After a minute or two, collect some responses. Students might say: The denominator tells how many pieces there are all together, so it stays the same. I think that s right. I m not sure what you d do if the denominators weren t the same. [Amelia] brings up a good question. What if the problem were 3_ 21_? Could we just subtract the numerators? Why or why not? The purpose of this question is to highlight that the reason numerators can be subtracted in the problems students have been working on is because the denominators are the same. Session Follow-Up Daily Practice Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page 26B or C30. Session 1.8A Subtracting Fractions INV12_TE0_U06_S1.8A.indd 51 CC51 6/3/11 5:05 PM

s e s s i o n 2. 7 A Adding and Subtracting Mixed Numbers Math Focus Points Making a line plot to display a data set of measurements involving fractions Adding and subtracting mixed numbers with like denominators using representations and reasoning about fractions and the operations Today s Plan Activity Data on a Line Plot activity Butterfly Wingspans Discussion Adding and Subtracting Mixed Numbers SESSION FOLLOW-UP Daily Practice 20 Min Class individuals 25 Min individuals 15 Min Class Materials Student Activity Book, p. A or C32, Butterfly Wingspans (page 1 of 2) Make copies. (as needed) Student Activity Book, p. B or C33, Butterfly Wingspans (page 2 of 2) Make copies. (as needed) Students completed copies of Student Activity Book, p. B or C33 (from Activity 2) Student Activity Book, p. C or C3, Pepper s Puppies Make copies. (as needed) Ten-Minute Math Counting Around the Class Today we re going to count around the class, but instead of using whole numbers, we re going to count by fractions. Students count around the class by 1_ 2 s until all students have counted once. Ask students to say each number as a fraction, not a mixed number ( 1_ 2, 2_ 2, 3_ 2, _ 2, etc.). Draw a number line marked in halves, but not numbered. As students count, ask them to help you figure out where to put each fraction on the number line. What number did the 6th person say? How do you write 6_ 2 as a whole number? (3) What number did the 9th person say? How do you write 9_ 2 as a mixed number? ( 1_ 2 ) CC52 INVESTIGATION 2 Ordering Fractions

INV12_SE0_U6.indd 1 Pearson Education 6/1/11 3:09 PM 1 Activity 2 Activity 3 Discussion Session Follow-Up A c t i v i t y Data on a Line Plot 20 Min Class Individuals Name Date Fraction Cards and Decimal Squares Butterfly Wingspans (page 1 of 2) Yuki went to the Natural History Museum to study butterflies. The information he has about some of the butterflies in the collection is shown below. Wingspan Wingspan Name Name (inches) (inches) American Snout 1 1_ 2 Pearl Crescent 1 5_ 8 Have students look at Student Activity Book page A or C32. Ask them what they notice about the data. If necessary, explain that wingspan refers to the longest distance possible across the wings of a butterfly. Draw the number line for the line plot on the board. Ask students what each of the tick marks between the whole numbers on the line plot represents; establish that each mark represents 1_ of an inch and that 2_ is equivalent to 1_ 2. Have volunteers label each of the tick marks (e.g., 1_, 1_, 3_ 2, ). You re going to use the data in the table to create a line plot. Let s start with the American Snout butterfly. Where would we put the X to show its wingspan on the line plot? Once students have agreed, place an X above 1 1_ on the line plot on 2 the board and have students do the same at their desks. Now let s look at the Milbert s Tortoiseshell butterfly. Where would we put the X to show its wingspan? Talk to a neighbor and see if you can agree where the X would go. Point to the location on the line plot that shows 2 5_ 8. [Lucy] says the X should go here, and that s correct. Why does the X go halfway between 2 1_ and 2 3_? There aren t marks that show 2 eighths on our line plot, so use what you know about fractions to correctly complete the line plot. After students complete the line plot, tell them to write statements about the data. When they are done, they should check with a neighbor to make certain they have all the data correctly displayed. When there are a few minutes remaining, call students back together. Ask how they would describe the shape of the data. Students are likely to mention that there are 12 pieces of data, most of the data are clumped between 2 and inches, the lowest value is 1 1_ inches, and the highest is 5 1_ inches. (Some students may 2 determine that the range is 3 3_ inches.) Giant Swallowtail 5 1_ Postman 2 1_ Red Admiral 3 1_ 8 Julia 3 1_ 2 Saturn 1_ Milbert s Tortoiseshell 2 5_ 8 Tiger Swallowtail 3 3_ Monarch 3 1_ 2 Viceroy 2 7_ 8 Painted Lady 2 1_ 2 Record the measurements on the line plot below. 0 1 2 3 5 6 Butterfly Wingspans (inches) Write three statements that describe the data. A Unit 6 Session 2.7A Student Activity Book, Unit 6, p. A; Resource Masters, C32 Session 2.7A Adding and Subtracting Mixed Numbers CC53

1 Activity 2 Activity 3 Discussion Session Follow-Up Name Date Fraction Cards and Decimal Squares Ongoing Assessment: Observing Students at Work Butterfly Wingspans (page 2 of 2) Use the information on the previous page to solve the following problems. Show your work. Students use the information from the table to complete the line plot. 1. How much longer is the wingspan of the Viceroy butterfly than the wingspan of the Pearl Crescent butterfly? Can students correctly plot the data? Are students statements about the data accurate? 2. How much longer is the wingspan of the Giant Swallowtail butterfly than the wingspan of the Tiger Swallowtail butterfly? 3. The American Snout butterfly and the Postman butterfly are side-by-side. What is the length of their combined wingspans?. How much longer is the wingspan of the Red Admiral butterfly than the wingspan of Milbert s Tortoiseshell butterfly? Differentiation: Supporting the Range of Learners Pearson Education 5. The Pearl Crescent butterfly and the Viceroy butterfly are sideby-side. What is the length of their combined wingspans? Some students are still working on understanding fourths and halves. Help these students put marks on the line plot for eighths. 6. The Saturn butterfly and the Tiger Swallowtail butterfly are sideby-side. What is the length of their combined wingspans? Session 2.7A Unit 6 B Student Activity Book, Unit 6, p. B; Resource Masters, C33 INV12_SE0_U6.indd 2 6/1/11 3:10 PM AC TIVIT Y 25 Min Individuals Butterfly Wingspans Let s look at Problem 1 on Student Activity Book page B or C33, together. First find the wingspan of the Viceroy butterfly (2 _78 inches) and the Pearl Crescent butterfly (1 _58 inches). Then work alone or with a partner to find the answer to the problem. Think about what you know about fractions and subtraction. Give students several minutes to work. Then ask how they determined the difference in the wingspans. Students might say: I just subtracted. 2 1 = 1, and 7_8 5_8 is _28, so it s 1 _28. I sort of used the line plot as a number line. I started at 1 _58. _38 more is 2, then I have to 10, or 1 _ 2. go _78 more to 2 _78. That s 8 8 [Andrew] says he thought of the line plot as a number line. Let s take a look at that. _7 _3 8 8 0 CC5 _1 8 _1 _3 8 _1 2 _5 8 _3 _7 8 1 1 1 3 1 5 3 7 1_8 1_ 1_8 1_2 1_8 1_ 1_8 2 1 1 3 1 5 3 7 2_8 2_ 2_8 2_2 2_8 2_ 2_8 3 INVESTIGATION 2 Ordering Fractions INV12_TE0_U06_S2.7A.indd 5 6/1/11 2:1 PM

1 Activity 2 Activity 3 Discussion Session Follow-Up What equation represents the problem? Write 2 7_ 8 1 5_ 8 = 1 2_ 8 (or 1 1_ ) on the board. As you work on this page, read the problems carefully to decide whether they are addition or subtraction situations. When we come back together, we re going to discuss Problems 2 and 5. As students work, identify students who used different strategies, and ask them to be prepared to explain their solutions. Ongoing Assessment: Observing Students at Work Students use the information from the table and line plot to solve addition and subtraction problems involving mixed numbers with like denominators. What strategies are students using to solve addition problems? Are they using a visual representation, such as extending the number line? Are they reasoning and using what they know about fractions? What strategies are students using to solve subtraction problems? Are they using the line plot as a number line? Are they reasoning and using what they know about fractions? How are students keeping track of the numbers? Are they keeping the whole numbers and fractions separate, and then combining them for their answer? If they are adding up, do they recognize when they reach the next whole number? Differentiation: Supporting the Range of Learners Some students have difficulty transferring data from the table and line plot to the word problems. Help these students identify each of the numbers needed to solve the problem. Also consider modeling how to use a number line to solve the subtraction problems. Students who easily solve these problems can be asked to make up their own problems using the butterfly wingspans listed in the table. Encourage them to use numbers with unlike denominators. Session 2.7A Adding and Subtracting Mixed Numbers CC55

1 Activity 2 Activity 3 Discussion Session Follow-Up Name Date Fraction Cards and Decimal Squares 1 8 1 3 8 1 2 Adding and Subtracting Mixed Numbers note Students solve addition and subtraction problems involving fractions using data given in a line plot. Cheyenne s dog, Pepper, had puppies. Cheyenne recorded their weights in the line plot below. 0 Discussion Daily Practice Pepper s Puppies X X X X X X 5 8 3 7 8 1 1 18 1 1 1 38 1 12 Weights of Pepper s Puppies (pounds) Solve each problem and show your work. 1. Two puppies weighed the same amount. What was the total weight of the two puppies? Adding and subtracting mixed numbers with like denominators using representations and reasoning about fractions and the operations Pearson Education 3. The heaviest puppy gained _8 of a pound in its first month. How much did it weigh after the first month? C Unit 6 class Math Focus Points for Discussion 2. How many more pounds did the heaviest puppy weigh than the lightest puppy? Session 2.7A Student Activity Book, Unit 6, p. C; Resource Masters, C3 INV12_SE0_U6.indd 3 15 Min 6/1/11 3:12 PM As you discuss Problems 2 and 5 from Student Activity Book page B or C33, ask students you identified earlier to explain their solutions. Let s start with Problem 2. Was this an addition or subtraction situation? How did you know? Students might say: I knew I had to subtract to find the difference. It was _1 more to inches, and then another inch and _1. So that made it 1 _2 inches, or 1 _12 inches. Let s look at Problem 5. Was this an addition or subtraction situation? How did you know? Students might say: I knew I was adding because I needed to find the total of both wingspans. I changed the 2 _78 to 3, because it s only _18 away. I added 1 _58 to 3 and got _58, but then I had to take the _18 away so it s _8, which is the same as _12. SESSION FOLLOW-UP Daily Practice Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page C or C3. CC56 INVESTIGATION 2 Ordering Fractions INV12_TE0_U06_S2.7A.indd 56 6/3/11 2:28 PM

s e s s i o n 3 A. 1 Multiplying Whole Numbers and Fractions Math Focus Points Multiplying a whole number and a fraction Using visual models to solve word problems involving multiplication of a whole number and a fraction Today s Plan Discussion Counting Around the Class activity Multiplying Whole Numbers and Fractions Discussion Strategies for Multiplying Fractions Session Follow-Up Daily Practice 10 Min Class 30 Min Class Individuals 20 Min Class Materials Student Activity Book, p. D or C35, Multiplying Whole Numbers and Fractions Make copies. (as needed) Students completed copies of Student Activity Book, p. D or C35 (from Activity 2) Student Activity Book, p. E or C36, Chunks of Cheese Make copies. (as needed) Ten-Minute Math Counting Around the Class Students count around the class by 1_ 3 s until all students have counted once. Ask students to say each number as a fraction, not a mixed number ( 1_ 3, 2_ 3, 3_ 3, _ 3, etc.). Draw a number line marked in thirds, but not numbered. As students count, ask them to help you figure out where to put each fraction on the number line. What number did the 6th person say? How do we write 6_ 3 as a whole number? (2) What number did the 10th person say? How do we write 10 as a mixed number? 3 (3 1_ 3 ) S session 3A.1 Multiplying Whole Numbers and Fractions CC57

1 Discussion 2 Activity 3 Discussion Session Follow-Up Teaching Note Discussion 1 Multiplying Whole Numbers and Fractions This Investigation focuses on multiplying whole numbers and fractions less than 1. Unless otherwise noted, the word fraction in this Investigation refers to numbers between 0 and 1. _ or _3 3? 2 Is it 3 3 Investigations has opted to show 3 groups of 3_ as 3 3_, and _3 group of 3 as _3 3, using the same convention used for whole numbers. However, it is not necessary for students to follow this system rigidly. When students suggest a multiplication expression for a multiplication situation, what is important is that they understand what the numbers mean. For example, in the situation of the 3 pizzas, students need to understand that the 3 represents the number of groups and the 3_ represents the size of each group. Name Fraction Cards and Decimal Squares Multiplying Whole Numbers and Fractions Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. Using visual models to solve problems involving multiplication of a whole number and a fraction Ask five students to count by 1_ s. Ask students to say each number as a fraction, not a mixed number ( _1, _2, _3, _, _5, etc.). Keep track of the fractions on a number line. What number did the 5th person say? How do we write _5 as a mixed number? (1 1_ ) 0 _1 _2 _3 1 5 _6 _7 2 If we counted around by 7s instead, and 5 people counted, what equation would represent 5 people counting by 7s? Why would this be the equation? So, what is an equation that would represent 5 people counting by _1 s? 2. A class is counting by _62s. What number does the 7th person say? 1 3. 6 = 3 3. 3 = 8 Pearson Education Math Focus Points for Discussion If students are having trouble coming up with an equation, suggest that they think about whole numbers. 1. Jake bought three kinds of pizza for a party. Each pizza was the same size. People were not very hungry, and at the end of the party there was _3 of each pizza left. How much pizza was left in all? Ac tivit y Unit 6 D Student Activity Book, Unit 6, p. D; Resource Masters, C35 INV12_SE0_U6.indd Counting Around the Class Class Five people counting by _1 is five fourths, or five groups of _1. What is an equation that would represent 5 people counting by _1 s?... Why would this be an equation for this situation? Date Session 3A.1 10 Min 6/1/11 3:12 PM Multiplying Whole Numbers and Fractions 30 Min class individuals Ask students to look at Problem 1 on Student Activity Book page D or C35 as you read it aloud. 1 Jake bought three kinds of pizza for a party. Each pizza was the same size. People were not very hungry, and at the end of the party there was _3 of each pizza left. How much pizza was left in all? What equation could represent this problem? (3 _3 = ) CC58 2 Investigation 3A Multiplying Fractions INV12_TE0_U06_S3A.1.indd 58 6/1/11 2:15 PM

1 Discussion 2 Activity 3 Discussion Session Follow-Up Draw a square on the board. One way to solve this problem would be to represent it on a number line like we did for counting around the class. Another way would be to draw a picture. How could we use squares to help us solve the problem? Students might say: We could draw 3 squares to represent the 3 pizzas, divide them into fourths and color in 3_ of each. Those squares would be like the squares on the fraction cards. You only have one 3_ card, so you couldn t actually use the fraction cards. But you could draw squares or rectangles and divide them into fractional pieces to help you solve this problem. As you solve each problem on Student Activity book page D (or C35), think carefully about which number represents the number of groups and which represents the size of the group. 3 As students solve the problems, look for a variety of strategies used to solve Problem 1. Ask students to share these strategies during the discussion at the end of the session. Possible strategies are shown in the discussion section. 5 Ongoing Assessment: Observing Students at Work Students solve problems in which they multiply whole numbers by fractions. What representations and strategies do students use to solve the problems? Are they using pictures or number lines? How are they keeping track of each part of the problem and the product? Can students write a multiplication equation for the problem? Can they identify which number in the equation and in the word problem represents the number of groups and which represents the size of the group? differentiation: Supporting the Range of Learners If students are unsure how to start solving the problem, suggest drawing rectangles. Discuss each part of the problem and have them show each part on the rectangles. Teaching Note 3 Teaching Note: The Commutative Property of Multiplication Students know from their work with whole numbers that multiplication is commutative. In this Investigation they may notice that, for example, 3 3_ = 3_ 3. If students do notice, use this opportunity to ask students whether they think multiplication is still commutative when one of the factors is a fraction: We ve talked about how if you change the order of the factors in multiplication, the product doesn t change. Do you think that is still the case when you re multiplying a whole number and a fraction? While this is a good opportunity to consider this question, students do not yet have the tools to resolve this question during this Investigation: 3_ of a group of 3 can appear very different to them than 3 groups of 3_. For now, students need time to make sense of the operation of multiplication with fractions. Representations for Multiplying Fractions Both the number line and dividing rectangles into fractional pieces are useful representations to use when multiplying a whole number and a fraction. Even though students have used arrays for multiplication with whole numbers, arrays with a fraction as one or both dimensions of the rectangle is more challenging to understand. Students will use the array model in Grade 5 when they continue their work on multiplication of fractions. 5 Fractions Greater than One or Mixed Numbers When students solve these problems they may come up with answers that are mixed numbers (e.g., 2 1_ ) or fractions greater than 1 (e.g., 9_ ). Either answer is fine, and the fact that the answers are equivalent is discussed further in the discussion at the end of this session. Session 3A.1 Multiplying Whole Numbers and Fractions CC59

1 Discussion 2 Activity 3 Discussion Session Follow-Up D i s c u s s i o n Strategies for Multiplying Fractions Math Focus Points for Discussion Multiplying a whole number and a fraction 20 Min Using visual models to solve word problems involving multiplication of a whole number and a fraction Refer students to Problem 1 on Student Activity Book page D or C35. What multiplication equation fits this problem? ( 3 3_ = ) Ask students to share the strategies you identified during the last activity. These strategies may include the following: Diagram A class 0 _ 3 _ 2 1 2 _ 1 Diagram B There are three 1_ s left in each pizza. There are 3 pizzas. So that is 3 3 1_ pieces. That s nine 1_ pieces left, which means there is 9_ of a pizza left. Diagram C _ 1 _ 2 _ 3 _ 1 _ 2 _ 3 _ 1 _ 2 _ 3 1 2 3 three 3_ pizzas = 2 wholes and 1_ = 2 1_ CC60 Investigation 3A Multiplying Fractions

INV12_SE0_U6.indd 5 Pearson Education 6/1/11 3:15 PM 1 Discussion 2 Activity 3 Discussion Session Follow-Up We said the equation for this problem is 3 3_ =. Which number tells us the number of groups? Which number tells us the size of the group? Where do you see the number of groups and the size of the groups in these representations? In Diagram A, the number of groups is the number of jumps, and the size of the group is the size of the jump. In Diagram B, the number of groups is the number of squares, and the size of the group is the amount shaded on each square. In Diagram C, the number of groups is the number of times you can count off 1_, 2_, 3_ and the size of the group is the amount shaded in each group you count. Discuss students answers to the problem. Some may have an answer of 9_ and some may have an answer of 2 1_. Ask students about these two answers. [Terrell] said the answer to this problem is 9_. [Jill] said the answer is 2 1_. Are these answers equal? Encourage students to use one of the representations to explain their ideas. Discuss that one way to think about multiplying fractions and whole numbers is to think of 3_ as 3 1_. Then 3 3_ = 3 3 1_. In our representation of 3 pizzas with 3_ of each pizza shaded, we can think about this as being three 1_ s shaded in each pizza. We notate this as 3 3 1_ = 9_. You can change this to 2 1_, which helps you see that there are between 2 and 3 pizzas left., Name Date Fraction Cards and Decimal Squares Daily Practice Chunks of Cheese note Students solve problems involving multiplication of a Morris Mouse s Cheese House sells chunks of cheese. whole number and a fraction. Each chunk weighs 3_ of a pound. Find the total weight of each kind of cheese. Use a representation to solve each problem. Also, write a multiplication equation that represents the problem. Show your work. 1. 5 chunks of cheddar cheese 2. 10 chunks of Swiss cheese Total weight Total weight 3. chunks of American cheese. 8 chunks of parmesan cheese Total weight Total weight E Unit 6 Session 3A.1 Student Activity Book, Unit 6, p. E; Resource Masters, C36 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 E or C36. Session 3A.1 Multiplying Whole Numbers and Fractions CC61

s e s s i o n 3 A. 2 Multiplying Whole Numbers and Fractions, continued Math Focus Points Multiplying a fraction and a whole number Using visual models to solve word problems involving multiplication of a fraction and a whole number Today s Plan Discussion Multiplying Whole Numbers and Fractions Math Workshop Multiplying with Fractions 2a Multiplying Fractions and Whole Numbers 2B More Multiplying Fractions and Whole Numbers Session Follow-Up Daily Practice 20 Min Class 0 Min Materials Chart paper (Copy the story problems and table shown in the discussion section.) 2A Student Activity Book, p. F or C37, Multiplying Fractions and Whole Numbers Make copies. (as needed) 2b Student Activity Book, p. G or C38, More Multiplying Fractions and Whole Numbers Make copies. (as needed) Student Activity Book, p. H or C39, Multiplying with Fractions Make copies. (as needed) Student Math Handbook, p. 55 Ten-Minute Math Counting Around the Class Students count around the class by 2_ 5 s until all students have counted once. Ask students to say each number as a fraction, not a mixed number ( 2_ 5, _ 5, 6_ 5, etc.). Draw a number line marked in fifths, but not numbered. As students count, ask them to help you figure out where to put each fraction on the number line. What number did the 6th person say? How do we write 12 5 as a mixed number? (2 2_ 5 ) What number did the 12th person say? How do we write 2 5 as a mixed number? ( _ 5 ) What is a multiplication equation that would represent 12 people counting by 2_ 5 s? (12 2_ 5 = 2 5, or _ 5 ) CC62 Investigation 3A Multiplying Fractions

1 Discussion 2 Math Workshop 3 Session Follow-Up D i s c u s s i o n Multiplying Whole Numbers and Fractions Math Focus Points for Discussion Multiplying a fraction and a whole number 20 Min Using visual models to solve word problems involving multiplication of a fraction and a whole number Call attention to the following two stories you have written on chart paper: class (1) Eggs come in cartons of 12. Richard was making cakes for a party and used 2 cartons of eggs. How many eggs did he use? (2) Sabrina was making a cake for herself. She used 1_ of a carton of eggs. There are 12 eggs in each carton. How many eggs did she use? Give students some time to work with a partner to solve each problem. Below the stories make a table to record the information from each problem. Teaching Note 1 Parts of a Group: Students may find it confusing to think about 1_ of a group as being the number of groups. Consider these two phrases: 2 groups of 12 and 1_ group of 12. In each, the 12 is the number in the group. In the first phrase, 2 tells us how many full groups of 12, and in the second phrase, 1_ tells us how much of a group of 12. Math Note 2 Division Equation Some students may say that the second problem seems like a division situation and suggest 12 = 3 as an equation that represents the problem. This division equation does represent what is happening in the problem and is equivalent, but the focus in this session is on multiplying a whole number and a fraction. Students are specifically asked to write a multiplication equation using 1_, 12, and 3. (1) (2) Number of Cartons Number of Eggs in a Carton Number of Eggs Equation Work with the class to fill out the table. As you ask students the following questions, they should refer back to the problem or to the table to answer the questions. What multiplication equation represents action in the first problem? Which number represents the number of groups and which represents the size of the group? What multiplication equation, using 1_, 12, and 3, represents what is happening in the second problem? Which number represents the number of groups and which represents the size of the group? 1 We came up with multiplication equations for both problems. What makes them both multiplication problems? 2 Session 3.A2 Multiplying Whole Numbers and Fractions, continued CC63

1 Discussion 2 Math Workshop 3 Session Follow-Up Students might say: Math Note It is likely going to be more difficult for students to use a number line to represent _23 group of 9. Rather than skip counting by _23 on the number line, as they have done previously, to represent this problem they would mark the number line from 0 to 9, and then have to figure out how to divide that distance into thirds. 3 Number Line Name Date They are multiplication problems because they talk about groups of things. Write Problem 1 from Student Activity Book page F on the board: A grocery store sells bags of 9 apples. Anna used _23 of the apples in a bag in an apple pie. How many apples did she use in the pie? What equation could we write using 9 and _23 that represents the problem? ( 2_3 9 = ) If students are unsure what the equation for this problem would be, then ask the following questions: Fraction Cards and Decimal Squares Multiplying Fractions and Whole Numbers Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. What would the equation be if Anna used 5 bags of 9 apples? So then, what would the equation be for this problem? 1. A grocery store sells bags of 9 apples. Anna used _32 of the apples in a bag in an apple pie. How many apples did she use in the pie? 2. Steve was in a 7 mile race. He ran _12 of it and walked the rest. How many miles did he run? What representations might you use to help you solve this problem? 2 3. 12 = 3 Students are likely to say they could start by drawing 9 apples. Some students may suggest using a number line. 3. There are 10 boys in class. _5 of them have brown hair. How many boys have brown hair? 5 5. 16 = Pearson Education 8 1 6. 11 = M ath Work shop 2 Session 3A.2 Unit 6 F Student Activity Book, Unit 6, p. F; Resource Masters, C37 INV12_SE0_U6.indd 6 6/3/11 10:27 AM Multiplying with Fractions 0 Min Students continue to work on problems in which they multiply with fractions. They continue using representations (drawings or a number line) to show solutions. Students will continue to work on these activities in Session 3A.3. 2A Multiplying Fractions and Whole Numbers individuals Students solve problems on Student Activity Book page F or C37 in which they multiply fractions and whole numbers. If students seem uncertain about how to solve these problems, remind them they solved similar problems in Investigation 1, and the strategies they used then also work for these problems. CC6 Investigation 3A Multiplying Fractions INV12_TE0_U06_S3A.2.indd 6 6/1/11 2:28 PM

1 Discussion 2 Math Workshop 3 Session Follow-Up Name Date Fraction Cards and Decimal Squares Students solve problems in which they multiply fractions and whole numbers. What strategies do students use to solve the problems? Are they using pictures or number lines? How are they keeping track of each part of the problem and the product? Can students write a multiplication equation for the problem? Can they identify which number in the equation and in the word problem represents the number of groups and which represents the size of the group? Can students decide whether their answers to the More Multiplying Fractions and Whole Numbers Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. 1. Sabrina walks to school. Her house is _38 of a mile from school. How many miles would she walk to and from school in 5 days? 2 2. 6 = 5 3. Damian has a recipe that calls for _23 of a cup of flour. He wants to make times the recipe. How much flour does he need? 3. 3 = Pearson Education Ongoing Assessment: Observing Students at Work G problems are reasonable? Unit 6 Session 3A.2 S tudent Activity Book, Unit 6, p. G; Resource Masters, C38 INV12_SE0_U6.indd 7 6/3/11 10:26 AM differentiation: Supporting the Range of Learners Name If students are unsure how to start solving a problem, suggest drawing the objects in the problem. Discuss each part of the problem and have them illustrate each part of the problem in the picture. Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. 3 2. 16 = 1 3. 9 = 1. 12 = 5 6 2 5. Mr. Garcia has 15 grandchildren. _23 of them are girls. How many are girls? 6. Helena needs 8 pieces of wire. Each piece needs to be _3 of a foot long. What is the total length of the wire Helena needs? individuals Students solve problems on Student Activity Book page G or C38 in which they multiply fractions and whole numbers. 1 1. = note Students solve problems involving multiplication of whole numbers and fractions. Pearson Education Whole Numbers Daily Practice Multiplying with Fractions If students easily solve both sets of problems, encourage them to use a number line to represent each problem as well. 2B More Multiplying Fractions and Date Fraction Cards and Decimal Squares Session 3A.2 Unit 6 H S tudent Activity Book, Unit 6, p. H Resource Masters, C39 INV12_SE0_U6.indd 8 6/1/11 3:18 PM Session Follow-Up Daily Practice Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page H or C39. Student Math Handbook: Students and families may use Student Math Handbook page 55 for reference and review. See pages 170 176 in the back of Unit 6. Session 3.A2 Multiplying Whole Numbers and Fractions, continued INV12_TE0_U06_S3A.2.indd 65 CC65 6/1/11 2:29 PM

s e s s i o n 3 A. 3 Assessment: Multiplying with Fractions Math Focus Points Multiplying fractions and whole numbers Using visual models to solve word problems involving multiplication of a fraction and a whole number Today s Plan Math Workshop Multiplying with Fractions 2a Multiplying Fractions and Whole Numbers 2B More Multiplying Fractions and Whole Numbers 2C Multiplying with Fractions Discussion Multiplying with Fractions Assessment Activity Multiplying with Fractions Session Follow-Up Daily Practice 20 Min 20 Min Class 20 Min Individuals Materials 2A Students copy of Student Activity Book, p. F or C37 (from Session 3A.2) 2b Students copy of Student Activity Book, p. G or C38 (from Session 3A.2) 2C Student Activity Book, p. I or C0, Multiplying Fractions Make copies. (as needed) Students completed copies of Student Activity Book p. I or C0 (from Math Workshop 2C) C1, Assessment: Multiplying with Fractions Make copies. (one per student) Student Activity Book, p. J or C2, All Kinds of Nuts Make copies. (as needed) Student Math Handbook, p. 55 Ten-Minute Math Counting Around the Class Students count around the class by _ 6 s until all students have counted once. Ask students to say each number as a fraction, not a mixed number ( _ 6, 8_ 6, 12 6, etc.). Draw a number line marked in sixths, but not numbered. As students count, ask them to help you figure out where to put each fraction on the number line. What number did the 7th person say? How do we write 28 6 as a mixed number? ( _ 6 ) What number did the 9th person say? How do we write 36 6 as a whole number? (6) What is a multiplication equation that would represent 9 people counting by _ 6 s? (9 _ 36 6 = 6, or 6) CC66 INVESTIGATION 3A Multiplying Fractions

INV12_SE0_U6.indd 9 Pearson Education 6/1/11 :0 PM 1 Math Workshop 2 Discussion 3 Assessment Activity Session Follow-Up M ath Work shop Multiplying with Fractions In addition to the activities students worked on in Session 3A.2, students solve another set of problems in which they multiply fractions and whole numbers. 20 Min Name Fraction Cards and Decimal Squares Multiplying Fractions Date Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. 1. In the store Damian found pretzels that came in 1_ -pound bags. 3 He bought 5 bags of pretzels. How many pounds of pretzels did he buy? 2. 3 6 8 = 3. There were 25 students in class. One day, 3_ of them wore 5 sneakers. How many students wore sneakers? 2A Multiplying Fractions and Whole Numbers individuals Students continue to work on Student Activity Book page F or C37. For complete details of this activity, see Session 3A.2, pages CC6 and CC65.. 7 10 = 5. Jill used stones that were each 3_ of a foot high to build a wall. She piled 6 stones on top of each other. How many feet high was her wall? 6. 5 6 12 = 2B More Multiplying Fractions and Whole Numbers Students continue to work on Student Activity Book page G or C38. individuals I Unit 6 Session 3A.3 Student Activity Book, Unit 6, p. I; Resource Masters, C0 2C Multiplying with Fractions individuals Students solve problems on Student Activity Book page I or C0 in which they multiply fractions and whole numbers. Ongoing Assessment: Observing Students at Work Students multiply whole numbers and fractions. What strategies do students use to solve the problems? Are they using pictures or number lines? How are they keeping track of each part of the problem and the product? Can students write a multiplication equation for the problem? Can they identify which number in the equation and in the word problem represents the number of groups and which represents the size of the group? Can students decide whether their answers to the problems are reasonable? differentiation: Supporting the Range of Learners If students are unsure how to start solving a problem, suggest drawing the objects in the problem. Discuss each part of the problem and have them show each part of the problem in the picture. Session 3A.3 Assessment: Multiplying with Fractions CC67

1 Math Workshop 2 Discussion 3 Assessment Activity Session Follow-Up Some students may notice that to solve a problem that involves multiplying a fraction and a whole number you can multiply the numerator by the whole number and put that product over the denominator. Ask the students to show why this works and then encourage them to use this method to solve the problems using just numbers. D i s c u s s i o n Multiplying with Fractions Math Focus Points for Discussion Multiplying fractions and whole numbers 20 Min class Ask students to bring Student Activity Book page I or C0 with them to the discussion. Ask students what product they got for each problem. Write the equation for each problem on the board. Record each product as both a fraction and a mixed number or whole number. 1. 5 1_ 3 = 5_, or 1 2_. 7 3 3 2. 3 6_ 8 = 18 8 3. 3_ 5 25 = 75, or 2 2_ 8 5, or 2 1_ 5. 6 3_, or 15 6. 5_ 6 10 = 28 10 = 18, or 2 8, or 2 _ 10 5, or 2_, or 1_ 2 12 = 60, or 10 You solved a variety of problems which involved multiplying fractions and whole numbers. What do you notice about multiplying fractions and whole numbers? Ideas to highlight include: Unlike multiplication with nonzero whole numbers, where the product is larger than either factor, the product of a fraction less than one and a nonzero whole number is larger than the fraction and smaller than the whole number. The product is equal to the numerator of the fraction multiplied by the whole number, placed over the denominator of the fraction. ( _ 5 = 1_ 5 = 5 1 ) If your class has discussed the commutative property, this idea could also be included. (3 3_ = 3_ 3) Ask students to use representations to show and support their thinking. 6 CC68 Investigation 3A Multiplying Fractions

1 Math Workshop 2 Discussion 3 Assessment Activity Session Follow-Up A ssessment Ac tivit y Multiplying with Fractions Professional Development 20 Min individuals Assessment: Multiplying with Fractions, p. CC70 1 Teacher Note: Students work on Assessment: Multiplying with Fractions (page C1) to assess their understanding of multiplication of whole numbers and fractions. They solve one word problem and are asked to write an equation for it, and they solve one number problem. 1 Name Date Fraction Cards and Decimal Squares Assessment: Multiplying with Fractions Use a representation to solve each problem. For the word problem, write an equation that represents the problem. 1. Ursula bought 30 apples. _35 of them are green. How many of the apples are green? Ongoing Assessment: Observing Students at Work Students solve problems in which they multiply fractions and whole numbers. What strategies do students use to solve the problems? Do 2 2. 5 = 3 they use visual models? Do they draw pictures or use a number line? Can students write a multiplication equation for the problem? Unit 6 Session 3A.3 C1 Pearson Education, Inc., or its affiliates. All Rights Reserved. Resource Masters, C1 INV12_BLM0_U6.indd 1 6/1/11 3:5 PM Session Follow-Up Daily Practice Name Date Fraction Cards and Decimal Squares All Kinds of Nuts Use a representation to solve each problem. Also, write an equation that represents the problem. Daily Practice note Students solve problems involving multiplication of whole numbers and fractions. 1. Emaan bought 6 bags of walnuts. Each bag contained _3 of a pound of walnuts. What was the total weight of the walnuts? Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page J or C2. 2. A man bought 12 boxes of nuts. He took _16 of the boxes to his office. How many boxes of nuts did he take to the office? Student Math Handbook: Students and families may use Student Math Handbook page 55 for reference and review. See pages 170 176 in the back of Unit 6. 3. Kimberly is making 3 loaves of nut bread. For each loaf, she needs _3 of a cup of pecans. How many cups of pecans does she need? Circle the best answer below. between 3 and cups between 2 and 3 cups Pearson Education between 1 and 2 cups Session 3A.3 Unit 6 J S tudent Activity Book, Unit 6, p. J; Resource Masters, C2 INV12_SE0_U6.indd 10 Session 3A.3 Assessment: Multiplying with Fractions INV12_TE0_U06_S3A.3.indd 69 5/13/11 11:06 AM CC69 6/3/11 3:2 PM

Teacher Note Assessment: Multiplying with Fractions Benchmarks addressed: Multiply a fraction (less than 1) and a whole number. In order to meet the benchmark, students work should show that they can: Use a visual representation to solve a multiplication problem involving a fraction (less than 1) and a whole number; Determine the correct product, either as a fraction (greater than 1), or as a mixed number or whole number. Meeting the Benchmark Students who meet the benchmark are able to correctly multiply the fraction and whole number by using visual representations such as a number line, rectangles divided into equal parts, or other types of drawings. Students find the correct product for both problems and their representations clearly show their thinking. For Problem 1, students write an equation that matches their representation. Partially Meeting the Benchmark Students who partially meet the benchmark show some knowledge of fractions and multiplication, but solve only one problem correctly. Students are likely to have more difficulty with Problem 1. They might draw 30 apples/objects, but are unsure how to determine 3_ of 30. They also may not be able to write 5 an equation. For Problem 2, students draw a correct representation of 5 2_, such as showing 5 jumps of 2_ 3 3 on a number line, or drawing 5 wholes and correctly shading in 2_ of each. They are likely to get 3 1_ (or 10 3 3 3 ) as an answer, but some students may be unable to determine what the product is. Not Meeting the Benchmark Students who do not meet the benchmark may draw a separate representation for each of the numbers in the problems and/or manipulate the numbers in some way that is not based on an understanding of the problem (e.g., by adding the numbers). They might not draw any representation. They might treat each of the numbers as whole numbers, and randomly multiply two or all three of those numbers (e.g., 5 2 3). CC70 Investigation 3A Multiplying Fractions

Name Fraction Cards and Decimal Squares Date Subtracting Fractions Solve each problem and show your work. For the word problems, write an equation. 1. There was 7_ of a pan of brownies on the table. Some friends 8 came over and ate _ of the pan of brownies. What fraction of 8 the pan of brownies is left? 2. Marisol walks to school. The school is 6 of a mile from her 10 house. She has already walked of a mile. How much farther 10 does Marisol have to walk? 3. There was 7 of a gallon of milk in the refrigerator. The Jones 12 family used 3 of the gallon during breakfast. How much milk 12 remains?. 5 2 5 = 5. 9 12 5 12 = Unit 6 Session 1.8A C29 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice More Subtracting Fractions Solve each problem and show your work. For the word problems, write an equation. note Students solve subtraction problems involving fractions with like denominators. 1. There is 7_ of a carton of juice in the refrigerator. The Ortega 8 family drank 5_ of the carton with their breakfast. What fraction 8 of the carton remains? 2. Venetta was walking to the library, which is 3_ of a mile away. She has walked 1_ of a mile. How much farther does Venetta have to walk? 3. Richard had _ of a bag of carrots. He fed 2_ of the bag to his 5 5 rabbit. What fraction of the bag did Richard have left?. 7 10 10 = 5. 6 8 1 8 = Unit 6 Session 1.8A C30 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice Fraction Subtraction Solve each problem and show your work. For the word problems, write an equation. note Students solve subtraction problems involving fractions with like denominators.. 1. There is 5_ of a pot of soup on the stove. The Kim family ate _ of the 6 6 pot of soup. What fraction of the pot of soup remains? 2. Nadeem is walking to the park, which is 9 of a mile away. He has 10 walked of a mile. How much farther does Nadeem have to walk? 10 3. Tonya had 10 of a yard of fabric. She used 5 of a yard of fabric to 12 12 make a lamp shade. What fraction of a yard of fabric is left?. 7 8 2 8 = 5. 3 5 1 5 = Unit 6 Session 2.1 C31 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Butterfly Wingspans (page 1 of 2) Yuki went to the Natural History Museum to study butterflies. The information he has about some of the butterflies in the collection is shown below. Name Wingspan (inches) Name Wingspan (inches) American Snout 1 1_ 2 Pearl Crescent 1 5_ 8 Giant Swallowtail 5 1_ Postman 2 1_ 2 Julia 3 1_ 2 Red Admiral 3 1_ 8 Milbert s Tortoiseshell 2 5_ 8 Saturn 1_ Monarch 3 1_ 2 Painted Lady 2 1_ 2 Tiger Swallowtail Viceroy 3 3_ 2 7_ 8 Record the measurements on the line plot below. 0 1 2 3 5 6 Butterfly Wingspans (inches) Write three statements that describe the data. Unit 6 Session 2.7A C32 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Butterfly Wingspans (page 2 of 2) Use the information on the previous page to solve the following problems. Show your work. 1. How much longer is the wingspan of the Viceroy butterfly than the wingspan of the Pearl Crescent butterfly? 2. How much longer is the wingspan of the Giant Swallowtail butterfly than the wingspan of the Tiger Swallowtail butterfly? 3. The American Snout butterfly and the Postman butterfly are side-by-side. What is the length of their combined wingspans?. How much longer is the wingspan of the Red Admiral butterfly than the wingspan of Milbert s Tortoiseshell butterfly? 5. The Pearl Crescent butterfly and the Viceroy butterfly are sideby-side. What is the length of their combined wingspans? 6. The Saturn butterfly and the Tiger Swallowtail butterfly are sideby-side. What is the length of their combined wingspans? Unit 6 Session 2.7A C33 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice Pepper s Puppies Cheyenne s dog, Pepper, had puppies. Cheyenne recorded their weights in the line plot below. note Students solve addition and subtraction problems involving fractions using data given in a line plot. X X X X X X 0 1 8 1 3 8 1 2 5 8 3 7 1 1 1 1 1 1 3 1 1 8 8 8 2 Weights of Pepper s Puppies (pounds) Solve each problem and show your work. 1. Two puppies weighed the same amount. What was the total weight of the two puppies? 2. How many more pounds did the heaviest puppy weigh than the lightest puppy? 3. The heaviest puppy gained _ of a pound in its first month. 8 How much did it weigh after the first month? Unit 6 Session 2.7A C3 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Multiplying Whole Numbers and Fractions Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. 1. Jake bought three kinds of pizza for a party. Each pizza was the same size. People were not very hungry, and at the end of the party there was 3_ of each pizza left. How much pizza was left in all? 2. A class is counting by 2_ s. What number does the 7th person say? 6 3. 6 1 3 =. 3 3 8 = Unit 6 Session 3A.1 C35 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice Chunks of Cheese Morris Mouse s Cheese House sells chunks of cheese. Each chunk weighs 3_ of a pound. Find the total weight of each kind of cheese. Use a representation to solve each problem. Also, write a multiplication equation that represents the problem. Show your work. note Students solve problems involving multiplication of a whole number and a fraction. 1. 5 chunks of cheddar cheese 2. 10 chunks of Swiss cheese Total weight Total weight 3. chunks of American cheese. 8 chunks of parmesan cheese Total weight Total weight Unit 6 Session 3A.1 C36 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Multiplying Fractions and Whole Numbers Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. 1. A grocery store sells bags of 9 apples. Anna used 2_ of the apples 3 in a bag in an apple pie. How many apples did she use in the pie? 2. Steve was in a 7 mile race. He ran 1_ 2 many miles did he run? of it and walked the rest. How 3. 2 12 = 3. There are 10 boys in class. _ of them have brown hair. How many 5 boys have brown hair? 5. 5 16 = 8 6. 1 11 = 2 Unit 6 Session 3A.2 C37 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date More Multiplying Fractions and Whole Numbers Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. 1. Sabrina walks to school. Her house is 3_ of a mile from school. 8 How many miles would she walk to and from school in 5 days? 2. 6 2 5 = 3. Damian has a recipe that calls for 2_ of a cup of flour. He wants to 3 make times the recipe. How much flour does he need?. 3 3 = Unit 6 Session 3A.2 C38 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice Multiplying with Fractions Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. note Students solve problems involving multiplication of whole numbers and fractions. 1. 1 5 = 2. 3 16 = 3. 1 6 9 =. 12 1 2 = 5. Mr. Garcia has 15 grandchildren. 2_ of them are girls. 3 How many are girls? 6. Helena needs 8 pieces of wire. Each piece needs to be 3_ of a foot long. What is the total length of the wire Helena needs? Unit 6 Session 3A.2 C39 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Multiplying Fractions Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. 1. In the store Damian found pretzels that came in 1_ -pound bags. 3 He bought 5 bags of pretzels. How many pounds of pretzels did he buy? 2. 3 6 8 = 3. There were 25 students in class. One day, 3_ of them wore 5 sneakers. How many students wore sneakers?. 7 10 = 5. Jill used stones that were each 3_ of a foot high to build a wall. She piled 6 stones on top of each other. How many feet high was her wall? 6. 5 12 = 6 Unit 6 Session 3A.3 C0 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Assessment: Multiplying with Fractions Use a representation to solve each problem. For the word problem, write an equation that represents the problem. 1. Ursula bought 30 apples. 3_ of them are green. How 5 many of the apples are green? 2. 5 2 3 = Unit 6 Session 3A.3 C1 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice All Kinds of Nuts Use a representation to solve each problem. Also, write an equation that represents the problem. note Students solve problems involving multiplication of whole numbers and fractions. 1. Emaan bought 6 bags of walnuts. Each bag contained 3_ of a pound of walnuts. What was the total weight of the walnuts? 2. A man bought 12 boxes of nuts. He took 1_ of the boxes to his 6 office. How many boxes of nuts did he take to the office? 3. Kimberly is making 3 loaves of nut bread. For each loaf, she needs 3_ of a cup of pecans. How many cups of pecans does she need? Circle the best answer below. between 3 and cups between 2 and 3 cups between 1 and 2 cups Unit 6 Session 3A.3 C2 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice Bug Collections The science class collected crickets and beetles. The students made line plots to show the lengths of the insects. note Students solve addition and subtraction problems involving fractions using data given in a line plot. X X X X X X X X X X X 0 1 8 1 3 8 1 2 5 8 3 7 1 1 1 1 1 1 3 1 1 1 5 1 3 1 2 8 8 8 2 8 8 7 Lengths of Crickets (inches) X X X X X X X X X X X X X X 0 1 8 1 3 8 1 2 5 8 3 7 1 1 1 1 1 1 3 1 1 1 5 1 3 1 2 8 8 8 2 8 8 7 Lengths of Beetles (inches) 1. How much longer is the longest cricket than the shortest cricket? 2. How much longer is the longest beetle than the shortest beetle? 3. The cricket Benson found is 1 1_ inches long. How much longer is 8 this cricket than the shortest one in the collection?. The beetle Tonya found is 1 1_ inches long. How much shorter is this beetle than the longest one in the collection? Unit 6 Session 3.1 C3 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice Buying Fabric Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. note Students solve problems involving multiplication of a whole number by a fraction. 1. Bill bought 6 pieces of yellow fabric. Each piece was 1_ 3 of a yard long. How many yards of fabric did Bill buy in all? 2. Kimberly bought 2 pieces of blue fabric. Each piece was 7_ 8 of a yard long. How many yards of fabric did Kimberly buy in all? 3. Alejandro bought 7 pieces of red fabric. Each piece was 3_ of a yard long. How many yards of fabric did Alejandro buy in all?. 2 3 10 = 5. 9 1 6 = Unit 6 Session 3. C Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice Multiplying with Fractions Use a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem. note Students solve problems involving multiplication of whole numbers and fractions. 1. 1 5 8 = 2. 6 2 3 = 3. 2 5 6 =. 7 8 8 = 5. LaTanya had a piece of fabric that was 3 yards long. She used 1_ of it to make a skirt. How much of the fabric did she use? 2 6. Benson had 16 marbles. He gave 3_ 8 of them away. How many marbles did he give away? Unit 6 Session 3.5 C5 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name Fraction Cards and Decimal Squares Date Daily Practice Working Hard Use a representation to solve each problem. Also, write an equation that represents the problem. note Students solve problems involving multiplication of whole numbers and fractions. 1. Last week, Ms. Cortez sold 2 computers. 5_ of them were laptops. 8 How many laptops did Ms. Cortez sell? 2. An office building has 1 offices, all the same size. A painter uses 3_ of a gallon of paint to paint one office ceiling. How much paint will the painter need to paint all of the office ceilings? 3. Mr. Stein bikes to work. The roundtrip distance he bikes each day is 7_ of a mile. What is the total distance he bikes in 5 days? Circle 8 the best answer below. between 6 and 7 miles between 5 and 6 miles between and 5 miles Unit 6 Session 3.6 C6 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Restas de fracciones Resuelve cada problema y muestra tu trabajo. Para los problemas verbales, escribe una ecuación. 1. Había 7_ de una bandeja de brownies sobre la mesa. Vinieron 8 algunos amigos y se comieron _ de la bandeja de brownies. 8 Qué fracción de la bandeja de brownies queda? 2. Marisol camina a la escuela. La escuela está a 6 de milla 10 de su casa. Ya ha caminado de milla. Cuánto más tiene 10 que caminar Marisol? 3. Había 7 de un galón de leche en el refrigerador. La familia 12 Jones usó 3 del galón durante el desayuno. Cuánta 12 leche queda?. 5 2 5 = 5. 9 12 5 12 = Unidad 6 Sesión 1.8A C29 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Más restas de fracciones Resuelve cada problema y muestra tu trabajo. Para los problemas verbales, escribe una ecuación. Práctica diaria nota Los estudiantes resuelven problemas de resta que incluyen fracciones con el mismo denominador. 1. Hay 7_ de un envase de jugo en el refrigerador. La 8 familia Ortega bebió 5_ del envase en el desayuno. Qué 8 fracción queda del envase? 2. Venetta caminaba a la biblioteca, que está a 3_ de milla de distancia. Ha caminado 1_ de milla. Cuánto más tiene que caminar Venetta? 3. Richard tenía _ de una bolsa de zanahorias. Alimentó a su 5 conejo con 2_ de la bolsa. Qué fracción de la bolsa le queda 5 a Richard?. 7 10 10 = 5. 6 8 1 8 = Unidad 6 Sesión 1.8A C30 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Restas de fracciones Resuelve cada problema y muestra tu trabajo. Para los problemas verbales, escribe una ecuación. Fecha Práctica diaria nota Los estudiantes resuelven problemas de resta que incluyen fracciones con el mismo denominador. 1. Hay 5_ 6 de una olla de sopa sobre la estufa. La familia Kim comió _ 6 de la olla de sopa. Qué fracción queda de la olla de sopa? 2. Nadeem camina al parque, que está a 9 de milla de distancia. Ha 10 caminado de milla. Cuánto más tiene que caminar Nadeem? 10 3. Tonya tenía 10 de yarda de tela. Usó 5 de la yarda de tela para 12 12 hacer una pantalla de lámpara. Qué fracción queda de la yarda de tela?. 7 8 2 8 = 5. 3 5 1 5 = Unidad 6 Sesión 2.1 C31 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Envergaduras de mariposas (página 1 de 2) Yuki fue al Museo de Historia Natural a estudiar las mariposas. Abajo se muestra la información que tiene sobre algunas mariposas de la colección. Nombre Envergadura (pulgadas) Picuda 1 1_ 2 Mariposa macaón gigante Nombre Perla creciente Envergadura (pulgadas) 1 5_ 8 5 1_ Cartero 2 1_ 2 Julia 3 1_ 2 Almirante rojo 3 1_ 8 Mariposa concha de Milbert Monarca 3 1_ 2 2 5_ 8 Saturn 1_ Mariposa de cola de golondrina 3 3_ Vanesa de los cardos 2 1_ 2 Virrey 2 7_ 8 Anota las medidas en el diagrama de puntos de abajo. 0 1 2 3 5 6 Envergaduras de mariposas (pulgadas) Escribe tres enunciados que describan los datos. Unidad 6 Sesión 2.7A C32 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Envergaduras de mariposas (página 2 de 2) Usa la información de la página anterior para resolver los siguientes problemas. Muestra tu trabajo. 1. Cuánto más larga es la envergadura de la mariposa virrey que la envergadura de la mariposa perla creciente? 2. Cuánto más larga es la envergadura de la mariposa macaón gigante que la envergadura de la mariposa de cola de golondrina? 3. La mariposa picuda y la mariposa cartero están una junto a la otra. Cuál es la longitud de sus envergaduras combinadas?. Cuánto más larga es la envergadura de la mariposa almirante rojo que la envergadura de la mariposa concha de Milbert? 5. La mariposa perla creciente y la mariposa virrey están una junto a la otra. Cuál es la longitud de sus envergaduras combinadas? 6. La mariposa saturn y la mariposa de cola de golondrina están una junto a la otra. Cuál es la longitud de sus envergaduras combinadas? Unidad 6 Sesión 2.7A C33 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Los cachorros de Pepper La perra de Cheyenne, Pepper, tuvo cachorros. Cheyenne anotó sus pesos en el siguiente diagrama de puntos. Práctica diaria nota Los estudiantes resuelven problemas de suma y resta que incluyen fracciones usando los datos proporcionados en un diagrama de puntos. X X X X X X 0 1 8 1 3 8 1 2 5 8 3 7 1 1 1 1 1 1 3 1 1 8 8 8 2 Pesos Weights de los cachorros of Pepper s de Puppies Pepper (pounds) (libras) Resuelve cada problema y muestra tu trabajo. 1. Dos cachorros pesaban la misma cantidad. Cuál fue el peso total de los dos cachorros? 2. Cuántas libras más pesaba el cachorro más pesado que el cachorro más liviano? 3. El cachorro más pesado aumentó _ de libra durante su primer mes. 8 Cuánto pesaba después del primer mes? Unidad 6 Sesión 2.7A C3 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Multiplicar números enteros no negativos y fracciones Usa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema. 1. Jake compró tres tipos de pizza para una fiesta. Cada pizza era del mismo tamaño. Las personas no tenían mucha hambre y al final de la fiesta quedaron 3_ de cada pizza. Cuánta pizza quedó en total? 2. Una clase está contando de 2_ en 6 2_. Qué número dice la séptima 6 persona? 3. 6 1 3 =. 3 3 8 = Unidad 6 Sesión 3A.1 C35 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Trozos de queso Fecha La Casa de queso Morris Mouse vende trozos de queso. Cada trozo pesa 3_ de libra. Halla el peso total de cada tipo de queso. Usa una representación para resolver cada problema. También, escribe una ecuación de multiplicación que represente el problema. Muestra tu trabajo. Práctica diaria nota Los estudiantes resuelven problemas que incluyen la multiplicación de un número entero no negativo y una fracción. 1. 5 trozos de queso cheddar 2. 10 trozos de queso suizo Peso total Peso total 3. trozos de queso americano. 8 trozos de queso parmesano Peso total Peso total Unidad 6 Sesión 3A.1 C36 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Multiplicar fracciones y números enteros no negativos Usa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema. 1. Una tienda de abarrotes vende bolsas de 9 manzanas. Ana usó 2_ de las manzanas de una bolsa en una tarta 3 de manzana. Cuántas manzanas usó en la tarta? 2. Steve participó en una carrera de 7 millas. Corrió durante 1_ 2 de la carrera y caminó el resto. Cuántas millas corrió? 3. 2 12 = 3. Hay 10 chicos en la clase. _ de ellos tienen cabello café. 5 Cuántos chicos tienen cabello café? 5. 5 16 = 8 6. 1 11 = 2 Unidad 6 Sesión 3A.2 C37 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Multiplicar más fracciones y números enteros no negativos Usa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema. 1. Sabrina camina a la escuela. Su casa está a 3_ de milla de la 8 escuela. Cuántas millas caminará de ida y vuelta, entre su casa y la escuela, en 5 días? 2. 6 2 5 = 3. Damián tiene una receta que requiere 2_ de taza de harina. Quiere 3 preparar porciones más de la receta. Cuánta harina necesita?. 3 3 = Unidad 6 Sesión 3A.2 C38 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Multiplicar con fracciones Usa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema. Práctica diaria nota Los estudiantes resuelven problemas que incluyen la multiplicación de números enteros no negativos y fracciones. 1. 1 5 = 2. 3 16 = 3. 1 6 9 =. 12 1 2 = 5. El Sr. García tiene 15 nietos. 2_ de ellos son niñas. 3 Cuántas son niñas? 6. Elena necesita 8 pedazos de alambre. Cada pedazo debe medir 3_ de pie de largo. Cuál es la longitud total del alambre que necesita Elena? Unidad 6 Sesión 3A.2 C39 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Multiplicar fracciones Usa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema. 1. En la tienda, Damián buscó pretzels que vienen en bolsas de 1_ de libra. Compró 5 bolsas de pretzels. Cuántas libras 3 de pretzels compró? 2. 3 6 8 = 3. En la clase había 25 estudiantes. Un día, 3_ de ellos 5 llevaron tenis. Cuántos estudiantes llevaron tenis?. 7 10 = 5. Para construir una pared, Jill usó piedras que medían 3_ de pie de alto cada una. Apiló 6 piedras una sobre otra. Cuántos pies de alto medía su pared? 6. 5 12 = 6 Unidad 6 Sesión 3A.3 C0 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Evaluación: Multiplicar con fracciones escritura Usa una representación para resolver cada problema. Para el problema verbal, escribe una ecuación que represente el problema. 1. Úrsula compró 30 manzanas. 3_ de ellas son verdes. 5 Cuántas de las manzanas son verdes? 2. 5 2 3 = Unidad 6 Sesión 3A.3 C1 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Todo tipo de frutos secos Usa una representación para resolver cada problema. También, escribe una ecuación que represente el problema. Fecha Práctica diaria nota Los estudiantes resuelven problemas que incluyen la multiplicación de números enteros no negativos y fracciones. 1. Emaan compró 6 bolsas de nueces. Cada bolsa contenía 3_ de libra de nueces. Cuál era el peso total de las nueces? 2. Un hombre compró 12 cajas de frutos secos. Llevó 1_ de las 6 cajas a su oficina. Cuántas cajas de frutos secos llevó a la oficina? 3. Kimberly está preparando 3 panes de frutos secos. Para cada pan, necesita 3_ de taza de pacanas. Cuántas tazas de pacanas necesita? Encierra en un círculo la mejor respuesta. entre 3 y tazas entre 2 y 3 tazas entre 1 y 2 tazas Unidad 6 Sesión 3A.3 C2 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Colecciones de insectos La clase de ciencias recolectó grillos y escarabajos. Los estudiantes hicieron diagramas de puntos para mostrar las longitudes de los insectos. Práctica diaria X X X X X X X X X X X nota Los estudiantes resuelven problemas de suma y resta que incluyen fracciones usando los datos proporcionados en un diagrama de puntos. 0 1 8 1 3 8 1 2 5 8 3 7 1 1 1 1 1 1 3 1 1 1 5 1 3 1 2 8 8 8 2 8 8 7 Longitudes de los grillos (pulgadas) X X X X X X X X X X X X X X 0 1 8 1 3 8 1 2 5 8 3 7 1 1 1 1 1 1 3 1 1 1 5 1 3 1 2 8 8 8 2 8 8 7 Longitudes de los escarabajos (pulgadas) 1. Cuánto más largo es el grillo más largo que el grillo más corto? 2. Cuánto más largo es el escarabajo más largo que el escarabajo más corto? 3. El grillo que encontró Benson mide 1 1_ pulgadas de longitud. 8 Cuánto más largo es este grillo que el más corto de la colección?. El escarabajo que encontró Tonya mide 1 1_ pulgadas de longitud. Cuánto más corto es este escarabajo que el más largo de la colección? Unidad 6 Sesión 3.1 C3 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Comprar tela Usa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema. Práctica diaria 1. Bill compró 6 pedazos de tela amarilla. Cada pedazo medía 1_ de yarda de longitud. Cuántas yardas de tela 3 compró Bill en total? nota Los estudiantes resuelven problemas que incluyen la multiplicación de un número entero no negativo por una fracción. 2. Kimberly compró 2 pedazos de tela azul. Cada pedazo medía 7_ de yarda de longitud. Cuántas yardas de tela compró 8 Kimberly en total? 3. Alejandro compró 7 pedazos de tela roja. Cada pedazo medía 3_ de yarda de longitud. Cuántas yardas de tela compró Alejandro en total?. 2 3 10 = 5. 9 1 6 = Unidad 6 Sesión 3. C Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Fecha Multiplicar con fracciones Usa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema. Práctica diaria nota Los estudiantes resuelven problemas que incluyen la multiplicación de números enteros no negativos y fracciones. 1. 1 5 8 = 2. 6 2 3 = 3. 2 5 6 =. 7 8 8 = 5. LaTanya tenía un pedazo de tela que medía 3 yardas de longitud. Usó 1_ de la tela para hacer una falda. Cuánta 2 tela usó? 6. Benson tenía 16 canicas. Regaló 3_ 8 de las canicas. Cuántas canicas regaló? Unidad 6 Sesión 3.5 C5 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Tarjetas de fracciones y cuadrados de decimales Trabajar duro Usa una representación para resolver cada problema. También, escribe una ecuación que represente el problema. Fecha Práctica diaria nota Los estudiantes resuelven problemas que incluyen la multiplicación de números enteros no negativos y fracciones. 1. La semana pasada, la Srta. Cortez vendió 2 computadoras. 5_ 8 de ellas eran computadoras portátiles. Cuántas computadoras portátiles vendió la Srta. Cortez? 2. Un edificio de oficinas tiene 1 oficinas, todas del mismo tamaño. Un pintor usa 3_ de galón de pintura para pintar el techo de una oficina. Cuánta pintura necesitará el pintor para pintar los techos de todas las oficinas? 3. El Sr. Stein va en bicicleta al trabajo. La distancia del viaje de ida y vuelta en bicicleta cada día es de 7_ de milla. Cuál es la distancia 8 total que anda en bicicleta en 5 días? Encierra en un círculo la mejor respuesta. entre 6 y 7 millas entre 5 y 6 millas entre y 5 millas Unidad 6 Sesión 3.6 C6 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Unit 8 How Many Packages? How Many Groups? Common Core Mathematical Practices (MP) Domains Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) Measurement and Data (MD) INVESTIG ATION 1 Multiplication with 2-Digit Numbers Teach this Investigation as is. Day Session Common Core Adaptation Common Core Standards 1 1.1 Making Estimates MP1 2 1.2 Breaking Numbers Apart MP1.NBT.5 3 1.3 Multiplication Cluster Problems 1. Assessment: Solving Multiplication Problems MP7.NBT.5 MP7.OA.5,.NBT.5 5 1.5 Solving 2-Digit Problems MP7.OA.3,.OA.5,.NBT.5 CC82 Unit 8 How Many Packages? How Many Groups?

INVESTIG ATION 2 Strategies for Multiplication Day Session Common Core Adaptation Common Core Standards 6 2.1 Making an Easier Problem MP3.OA.3,.NBT.5,.MD.2 7 2.2 How Did You Start? MP3, MP8.OA.3,.NBT.5 8 2.3 How Did You Start?, continued 9 2.A Multiplying -Digit by 1-Digit Numbers See p. CC85. MP3, MP8.NBT.5 MP3, MP8.OA.3,.NBT.5,.MD.2 10 2. Practicing Multiplication MP3, MP8 SESSION FOLLOW-UP Daily Practice: In addition to Student Activity Book page 33,.OA.5,.NBT.5 Daily Practice students complete Student Activity Book page 31D or C60 (How Many Legs?) for reinforcement of the content of this unit. 11 2.5 Assessment: 3 68 MP8.OA.5,.NBT.5 Instructional Plan CC83

INVESTIG ATION 3 Solving Division Problems Day Session Common Core Adaptation Common Core Standards 12 3.1 How Many Groups Can You Make? MP1.NBT.5,.NBT.6,.MD.2 13 3.2 Solving Division Problems MP1, MP5.OA.5,.NBT.6 1 3.3 Solving Division Problems, continued 15 3. Sharing Division Strategies 16 3.5A Dividing -Digit Numbers See p. CC90. MP1.NBT.6 17 3.5 Solving Problems in Context SESSION FOLLOW-UP Daily Practice Daily Practice: In addition to Student Activity Book page 53, students complete Student Activity Book page 51D or C6 (Flea Market) for reinforcement of the content of this unit. MP1, MP5.OA.3,.OA.5,.NBT.6 MP1, MP5, MP8.OA.5,.NBT.5,.NBT.6 MP1.OA.3,.OA.5,.NBT.5,.MD.2 18 3.6 End-of-Unit Assessment MP1, MP2, MP3.OA.5,.NBT.5,.NBT.6 CC8 Unit 8 How Many Packages? How Many Groups?

s e s s i o n 2. A Multiplying -Digit by 1-Digit Numbers Math Focus Points Multiplying a -digit number by a 1-digit number Today s Plan activity Closest Estimate with -Digit Numbers activity Multiplying Larger Numbers Discussion Sharing Our Strategies SESSION FOLLOW-UP Daily Practice 10 Min Class 35 Min Class Individuals 15 Min Class Materials Student Activity Book, pp. 31A 31B or C57 C58, Multiplying -Digit Numbers by 1-Digit Numbers Make copies. (as needed) Students completed copies of Student Activity Book, p. 31A or C57 (from Activity 2) Student Activity Book, p. 31C or C59, Driving Around Make copies. (as needed) Student Math Handbook, pp. 0 3 Ten-Minute Math Note The Ten-Minute Math activity for today s session, Closest Estimate with -Digit Numbers, is introduced in this session. Plan to do today s Ten-Minute Math activity sometime after math class, or if it is not possible, do Practicing Place Value with -digit numbers, as in Session 1. of Curriculum Unit 6. Closest Estimate with -Digit Numbers Write each of the following problems on the board, one at a time: 1. 2,366 6 1,000 18,000 2,000 2.,227 8,000 33,000 0,000 3. 3,02 5 1,500 10,000 15,000 Give students approximately 30 seconds to look at the three possible estimates and determine which is the closest to the actual answer. Have two or three students explain their reasoning for each problem. Ask students: How did you break the numbers apart? How did you determine the magnitude of your answer? If you changed the numbers in the problem, how did you change them and why? Also ask if the closest estimate is greater than or less than the actual answer and how students know. Session 2.A Multiplying -Digit by 1-Digit Numbers CC85

1 Activity 2 Activity 3 Discussion Session Follow-Up A C T I V I T Y Closest Estimate with -Digit Numbers Write the following on the board: 1,25 6 700 7,000 70,000 10 Min Give students approximately 30 seconds to look at the three possible estimates that are provided and determine which is the closest to the actual answer. Have two or three students explain their reasoning for the problem. Ask students: How did you break the numbers apart? How did you determine the magnitude of your answer? If you changed the numbers in the problem, how did you change them and why? Ask if the closest estimate is greater than or less than the actual answer and how students know. Then ask questions about multiplying -digit numbers by 1-digit numbers. class In this problem you estimated the product of a -digit number and a 1-digit number. Was this harder or easier than estimating the product of two 2-digit numbers? If time permits, write another problem on the board: 3,560 3 1,000 10,000 15,000 Give students approximately 30 seconds to look at the three possible estimates that are provided and determine which is the closest to the actual answer. Have two or three students explain their reasoning for the problem. Ask the same questions as before. Today you will multiply -digit numbers by 1-digit numbers. As you solve these problems, think about the magnitude and reasonableness of your answers. A C T I V I T Y Multiplying Larger Numbers 35 Min class individuals Tell students that today they will use some of the multiplication strategies they ve practiced to multiply -digit numbers. Write Problem 1 from Student Activity Book page 31A or C57 on the board or overhead. CC86 Investigation 2 Strategies for Multiplication

1 Activity 2 Activity 3 Discussion Session Follow-Up 1,58 students attend the Sunset Elementary School. The principal wants to make sure each student gets 5 pencils to start the school year. How many pencils does she need to buy? Ask students to solve this problem. Suggest students might want to use a story context or array to help them keep track of the parts of the problem. As you listen to them discuss the problem, ask questions such as the following: What is a reasonable way to break up the problem? How can you keep track of all the parts? How can estimating the product help you check to see if your answer is reasonable? Give students time to complete the problem. Then ask them to share how they determined the number of pencils. As they respond, record their strategies on the board. Students might say: I broke up 1,58 into four parts: 1,000; 500; 0; and 8. Then I multiplied each part by 5 and added everything up. The principal should buy 7,70 pencils. 1,58 5 5 1,000 5,000 5 500 2,500 5 0 200 5 8 0 5,000 2,500 200 0 7,70 I did 1500 5 7,500 and 8 5 20, so it s 7,70. Ask if anyone drew an array for the problem or display one yourself. Session 2.A Multiplying -Digit by 1-Digit Numbers CC87

1 Activity 2 Activity 3 Discussion Session Follow-Up Name Date How Many Packages? How Many Groups? 1,58 Multiplying -Digit Numbers by 1-Digit Numbers (page 1 of 2) Solve each problem and show your work. 1. 1,58 students attend the Sunset Elementary School. The principal wants to make sure each student gets 5 pencils to start the school year. How many pencils does she need to buy? 1,000 5 2. The Fresh Fruit Company can fit 2,650 oranges in one truck. One day they sent out 3 trucks full of oranges to deliver the fruit to grocery stores. How many oranges did they send out that day? 5 1,000 500 0 8 5 500 5 5 0 8 3. 2,12 = Pearson Education. 3,670 9 = Session 2.A Unit 8 31A Student Activity Book, Unit 8, p. 31A; Resource Masters, C57 INV12_SE0_U8.indd 1 6/1/11 :2 PM Name Discuss the equation that represents this problem: 1,58 5 = 7,70. Ask students to relate each number in the equation to the story about the pencils. Have students complete Student Activity Book pages 31A and 31B or C57 and C58. Date How Many Packages? How Many Groups? Multiplying -Digit Numbers by 1-Digit Numbers (page 2 of 2) Ongoing Assessment: Observing Students at Work Solve each problem and show your work. Students multiply -digit numbers by 1-digit numbers. 5. There are 6 schools in town. Each school serves 1,09 lunches each week. How many lunches are served by the schools in the town each week? Can students solve the problems accurately? What strategies do students use to solve the problems? Were they able to keep track of all the parts of the four- 6. Seven truck drivers each drove,215 miles in a two-week period. How many miles did they drive in all? digit number? Do they use arrays or area models? Do they use equations? 7. 8,37 2 = Pearson Education 8.,750 8 = 31B Unit 8 Session 2.A Student Activity Book, Unit 8, p. 31B; Resource Masters, C58 INV12_SE0_U8.indd 2 6/1/11 :2 PM differentiation: Supporting the Range of Learners For students who have difficulty choosing strategies to solve these problems, provide them with a few strategies to choose from, including breaking the -digit number apart by place. For example, for the problem 1,58 5, give 1,000 5 and ask what else still needs to be done. For students who quickly solve these problems, give them some -digit by 2-digit or -digit by 3-digit multiplication problems to solve. CC88 Investigation 2 Strategies for Multiplication INV12_TE0_U08_S2.A.indd 88 6/3/11 :37 PM

1 Activity 2 Activity 3 Discussion Session Follow-Up Name Discussion Sharing Our Strategies Date How Many Packages? How Many Groups? 15 Min Daily Practice Driving Around class Ms. Ortega drives her truck to different cities throughout the year. The table shows the roundtrip distance to each city and how many times she made each trip last year. For each city in the table, show the total number of miles Ms. Ortega drove. NoTe Students multiply -digit numbers by 1-digit numbers. Use the space below the table to show your work. Math Focus Points for Discussion City Roundtrip Distance Number of Trips 1,8 3 Gainesville, FL 1,850 6 Seattle, WA 3,528 8 Sacramento, CA 2,922 5 Lincoln, NE Multiplying a -digit number by a 1-digit number Total Number of Miles Did you find that you could use the same multiplication strategies you ve been using with smaller numbers for these problems? What was the same or different? At first, you may think these problems are harder to solve than multiplication problems with 2-digit numbers. Is that true? Why or why not? Pearson Education Have one or two students share their strategies for Problem 3 on Student Activity Book page 31A or C57 and write their solutions on the board. Ask questions about multiplying with -digit numbers. Session 2.A Unit 8 31C Student Activity Book, Unit 8, p. 31C; Resource Masters, C59 INV12_SE0_U8.indd 3 6/3/11 10:27 AM Students might say: In some ways it s easier because you re only multiplying by one number, but there s more to keep track of. They look harder because one number is in the thousands. But since you only multiply by one number, it s easier! Session Follow-Up Daily Practice Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page 31C or C59. Student Math Handbook: Students and families may use Student Math Handbook pages 0 3 for reference and review. See pages 135 138 in the back of Unit 8. Session 2.A Multiplying -Digit by 1-Digit Numbers CC89 INV12_TE0_U08_S2.A.indd 89 6/3/11 :39 PM

s e s s i o n 3. 5 A Dividing -Digit Numbers Math Focus Points Dividing a -digit number by a 1-digit number Today s Plan activity Dividing Larger Numbers 5 Min Class Individuals Materials Student Activity Book, pp. 51A 51B or C61 C62, Dividing -Digit Numbers by 1-Digit Numbers Make copies. (as needed) Discussion First Steps 15 Min Class Student Activity Book, p. 51A or C61 (completed) Session Follow-Up Daily Practice Student Activity Book, p. 51C or C63, Dividing Large Numbers Make copies. (as needed) Student Math Handbook, pp. 50 52 Ten-Minute Math Closest Estimate with -Digit Numbers Write each of the following problems on the board, one at a time: 1. 3,725 90 700 900 2. 5,953 7 800 1,200 1,600 3. 8,68 6 1,000 1,00 1,800 Give students approximately 30 seconds to look at the three possible estimates and determine which is the closest to the actual answer. Have two or three students explain their reasoning for each problem. Ask students: How did you break the numbers apart? How did you determine the magnitude of your answer? If you changed the numbers in the problem, how did you change them and why? Also ask if the closest estimate is greater than or less than the actual answer and how students know. CC90 Investigation 3 Solving Division Problems

1 Activity 2 Discussion 3 Session Follow-Up A C T I V I T Y Dividing Larger Numbers 5 Min class individuals Tell students that today they will use some of the division strategies they ve practiced to divide -digit numbers. Write Problem 1 from Student Activity Book page 51A or C61 on the board or overhead. In one day at Honeysweet Apple Orchard, workers picked 1,59 apples. They want to put them in bags of 6. How many bags can they make? Ask students to solve this problem. Suggest students use a story context to help them keep track of the parts of the problem. As you listen to students discuss the problem, ask questions such as the following: Do you think there will be more or fewer than 10 bags? 100 bags? 1,000 bags? Why? How can multiplication help you solve the problem? Bring the class back together and ask students to share how they determined the number of bags. As they respond, record their strategies on the board. Students might say: I started with 100 bags. That was only 600 apples. I doubled that and I got 1,200 apples, so then I was getting closer. I had 39 more apples to put in bags. 6 60 360, so that was too much. I did 6 50 300, and had 9 more apples to go. That s 8 more bags and 1 apple left over. One apple isn t enough to fill another bag, so I just ignored it. Add up the bags: 200 50 8 258 bags. 6 100 = 600 1,59 6 6 60 = 360 6 200 = 1,200 1,59 1,200 = 39 6 50 = 300 39 300 = 9 200 + 50 + 8 = 258 9 6 is 8 R 1 Session 3.5A Dividing -Digit Numbers CC91

1 Activity 2 Discussion 3 Session Follow-Up Name Students might say: I broke up the 1,59 apples into 1,200 apples and 39 apples. I drew a big box for the 1,200 apples and a smaller one for the 39 apples. I made groups of 6 out of each part and I kept track of it under the drawing. Date How Many Packages? How Many Groups? Dividing -Digit Numbers by 1-Digit Numbers (page 1 of 2) Solve each problem and show your work. 1. In one day at Honeysweet Apple Orchard, workers picked 1,59 apples. They want to put them in bags of 6. How many bags can they make? 2. 1,00 children signed up to play in the Smith City youth basketball league. 8 children will be placed on each team. How many teams of 8 players will there be? 3. 2,831 5 = Pearson Education. 5,36 7 = Session 3.5A Unit 8 39 apples 1,200 6 = 200 300 6 = 50 9 6 is 8 R1 200 bags 58 bags 51A Student Activity Book, Unit 8, p. 51A; Resource Masters, C61 INV12_SE0_U8.indd 1 6/1/11 :58 PM Name 1,200 apples Date How Many Packages? How Many Groups? Dividing -Digit Numbers by 1-Digit Numbers (page 2 of 2) Solve each problem and show your work. 258 bags 5. 1,52 shirts were delivered to a large department store. They came in boxes of. How many boxes were delivered? 6. 3,018 letters need to be mailed out to members of the City Service Club. Five people are stuffing the envelopes. How should they divide up the task so that each person will stuff the same number of envelopes? 7.,698 9 = Pearson Education 8. 2,287 3 = 51B Unit 8 Session 3.5A Student Activity Book, Unit 8, p. 51B; Resource Masters, C62 INV12_SE0_U8.indd 2 6/1/11 :59 PM Some students might not need to make representations of the problem, but they should have a visual image of what is happening when a number of objects is divided into equal-sized groups. Emphasize the groups of 6 that are being made as students share their solutions. Discuss the idea that while the answer to 1,59 6 is 258 R1, the answer to the word problem is 258. Have students complete Student Activity Book pages 51A and 51B or C61 and C62. Ongoing Assessment: Observing Students at Work Students divide -digit numbers by 1-digit numbers. Can students solve the problems accurately? What strategies do students use to solve the problems? Can students accurately express any remainders in the context of the problem? CC92 Investigation 3 Solving Division Problems INV12_TE0_U08_S3.5A.indd 92 6/3/11 :8 PM

1 Activity 2 Discussion 3 Session Follow-Up differentiation: Supporting the Range of Learners Some students might not start the problem with large enough numbers of groups to be efficient. If you see students begin building groups in multiples of 10, give them extra practice generating multiples of 100. Then move on to multiples of 200, 300, and so on. For students who are able to quickly solve these problems, give them some problems in which they divide -digit numbers by 2-digit numbers. D i s c u s s i o n First Steps Math Focus Points for Discussion Dividing a -digit number by a 1-digit number 15 Min class Begin the discussion by asking how students chose to start Problem 3 on Student Activity Book page 51A or C61. Who will share their first step for 2,831 5? First steps will likely include 5 00 = 2,000 and 2,000 5 = 00. Discuss how to complete the problem beginning with each first step offered. Ask if anyone started with 2,500 5 = 500. Check that students understand the problem. Write 2,831 5 is 566 R1 and ask them what each of the numbers mean. You might want to provide a context for the problem, such as the following: The Nature Club collected $2,831 to buy boxes of dog food for a dog shelter. Each box costs $5. How many boxes can the club buy? Ask students to relate each number in the problem and the answer to the story. Then ask students what the remainder means. For these problems, did you find you could use the same division strategies you ve used with smaller numbers? What was the same or different? Session 3.5A Dividing -Digit Numbers CC93

1 Activity 2 Discussion 3 Session Follow-Up Name Do you think these problems are harder to solve than the division problems with 2-digit divisors? Date How Many Packages? How Many Groups? Dividing Large Numbers Solve each problem and show your work. Daily Practice note Students divide -digit numbers by 1-digit numbers. Students might say: These were a lot easier because if it s a 2-digit divisor you have to think about what to multiply by a 2-digit number to get to the number, and it s easier to multiply by 1 digit. 1. A football stadium has,890 seats. There are 6 sections of seats with the same number of seats in each section. How many seats are in each section? 2. A big company is planning to have a dinner for 1,18 people. How many tables are needed if 8 people will sit at each table? 3. 2,212 7 = I just started by multiplying the 1-digit number by a multiple of 100 that got me close to the number and then figured out what I still had left. This was pretty easy. Pearson Education.,676 2 = Session 3.5A Unit 8 51C Student Activity Book, Unit 8, p. 51C; Resource Masters, C63 INV12_SE0_U8.indd 3 6/1/11 5:52 PM The answers to problems were a lot bigger. It was harder for me to keep track of how many of such a small number would fit into such a big number. Session Follow-Up Daily Practice Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page 51C or C63. Student Math Handbook: Students and families may use Student Math Handbook pages 50 52 for reference and review. See pages 135 138 in the back of Unit 8. CC9 Investigation 3 Solving Division Problems INV12_TE0_U08_S3.5A.indd 9 6/3/11 :50 PM

Name How Many Packages? How Many Groups? Date Multiplying -Digit Numbers by 1-Digit Numbers (page 1 of 2) Solve each problem and show your work. 1. 1,58 students attend the Sunset Elementary School. The principal wants to make sure each student gets 5 pencils to start the school year. How many pencils does she need to buy? 2. The Fresh Fruit Company can fit 2,650 oranges in one truck. One day they sent out 3 trucks full of oranges to deliver the fruit to grocery stores. How many oranges did they send out that day? 3. 2,12 =. 3,670 9 = Unit 8 Session 2.A C57 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name How Many Packages? How Many Groups? Date Multiplying -Digit Numbers by 1-Digit Numbers (page 2 of 2) Solve each problem and show your work. 5. There are 6 schools in town. Each school serves 1,09 lunches each week. How many lunches are served by the schools in the town each week? 6. Seven truck drivers each drove,215 miles in a two-week period. How many miles did they drive in all? 7. 8,37 2 = 8.,750 8 = Unit 8 Session 2.A C58 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name How Many Packages? How Many Groups? Date Daily Practice Driving Around Ms. Ortega drives her truck to different cities throughout the year. The table shows the roundtrip distance to each city and how many times she made each trip last year. For each city in the table, show the total number of miles Ms. Ortega drove. Use the space below the table to show your work. note Students multiply -digit numbers by 1-digit numbers. City Roundtrip Distance Number of Trips Lincoln, NE 1,8 3 Total Number of Miles Gainesville, FL 1,850 6 Seattle, WA 3,528 8 Sacramento, CA 2,922 5 Unit 8 Session 2.A C59 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name How Many Packages? How Many Groups? How Many Legs? Solve these problems and show your work. How many legs do 1.,366 children have? Date Daily Practice note Students multiply -digit numbers by 1-digit numbers. 2. 2,066 spiders have? (A spider has 8 legs.) 3. 3,219 dogs have?. 1,077 three-legged stools have? 5. 5,910 beetles have? (A beetle has 6 legs.) Unit 8 Session 2. C60 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name How Many Packages? How Many Groups? Date Dividing -Digit Numbers by 1-Digit Numbers (page 1 of 2) Solve each problem and show your work. 1. In one day at Honeysweet Apple Orchard, workers picked 1,59 apples. They want to put them in bags of 6. How many bags can they make? 2. 1,00 children signed up to play in the Smith City youth basketball league. 8 children will be placed on each team. How many teams of 8 players will there be? 3. 2,831 5 =. 5,36 7 = Unit 8 Session 3.5A C61 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name How Many Packages? How Many Groups? Date Dividing -Digit Numbers by 1-Digit Numbers (page 2 of 2) Solve each problem and show your work. 5. 1,52 shirts were delivered to a large department store. They came in boxes of. How many boxes were delivered? 6. 3,018 letters need to be mailed out to members of the City Service Club. Five people are stuffing the envelopes. How should they divide up the task so that each person will stuff the same number of envelopes? 7.,698 9 = 8. 2,287 3 = Unit 8 Session 3.5A C62 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name How Many Packages? How Many Groups? Date Daily Practice Dividing Large Numbers Solve each problem and show your work. note Students divide -digit numbers by 1-digit numbers. 1. A football stadium has,890 seats. There are 6 sections of seats with the same number of seats in each section. How many seats are in each section? 2. A big company is planning to have a dinner for 1,18 people. How many tables are needed if 8 people will sit at each table? 3. 2,212 7 =.,676 2 = Unit 8 Session 3.5A C63 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name How Many Packages? How Many Groups? Flea Market Solve each problem and show your work. Date Daily Practice note Students divide -digit numbers by 1-digit numbers. 1. Mr. Diaz makes bracelets and sells them at flea markets. He uses 8 beads for each bracelet. Mr. Diaz has a bag of 1,500 beads. How many bracelets can he make? 2. Ms. Lang has a collection of 2,106 old postcards that she bought at flea markets. She stores them in 6 boxes, with the same number in each box. How many postcards are in each box? 3. 3,21 7 =. 6,708 = Unit 8 Session 3.5 C6 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Cuántos paquetes? Cuántos grupos? Fecha Multiplicar números de dígitos por números de 1 dígito (página 1 de 2) Resuelve cada problema y muestra tu trabajo. 1. La escuela primaria Sunset tiene 1,58 estudiantes. La directora quiere estar segura de que cada estudiante tenga 5 lápices para empezar el año escolar. Cuántos lápices debe comprar? 2. La Compañía Frutas Frescas puede meter 2,650 naranjas en un camión. Un día enviaron 3 camiones llenos de naranjas a repartir la fruta a las tiendas de abarrotes. Cuántas naranjas enviaron ese día? 3. 2,12 =. 3,670 9 = Unidad 8 Sesión 2.A C57 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Cuántos paquetes? Cuántos grupos? Fecha Multiplicar números de dígitos por números de 1 dígito (página 2 de 2) Resuelve cada problema y muestra tu trabajo. 5. En un pueblo hay 6 escuelas. Cada escuela sirve 1,09 almuerzos cada semana. Cuántos almuerzos sirven las escuelas del pueblo cada semana? 6. Siete camioneros manejaron,215 millas cada uno en un período de dos semanas. Cuántas millas manejaron en total? 7. 8,37 2 = 8.,750 8 = Unidad 8 Sesión 2.A C58 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Cuántos paquetes? Cuántos grupos? Fecha Práctica diaria Manejar La Srta. Ortega maneja su camión a diferentes ciudades durante el año. La tabla muestra la distancia de ida y vuelta a cada ciudad y cuántas veces hizo cada viaje el año pasado. Para cada ciudad de la tabla, muestra el número total de millas que la Srta. Ortega manejó. nota Los estudiantes multiplican números de dígitos por números de 1 dígito. Usa el espacio que está debajo de la tabla para mostrar tu trabajo. Ciudad Distancia de ida y vuelta Número de viajes Lincoln, NE 1,8 3 Número total de millas Gainesville, FL 1,850 6 Seattle, WA 3,528 8 Sacramento, CA 2,922 5 Unidad 8 Sesión 2.A C59 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Cuántos paquetes? Cuántos grupos? Fecha Práctica diaria Cuántas piernas tienen? Resuelve estos problemas y muestra tu trabajo. nota Los estudiantes multiplican números de dígitos por números de 1 dígito. Cuántas 1. piernas tienen,366 niños? 2. patas tienen 2,066 arañas? (Una araña tiene 8 patas). 3. patas tienen 3,219 perros?. patas tienen 1,077 taburetes de tres patas? 5. patas tienen 5,910 escarabajos? (Un escarabajo tiene 6 patas). Unidad 8 Sesión 2. C60 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Cuántos paquetes? Cuántos grupos? Fecha Dividir números de dígitos por números de 1 dígito (página 1 de 2) Resuelve cada problema y muestra tu trabajo. 1. Un día en el huerto de manzanas Honeysweet, los trabajadores recogieron 1,59 manzanas. Quieren ponerlas en bolsas de 6. Cuántas bolsas pueden hacer? 2. En la liga juvenil de básquetbol de Smith City, 1,00 niños se inscribieron para jugar. Habrá 8 niños en cada equipo. Cuántos equipos de 8 jugadores habrá? 3. 2,831 5 =. 5,36 7 = Unidad 8 Sesión 3.5A C61 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Cuántos paquetes? Cuántos grupos? Fecha Dividir números de dígitos por números de 1 dígito (página 2 de 2) Resuelve cada problema y muestra tu trabajo. 5. Se entregaron 1,52 camisas a una tienda de departamentos. Venían en cajas de. Cuántas cajas se entregaron? 6. Se deben enviar por correo 3,018 cartas a los miembros de City Service Club. Cinco personas están llenando los sobres. Cómo deben repartirse la tarea para que cada persona llene el mismo número de sobres? 7.,698 9 = 8. 2,287 3 = Unidad 8 Sesión 3.5A C62 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Cuántos paquetes? Cuántos grupos? Fecha Práctica diaria Dividir números grandes Resuelve cada problema y muestra tu trabajo. nota Los estudiantes dividen números de dígitos por números de 1 dígito. 1. Un estadio de futbol tiene,890 asientos. Hay 6 secciones de asientos con el mismo número de asientos en cada sección. Cuántos asientos hay en cada sección? 2. Una gran empresa está planeando ofrecer una cena para 1,18 personas. Cuántas mesas se necesitan si 8 personas se sentarán en cada mesa? 3. 2,212 7 =.,676 2 = Unidad 8 Sesión 3.5A C63 Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nombre Cuántos paquetes? Cuántos grupos? Fecha Práctica diaria Mercado de pulgas Resuelve cada problema y muestra tu trabajo. nota Los estudiantes dividen números de dígitos por números de 1 dígito. 1. El señor Díaz hace pulseras y las vende en los mercados de pulgas. Usa 8 cuentas para cada pulsera. El señor Díaz tiene una bolsa con 1,500 cuentas. Cuántas pulseras puede hacer? 2. La señora Lang tiene una colección de 2,106 tarjetas postales viejas que compró en un mercado de pulgas. Las guarda en 6 cajas y cada caja tiene el mismo número. Cuántas tarjetas postales hay en cada caja? 3. 3,21 7 =. 6,708 = Unidad 8 Sesión 3.5 C6 Pearson Education, Inc., or its affiliates. All Rights Reserved.