Use Place Value to Round Numbers Lesson 8 Part 1: Introduction
Develop Skills and Strategies Lesson 8 Part 1: Introduction CCSS 3.NBT.A.1 Use Place Value to Round Numbers You know that three-digit numbers are formed by groups of hundreds, tens, and ones. Take a look at this problem. Look at the number 384. Between which two tens does it fall? Between which Hundreds Tens Ones two hundreds does it fall? You can show 384 in a place-value chart. 3 8 4 Explore It Use math you already know to solve the problem. How many tens are in 384? What is the next greatest number of tens? How do you write both of these numbers of tens as numerals? Between which two tens does 384 fall? How many hundreds are in 384? What is the next greatest number of hundreds How do you write both of these numbers of hundreds as numerals? Between which two hundreds does 384 fall? 62 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 1: Introduction Lesson 8 Find Out More Rounding is finding a number that is close to another number. The reason for rounding is to find numbers that are easy to work with. That’s why you round threedigit numbers to the nearest ten or hundred. A number line can help you understand how rounding is done. Rounding to the Nearest Ten 0 2 4 6 8 10 12 14 16 18 20 The number line shows that 8 is nearer to 10 than to 0. It also shows that 13 is nearer to 10 than to 20. What about 5? The dot is at 5. It is halfway between 0 and 10. The rule for rounding is that 5 rounds up to 10. Rounding to the Nearest Hundred 0 25 50 75 100 125 150 175 200 The number line can help you see that 25 is nearer to 0 than to 100. Also, 175 is nearer to 200 than to 100. Even though 50 is halfway between 0 and 100, the rules says that it rounds to 100. But, 49 is nearer to 0 than to 100. Reflect 1 Use the number 145. What ten does it round to? What is the nearest hundred? Explain how you found your answer. L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 63 Part 2: Modeled Instruction Lesson 8 Read the problem below. Then explore different ways to round to the nearest 10. Ally keeps track of the time she spends doing homework. She rounds the times to the nearest ten minutes. If Ally spent 37 minutes on her homework, how would she record this time? Picture It You can use a hundreds chart to help round to the nearest 10. 37 is between the tens 30 and 40. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Solve It Use what you know about rounding to solve the problem. The halfway point between 30 and 40 is 35. 37 is greater than 35, so round 37 up to 40. Ally would record the time as 40 minutes. 64 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 2: Guided Instruction Lesson 8 Connect It Now you can round three-digit numbers to the nearest 10. Round 943 to the nearest ten. 2 The number 943 is between what two tens? 3 What number is halfway between these two tens? 4 Is 943 less than or greater than the halfway number? 5 Will you round up or round down? 6 What is 943 rounded to the nearest ten? 7 Explain how to round a number to the nearest ten. Try It 8 What is 106 rounded to the nearest ten? 9 Round to the nearest ten. What is a number less than 180 that rounds to 180? What is a number greater than 180 that rounds to 180? L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 65 Part 3: Modeled Instruction Lesson 8 Read the problem below. Then explore different ways to round to the nearest 100. There are 236 third graders at Huron Elementary School. What is 236 rounded to the nearest hundred? Picture It Use place-value drawings to show the number you are rounding. 236 has 2 hundreds, so it is between 200 and 300. The drawing shows that 236 is 2 hundreds 1 3 tens 1 6 ones. Solve It Use what you know about rounding to solve the problem. There are 10 tens in each hundred. Halfway between 0 tens and 10 tens is 5 tens. 236 has 3 tens, and 3 tens is less than 5 tens. Round 236 down. 236 rounded to the nearest 100 is 200. 66 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 3: Guided Instruction Lesson 8 Connect It Now you can round another three-digit number to the nearest 100. Round 358 to the nearest hundred. 10 The number 358 is between what two hundreds? 11 How many tens are in 358? 12 What number of tens is halfway between hundreds? 13 What is 358 rounded to the nearest hundred? 14 Did you round up or round down? Explain how you knew which hundred to round to. Try It 15 What is 476 rounded to the nearest hundred? 16 You are rounding to the nearest 100. What numbers less than 100 would round to 100? L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 67 Part 4: Guided Practice Lesson 8 Study the model below. Then solve problems 17–19. Student Model The blocks show the number of hundreds, tens, and ones in 362. Mr. Watson’s shoe store has 362 pairs of shoes in stock. What is 362 rounded to the nearest ten? Look at how you could show your work using base-ten blocks. Pair/Share Explain why 362 was rounded up or down. Read the problem carefully. Are you rounding to the nearest 10 or 100? Solution: 360 17 The school cafeteria has 879 plates. What is this number rounded to the nearest hundred? Show your work. Pair/Share Which digit in the number helps you decide whether to round up or down? 68 Solution: L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 4: Guided Practice 18 Eddie picked out a TV for $479 and a DVD player for $129. He rounded each price to the nearest $10 to estimate the total cost. What is each price rounded to the nearest $10? Lesson 8 Between what two tens is 479? Show your work. Pair/Share Solution: 19 There are 416 third grade students at the Lincoln School. What is this number rounded to the nearest hundred? A400 Why would Eddie round the prices? How many hundreds and tens are in the number? B410 C420 D500 Lien chose C as the correct answer. How did he get that answer? L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Pair/Share What kinds of mistakes could Lien have made? 69 Part 5: Common Core Practice Lesson 8 Solve the problems. 1 Jolon scored 194 points during the basketball season. Round his points to the nearest hundred. Jolon scored almost how many points? A100 B180 C190 D200 2 Round to the nearest 10. Which number will NOT round to 590? A596 B594 C588 D585 3 Tell whether each sentence is True or False. 70 a. 496 rounded to the nearest 100 is 500. True False b. 496 rounded to the nearest 10 is 500. True False c. 205 rounded to the nearest 10 is 300. True False d. 745 rounded to the nearest 100 is 800. True False L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 5: Common Core Practice Lesson 8 4 Which of the following numbers will round to 250 when rounded to the nearest 10? Circle the letter for all that apply. A B 200 Hundreds 2 250 Tens 2 Ones 6 C D259 E245 5 When rounding to the nearest hundred, what is the least whole number that rounds to 400? What is the greatest whole number that rounds to 400? Answer 6 A total of 778 tickets were sold to a charity event. A newspaper article rounded 778 when it listed the number of tickets sold. Round the number of tickets to the nearest 10 and to the nearest 100. Fill in the blanks to show about how many tickets were sold. Rounded to the nearest 10, almost tickets were sold. Rounded to the nearest 100, almost tickets were sold. Self Check Go back and see what you can check off on the Self Check on page 61. L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 71 Develop Skills and Strategies Lesson 8 Use Place Value to Round Numbers Lesson Objectives The Learning Progression •Round two- and three-digit numbers to the nearest 10. In grade 2, students learned that each digit in a threedigit number represents a quantity of hundreds, tens, and ones. This understanding leads to the concept of bundling groups of 10 ones to make tens and groups of 10 tens to make hundreds. In grade 3, students extend this place value knowledge to round numbers to the nearest 10 or 100. In grade 4, rounding whole numbers is extended to any place. •Round three-digit numbers to the nearest 100. •Explain how to round numbers to the nearest 10 and to the nearest 100. Prerequisite SkilLs In order to be proficient with the concepts/skills in this lesson, students should: •Identify the hundreds, tens, and ones places in numbers. Later in grade 3, students multiply one-digit whole numbers by multiples of 10 in the range 10–90. They will use place-value strategies to help them with this concept. •Understand the value of the hundreds, tens, and ones digits and places in numbers. Teacher Toolbox Prerequisite Skills •Skip count by 10s and 100s. •Identify whether a given digit is less than, equal to, or greater than 5. Vocabulary rounding: finding a number that is close to another number Teacher-Toolbox.com 3.NBT.A.1 Ready Lessons Tools for Instruction Interactive Tutorials ✓ CCSS Focus 3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100. ADDITIONAL STANDARDS: 3.OA.B.5, 3.NBT.A.3 (see page A42 for full text) STANDARDS FOR MATHEMATICAL PRACTICE: SMP 1, 5, 6, 7, 8 (see page A9 for full text) 72 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 1: Introduction Lesson 8 At a Glance Part 1: introduction ccss 3.nbt.a.1 use Place value to round numbers you know that three-digit numbers are formed by groups of hundreds, tens, and ones. take a look at this problem. Step By Step Look at the number 384. Between which two tens does it fall? Between which •Have students read the problem at the top of the page. ones •Tell students that this page models how to round a number to the nearest 10 and nearest 100. tens two hundreds does it fall? You can show 384 in a place-value chart. hundreds Students look at a number given in a place-value chart and answer a series of questions designed to help them round the number to the nearest 10 and then to the nearest 100. Develop skills and strategies Lesson 8 3 8 4 explore it •Work through Explore It as a class. use math you already know to solve the problem. How many tens are in 384? •Discuss how to find the number of tens in 384. 38 What is the next greatest number of tens? 39 How do you write both of these numbers of tens as numerals? •Ask students to explain how they used place value to write 38 tens and 39 tens as numerals. Between which two tens does 384 fall? 3 How many hundreds are in 384? What is the next greatest number of hundreds •Ask students to explain how they determined which two hundreds the given number is between. 380 and 390 380 and 390 4 How do you write both of these numbers of hundreds as numerals? 300 and 400 Between which two hundreds does 384 fall? 300 and 400 •Challenge students to answer these questions: Which ten is 384 closer to? [380] Which hundred? [400] SMP Tip: When rounding numbers, students are looking for and using the structure of place value. Students should know and be able to use the concept that 10 ones make ten and 10 tens make one hundred (SMP 7). 62 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Mathematical Discourse •How can you use place value to determine what two hundreds a number falls between? Given a number, students should be able to place the digits into a place value chart and identify the number of ones, tens and hundreds in each number. The lesser hundred has the same number of hundreds as the given number, but 0 tens and 0 ones. The greater hundred is 100 more than the lesser hundred. L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 73 Part 1: Introduction Lesson 8 At a Glance Students use place-value concepts to round numbers. They apply a rule about the halfway point between two numbers and use it to determine which way to round. Step By Step •Read Find Out More as a class. •Make sure students can read the number line. •Have students pinch their fingers to show how close 8 is to 10 and how close 8 is to 0. •Have students use the number lines to identify the halfway point between 0 and 10 and between 0 and 100. •Discuss why 145 rounds down to 100 but rounds up to 150. Part 1: introduction Lesson 8 Find out More rounding is finding a number that is close to another number. The reason for rounding is to find numbers that are easy to work with. That’s why you round threedigit numbers to the nearest ten or hundred. A number line can help you understand how rounding is done. rounding to the nearest ten 0 2 4 6 8 10 12 14 16 18 20 The number line shows that 8 is nearer to 10 than to 0. It also shows that 13 is nearer to 10 than to 20. What about 5? The dot is at 5. It is halfway between 0 and 10. The rule for rounding is that 5 rounds up to 10. rounding to the nearest hundred 0 25 50 75 100 125 150 175 200 The number line can help you see that 25 is nearer to 0 than to 100. Also, 175 is nearer to 200 than to 100. Even though 50 is halfway between 0 and 100, the rules says that it rounds to 100. But, 49 is nearer to 0 than to 100. reflect 1 Use the number 145. What ten does it round to? What is the nearest hundred? Explain how you found your answer. Possible answer: i know that 45 is halfway between 40 and 50, so it rounds Hands-On Activity to 50. 145 rounds to 150. i can see on the number line that 145 is nearer to 100 than to 200. the nearest 100 is 100. Use a number line to understand rounding numbers. Materials: number line marked 0 to 100 for each student, small beads •Demonstrate how to make a number line from 0 to 100 as students make their own. First, mark and label points for the tens from 0 to 100. Then make 9 tick marks between each ten, but don’t label the numbers. •Call out a random number between 1 and 99 and ask students to place a bead on the number line to represent that number. •Using rounding rules, students then move their bead up or down to the nearest 10 on the number line. Glance at their work, and have one student give the correct answer. L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 63 Real-World Connection Discuss with students how they can use rounding to estimate the cost of a group of items at a store. For example, ask: About how much will you spend on two dolls if each costs $27? Students should be able to round $27 to $30 and estimate that $30 1 $30 5 $60. •Continue to call out random numbers for students to round on the number line. Ask different students to give the answers. 74 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 2: Modeled Instruction Lesson 8 At a Glance Part 2: Modeled instruction Students round a value to the nearest 10. Lesson 8 read the problem below. then explore different ways to round to the nearest 10. Step By Step Ally keeps track of the time she spends doing homework. She rounds the times to the nearest ten minutes. If Ally spent 37 minutes on her homework, how •Read the problem at the top of the page as a class. would she record this time? •Read Picture It. Picture it you can use a hundreds chart to help round to the nearest 10. •Have students circle 37 on the hundreds chart. 37 is between the tens 30 and 40. •Ask students if 37 is closer to 30 or 40. [40] •Read Solve It. •Be sure students understand why the number 35 is halfway between 30 and 40. [It is as close to 30 as it is to 40.] SMP Tip: Students should make the connection that rounding numbers is a form of estimation. Rounding numbers helps students do calculations efficiently and express answers to a specified level of precision (SMP 6). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 solve it use what you know about rounding to solve the problem. The halfway point between 30 and 40 is 35. 37 is greater than 35, so round 37 up to 40. Ally would record the time as 40 minutes. 64 Concept Extension Explain to students that when rounding numbers, the digit that is rounded either stays the same or is increased by one, and one or more of the digits on the right are changed to zero. •First students should determine what place the number will be rounded to and identify that digit in the number. •Direct students to look to the digit directly to the right of the digit you are rounding to. L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Mathematical Discourse •How do you decide which ten a number is closest to when rounding to the nearest ten? Students should first be able to identify which tens a given number is between (for example, the number 16 is between 10 and 20). Students should be able to communicate an understanding of the concept that if the ones place is less than 5 the number is closer to the smaller ten and if the ones place is 5 or greater then number is closer to the larger ten. •If the digit to the right is less than 5, that digit becomes zero (along with any other digits to the right) and the digit to be rounded stays the same. •If the digit to the right is 5 or greater, that digit becomes zero (along with any other digits to the right) and the digit to be rounded is increased by one. L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 75 Part 2: Guided Instruction Lesson 8 At a Glance Students are guided through the steps to round a three-digit number to the nearest 10. Then students solve additional rounding problems. Part 2: guided instruction Lesson 8 connect it now you can round three-digit numbers to the nearest 10. Round 943 to the nearest ten. Step By Step •Read Connect It as a class. •Have students explain their answers to problem 2. •Ask students to explain why they round down. [The number 943 is less than the halfway point, 945, so round down.] •Encourage students to share their answers to problem 7 with a partner. 2 The number 943 is between what two tens? 940 and 950 3 What number is halfway between these two tens? 945 4 Is 943 less than or greater than the halfway number? less than 5 Will you round up or round down? round down 6 What is 943 rounded to the nearest ten? 940 7 Explain how to round a number to the nearest ten. Look for answers that describe finding the number halfway between the tens, rounding down if the number is less than the halfway number, and rounding up if the number is equal to or greater than the halfway number. try it 8 What is 106 rounded to the nearest ten? 110 9 Round to the nearest ten. What is a number less than 180 that rounds to 180? Possible answers: 175, 176, 177, 178, 179 What is a number greater than 180 that rounds to 180? Possible answers: 181, 182, 183, 184 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Visual Model Use the concept of a hill to model rounding to the nearest ten visually. For example, round 943 to the nearest ten: •Draw a diagram to represent a hill. Write the number 940 at the bottom left and the number 950 at the bottom right of the diagram. Write the number 945 at the peak. •Explain that the goal is to get from 940 to 950. If a number stops before reaching the peak, it will roll back. If a number makes it to the peak or over the peak it will roll to 950. Copying is not permitted. 65 Try It Solutions 8Solution: 110; The number 106 is between the tens 100 and 110. The halfway point between 100 and 110 is 105. 106 is greater than 105, so round up to 110. Error Alert: Students who wrote 100 could have rounded to the nearest hundred instead of the nearest ten. 9Solution: Possible answers: 175, 176, 177, 178, 179; Possible answers: 181, 182, 183, 184; Any number from 175 through 184 will round to 180. •Write “943” on the left of the diagram and “946” on the right of diagram. Help students understand that 943 rolls back to 940 and 945 and 946 roll to 950. 76 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 3: Modeled Instruction Lesson 8 At a Glance Part 3: Modeled instruction Students round a value to the nearest 100. read the problem below. then explore different ways to round to the nearest 100. Step By Step There are 236 third graders at Huron Elementary School. What is 236 rounded •Read the problem at the top of the page as a class. to the nearest hundred? • Read Picture It. Have a volunteer explain what is shown by the place-value drawings. Picture it use place-value drawings to show the number you are rounding. •Ask students how the drawings help you know that 236 is between 200 and 300. [There are 2 hundreds blocks, plus some tens and ones. The number is more than 200, but less than 300.] 236 has 2 hundreds, so it is between 200 and 300. The drawing shows that 236 is 2 hundreds 1 3 tens 1 6 ones. solve it •Read Solve It. use what you know about rounding to solve the problem. •Have a volunteer identify the number halfway between 200 and 300. [250] There are 10 tens in each hundred. Halfway between 0 tens and 10 tens is 5 tens. 236 has 3 tens, and 3 tens is less than 5 tens. Round 236 down. 236 rounded to the nearest 100 is 200. •Ask another student to explain why 236 rounds to 200. [The number is closer to 200 than 300.] 66 Hands-On Activity Use base-ten blocks to understand rounding numbers. Materials: base-ten blocks and paper for recording results •Use base-ten blocks to demonstrate that 5 ones are half the size of 1 ten. Do the same with tens and hundreds to establish the halfway point of 50. •Present a 3-digit number. Have students model the number with base-ten blocks, putting the blocks in order from hundreds to ones. Lesson 8 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Mathematical Discourse •What is the same and what is different when you round to the nearest ten and when you round to the nearest hundred? Students should be able to explain that you always look one digit to the right of the place you are rounding to determine if you should round up or down. They should communicate that when rounding to the nearest ten, the ones place becomes zero and when rounding to the nearest hundred, the tens and ones places become zero. •Ask a student to use the blocks to help explain how to round the number to the nearest 10. Have a different student explain rounding the number to the nearest 100. •Continue with other three-digit numbers and different student volunteers. L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 77 Part 3: Guided Instruction Lesson 8 At a Glance Students are guided through the steps to round a three-digit number to the nearest 100. Then students solve additional rounding problems. Part 3: guided instruction Lesson 8 connect it now you can round another three-digit number to the nearest 100. Round 358 to the nearest hundred. Step By Step •Read Connect It as a class. •Have students explain their answer to problem 10. •You may wish to invite two or three students to share their explanations for problem 14 to the class. 10 The number 358 is between what two hundreds? 11 How many tens are in 358? 300 and 400 5 5 12 What number of tens is halfway between hundreds? 13 What is 358 rounded to the nearest hundred? 400 14 Did you round up or round down? Explain how you knew which hundred to SMP Tip: Students can use physical objects, such as base-ten blocks or visual models, such as number lines to make sense of rounding numbers. Students should become aware that there are multiple methods that they can use to solve the same problem (SMP 1). round to. Possible answer: 358 has 5 tens and 5 tens is the halfway point between hundreds. i know that if a number has 5 or more tens, i round up. so, i rounded 258 up to 300. try it 15 What is 476 rounded to the nearest hundred? 500 16 You are rounding to the nearest 100. What numbers less than 100 would round to 100? all the numbers from 50 to 99 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 67 Try It Solutions 15 Solution: 500; The number 476 is between 400 and 500. 5 tens is halfway between hundreds. 7 tens is greater than 5 tens, so round up to 500. Error Alert: Students who wrote 480 rounded to the nearest ten. Students who wrote 400 did not round properly. Those students did not realize that 7 tens is greater than 5 tens. 16 Solution: All the numbers from 50 to 99; Any two-digit number with 5 or more tens will round to 100. 78 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Part 4: Guided Practice Lesson 8 Part 4: guided Practice Lesson 8 study the model below. then solve problems 17–19. Student Model The blocks show the number of hundreds, tens, and ones in 362. Mr. Watson’s shoe store has 362 pairs of shoes in stock. What is 362 rounded to the nearest ten? Look at how you could show your work using base-ten blocks. Part 4: guided Practice 18 Eddie picked out a TV for $479 and a DVD player for $129. He rounded each price to the nearest $10 to estimate the total cost. What is each price rounded to the nearest $10? Lesson 8 Between what two tens is 479? Show your work. student work will vary. students may show their work using number lines, base-ten blocks, or a hundreds chart. Pair/share Explain why 362 was rounded up or down. Read the problem carefully. Are you rounding to the nearest 10 or 100? Solution: 360 Pair/share 17 The school cafeteria has 879 plates. What is this number rounded to the nearest hundred? Show your work. Solution: $480 and $130 19 There are 416 third grade students at the Lincoln School. What is this number rounded to the nearest hundred? Possible student work using a number line: a 400 800 825 850 875 900 Pair/share Which digit in the number helps you decide whether to round up or down? 68 b 410 c 420 Why would Eddie round the prices? How many hundreds and tens are in the number? D 500 Lien chose c as the correct answer. How did he get that answer? Possible answer: Lien rounded 416 to the nearest ten Solution: 900 instead of the nearest hundred. L8: Use Place Value to Round Numbers L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. At a Glance Students use place value concepts to solve problems involving rounding whole numbers to the nearest 10 or to the nearest 100. Step By Step •Ask students to solve the problems individually and label their work appropriately. •When students have completed each problem, have them Pair/Share to discuss their solutions with a partner or in a group. Solutions Ex Base-ten blocks are shown as one way to solve the problem. The number 362 is between the tens 360 and 370. The halfway point between 360 and 370 is 365. 362 is less than 365, so round down to 360. L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. ©Curriculum Associates, LLC Copying is not permitted. Pair/share What kinds of mistakes could Lien have made? 69 17 Solution: 900; The number 879 is between 800 and 900. 5 tens is halfway between any two hundreds. 7 tens is greater than 5 tens, so round up to 900. (DOK 1) 18 Solution: $480 and $130; Students can reason that 479 is greater than 475, so it rounds up to 480. Also, 129 is greater than 125, so it rounds up to 130. (DOK 1) 19 Solution: A; The digit in the tens place is less than 5, so leave 4 as the digit in the hundreds place and replace the digits in the tens and ones places with zeros. Explain to students why the other two answer choices are not correct: B is not correct because the number needs to be rounded to the nearest hundred; the student tried to round to the nearest ten but erroneously rounded 6 down instead of up. D is not correct because 5 tens is halfway between any two hundreds, and 1 ten is less than 5 tens; round down to 400 instead of up to 500. (DOK 3) 79 Part 5: Common Core Practice Part 5: common core Practice Lesson 8 Solve the problems. 1 2 Lesson 8 Part 5: common core Practice 4 A 100 B 180 C 190 D 200 B 596 B 594 C 588 D 585 200 hundreds 2 250 tens 2 ones 6 C Round to the nearest 10. Which number will NOT round to 590? A Which of the following numbers will round to 250 when rounded to the nearest 10? Circle the letter for all that apply. A Jolon scored 194 points during the basketball season. Round his points to the nearest hundred. Jolon scored almost how many points? Lesson 8 5 D 259 E 245 When rounding to the nearest hundred, what is the least whole number that rounds to 400? What is the greatest whole number that rounds to 400? Answer the least whole number that rounds to 400 is 350. the greatest whole number that rounds to 400 is 449. 3 Tell whether each sentence is True or False. a. 496 rounded to the nearest 100 is 500. b. 496 rounded to the nearest 10 is 500. 3 True 3 True c. 205 rounded to the nearest 10 is 300. True d. 745 rounded to the nearest 100 is 800. True False False 3 False 3 False 6 A total of 778 tickets were sold to a charity event. A newspaper article rounded 778 when it listed the number of tickets sold. Round the number of tickets to the nearest 10 and to the nearest 100. Fill in the blanks to show about how many tickets were sold. Rounded to the nearest 10, almost Rounded to the nearest 100, almost 780 800 tickets were sold. tickets were sold. self check Go back and see what you can check off on the Self Check on page 61. 70 L8: Use Place Value to Round Numbers L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. At a Glance Students use rounding rules to solve problems that might appear on a mathematics test. Solutions 1Solution: D; The number 194 is between 100 and 200. 9 tens is greater than 5 tens, so round to 200. (DOK 1) 2Solution: A; The number 596 is between the tens 590 and 600. The halfway point between 590 and 600 is 595. 596 is greater than 595, so round to 600. (DOK 1) ©Curriculum Associates, LLC Copying is not permitted. 71 4Solution: E; The number 245 is exactly halfway between the tens 240 and 250, so round up to 250. (DOK 2) 5Solution: 350; 449; Numbers with 3 hundreds can round up to 400. Numbers with 4 hundreds can round down to 400. The numbers with 3 hundreds must have 5 or more tens. The numbers with 4 hundreds must have less than 5 tens. (DOK 2) 6Solution: 780; 800; The halfway point between 770 and 780 is 775. 778 is greater than 775, so round up to 780. The number 778 is between 700 and 800. 7 tens is greater than 5 tens, so round up to 800. (DOK 1) 3Solution: a. True; b. True; c. False; d. False (DOK 2) 80 L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. Differentiated Instruction Lesson 8 Assessment and Remediation •Ask students to round 453 to the nearest ten. [450] •For students who are still struggling, use the chart below to guide remediation. •After providing remediation, check students’ understanding. Ask students to explain their thinking while rounding 648 to the nearest hundred. [600] If the error is . . . Students may . . . To remediate . . . 400 have incorrectly rounded down to the nearest hundred. Remind students to read the question carefully. The question asks to round 453 to the nearest ten, not hundred. Even when rounding to the nearest hundred, 453 would round up to 500 because 453 is closer to 500 than to 400. 460 have rounded up to the nearest ten. Demonstrate with a number line that 455 is halfway between 450 and 460 and that 453 is closer to 450 than to 460. 500 have rounded to the nearest hundred. Remind students to read the question carefully. The question asks to round 453 to the nearest ten, not hundred. be struggling with rounding. Allow students to practice with smaller numbers, and use a number line. Focus on understanding the halfway point. other answers Hands-On Activity Challenge Activity Use a rounding game to understand rounding numbers. Tell students that a number rounds down to the nearest ten but rounds up to the nearest hundred. Ask students to show two different numbers that fit this situation. [Possible answer: 272 rounds down to 270 but up to 300. 361 rounds down to 360 but up to 400.] Materials: playground ball, card stock paper, tape. •Assign each student a number in tens or hundreds. Have students write the numbers on paper and tape them on the front of their shirts. •Have students stand in a large circle facing in. •Randomly call out a number and whether it should be rounded to the nearest 10 or 100. Be sure to describe situations that fit with the students’ numbers. The student holding the ball will toss it to the student who has the rounded number. •Continue the cycle of play until all students have had at least one chance to toss the ball. L8: Use Place Value to Round Numbers ©Curriculum Associates, LLC Copying is not permitted. 81
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