Lesson 12: Comparing Numbers - 3rd Grade Math

A STORY OF UNITS – TEKS EDITION Lesson 12 3 2 Lesson 12 Objective: Compare numbers based on the meaning of the digits using , or = to record the comparison. Suggested Learning Structure Fluency Practice...

A STORY OF UNITS – TEKS EDITION Lesson 12 3 2 Lesson 12 Objective: Compare numbers based on the meaning of the digits using , or = to record the comparison. Suggested Learning Structure Fluency Practice (10 minutes) Application Problem (5 minutes) Concept Development (34 minutes) Student Debrief (11 minutes) Total Time​ (60 minutes)​ Fluency Practice (10 minutes) ⬛ Halfway on the Number Line 3.2C​ (4 minutes) ⬛ Group Counting 3.4E​ (4 minutes) ⬛ Determine the Unit of Measure 3.7D​ (2 minutes) Halfway on the Number Line (4 minutes) Materials: (S) Personal white board Note: This activity anticipates rounding in the next topic. Practicing this skill in isolation lays a foundation for conceptually understanding rounding on a vertical number line. T: (Project a vertical line with endpoints labeled 0 and 10.) What number is halfway between 0 tens and 1 ten? S: 5. T: (Write 5 halfway between 0 and 10.) Repeat the process with endpoints labeled 10 and 20. T: Draw a vertical number line on your board. Make tick marks at each end and one for the halfway point. S: (Draw number line.) T: (Write 7 tens and 8 tens.) Label the tick marks at each end and at the halfway point. S: (Label 70 as the bottom point, 80 at the top point, and 75 as the halfway point.) Continue with the following possible sequence: 50 and 60, 90 and 100, 40 and 50, 60 and 70. Lesson 12: Compare numbers based on the meaning of the digits using , or = to record the comparison. 139 © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 3 2 Group Counting (4 minutes) Note: Group counting reviews interpreting multiplication as repeated addition. The counting by groups in this activity reviews foundational strategies for multiplication from Module 1 and anticipates Module 3. Direct students to count forward and backward, occasionally changing the direction of the count using the following suggested sequence: ⬛ Threes to 30 ⬛ Fours to 40 ⬛ Sixes to 60 ⬛ Sevens to 70 ⬛ Eights to 80 ⬛ Nines to 90 As students’ fluency with skip-counting improves, help them make a connection to multiplication by tracking the number of groups they count using their fingers. Determine the Unit of Measure (2 minutes) Note: This activity reviews the difference in size between grams and kilograms as units of measure from Lesson 5. T: I’ll name an object. You say if it should be measured in grams or kilograms. Pear. S: Grams. Continue with the following possible sequence: tomato, horse, crayon, desk, motorcycle, eraser. hundred ten Application Problem (5 minutes) thousands thousands thousands hundreds tens ones 4 2 9 7 6 Draw and label the units on the place value chart to hundred thousands. Use each of the digits 9, 7, 6, 4, and 2 once to create a number that is between 4 ten thousands and 6 ten thousands. Write the number you created in expanded form and expanded notation. Extension: Create two more numbers following the same directions as above. Note: This Application Problem builds on the content of the previous lesson, requiring students to read and write numbers to 40,000 + 2,000 + 900 + 70 + 6 100,000 using base ten numerals, number (4 x 10,000) + (2 x 1,000) + (9 x 100) + (7 x 10) + (6 x 1) names, expanded form and expanded notation. Lesson 12: Compare numbers based on the meaning of the digits using , or = to 140 record the comparison. © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 3 2 Concept Development (34 minutes) 10,000 100 10,000 100 Materials: (S) Personal white board, unlabeled hundred thousands 10,000 100 place value chart (Lesson Template) 10,000 10,000 100 Problem 1: Comparing two numbers with the same largest unit. 10,000 100 100 100 Display: 40,300 20,500 100 T: Let’s compare two numbers. Model each number on your place value chart. What is the name of the unit with the greatest value? S: Ten thousands. T: Compare the value of the ten thousands. NOTES ON S: 4 ten thousands is greater than 2 ten thousands. 2 ten MULTIPLE MEANS thousands is less than 4 ten thousands. OF REPRESENTATION: T: Tell your partner what would happen if we only compared Provide sentence frames for English hundreds rather than the unit with the greatest value. language learners and other students S: We would say that 40,300 is less than 20,500, but that isn’t to refer to when using comparative correct. à The greater number is the one with more of the statements. largest unit being compared. à We don’t need to compare the hundreds because the ten thousands are different. T: Ten thousands is our largest unit. 4 ten thousands is greater than 2 ten thousands, so 40,300 is the greater number. (Write the comparison symbol > in the circle.) Write the comparison statement on your board, and say it to your partner in two different ways. S: (Write 40,300 > 20,500.) 40,300 is greater than 20,500. 20,500 is less than 40,300. Problem 2: Comparing two numbers with an equal amount of the largest units. Display: 34,051 36,200 T: Model and read each number. How is this comparison like 1,000 10 1 10,000 the last comparison? How is it different? 10,000 1,000 10 1,000 10 S: Thirty-four thousand, fifty-one. Thirty-six thousand, two 10,000 1,000 10 10 hundred. Before, the two numbers had different numbers 1,000 100 of ten thousands. Now, the two numbers have the same 10,000 1,000 100 10,000 number of ten thousands. 10,000 1,000 1,000 1,000 T: If the digits of the largest unit are equal, how do we 1,000 compare? S: We compare the next largest unit. à We compare the digits one place to the right. à We compare the thousands. Lesson 12: Compare numbers based on the meaning of the digits using , or = to record the comparison. 141 © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 3 2 T: Write your comparison statement on your board. Say the comparison statement in two ways. S: (Write 34,051 < 36,200 and 36,200 > 34,051.) 34,051 is less than 36,200. 36,200 is greater than 34,051. Repeat the comparison process using 6,520 and 6,250 and then 18,407 and 12,740. T: Write your own comparison problem for your partner to solve. Create a two-number comparison problem in which the largest unit in both numbers is the same. Problem 3: Comparing values of multiple numbers using a place value chart. Display: 52,103, 52,310, and 52,013 T: Write these numbers in your place value chart. Whisper the value of each digit as you do so. T: When you compare the value of these three numbers, what do you notice? 5 2, 1 0 3 S: All three numbers have 5 ten thousands. à All three numbers have 2 thousands. à We can compare the hundreds because they 5 2, 3 1 0 are different. 5 2, 0 1 3 T: Which number has the greatest value? S: 52,310. T: Tell your partner which number has the least value and how you know. S: 52,013 is the least of the three numbers because it has the least number of hundreds. T: Write the numbers from least to greatest. Use comparison symbols to express the relationships of the numbers. S: (Write 52,013 < 52,103 < 52,310.) Problem 4: Comparing numbers in different number forms. Display: Compare 90,000 + 8,000 + 70 + 6 and 98,706. NOTES ON T: Discuss with a partner how to solve and write your MULTIPLE MEANS comparison. OF ACTION AND S: I will write numerals in my place value chart to compare. à EXPRESSION: I will draw disks for each number. à I will write the first For students who have difficulty number in standard form and then compare. converting numbers from expanded S: (Write 98,076 < 98,706.) form into standard form, have them T: Tell your partner which units you compared and why. write the addition vertically and add, then write the other number below the S: I compared hundreds because the digits for the greater units sum and compare. Alternatively, have were the same. 0 hundreds are less than 7 hundreds, so them write the two numbers in a place 98,076 is less than 98,706. value chart and then compare them. Repeat the comparison process using 6 ten thousands 5 hundreds 8 tens and (6 × 10,000) + (5 × 1,000) + (8 × 10). Lesson 12: Compare numbers based on the meaning of the digits using , or = to 142 record the comparison. © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 3 2 Problem Set (10 minutes) Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students should solve these problems using the RDW approach used for Application Problems. A STORY OF UNITS – TEKS EDITION Lesson 12 Problem Set 3 2 Student Debrief (11 minutes) Name Lesson 12 Problem Set Katrina Date Lesson Objective: Comparing numbers based on meaning 1. Label the units in the place value chart. Draw dots to represent each number in the place value chart. Use , or = to compare the two numbers. Write the correct symbol in the circle. of the digits using , or = to record the comparison. a. 40,603 > 4,087 hundred ten thousands hundreds tens ones thousands thousands The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the b. 67,902 > 63,546 lesson. hundred thousands ten thousands thousands hundreds tens ones Any combination of the questions below may be used to lead the discussion. ⬛ In Problem 1, how does the place value chart help you compare the two numbers? ⬛ In Problem 2, is it necessary to start by writing the numbers in standard form? Why or why not? (Encourage students to notice that we can use the largest unit to begin the comparison regardless of Lesson 12: Comparing numbers based on the meaning of the digits using , or = to record the comparison. 151 the form used to express the number.) © 2020 Great Minds PBC TEKS Edition | greatminds.org/texas ⬛ What challenges arise in comparing numbers that are written in different forms? When you are work- ing a problem like that, what do you think about first? (Encourage students to share their personal 110-161_EM1_TX_E_G03_M02_TE_TopicC_29669.indd 151 21/10/20 2:00 PM strategies.) ⬛ In Problem 2(e), how can you tell which number is greater? ⬛ In Problem 3, how does your understanding of place value help you order the numbers? Lesson 12: Compare numbers based on the meaning of the digits using , or = to record the comparison. 143 © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 3 2 A STORY OF UNITS – TEKS EDITION Lesson 12 Problem Set 3 2 Exit Ticket (3 minutes) Name __________________________________________ Date _____________________ 2. Compare the two numbers by using the symbols , or =. Write the correct symbol in the circle. After the Student Debrief, instruct students to complete a. 5,842 < 40,441 5 8 4 2 the Exit Ticket. A review of their work will help with 4 0 4 4 1 assessing students’ understanding of the concepts that were presented in today’s lesson and planning more b. 92,340 < 98,000 9 2 3 4 0 9 8 0 0 0 effectively for future lessons. The questions may be read aloud to the students. c. 75,311 > 75,199 7 5 3 1 1 7 5 1 9 9 d. 32,014 > 2 ten thousands 8 hundreds 7 tens 6 ones 3 2 0 1 4 2 0 8 7 6 e. 20,000 + 8,000 + 9 > (2 × 10,000) + (8 × 100) + (9 × 1) 2 8 0 0 9 2 0 8 0 9 f. 5 ten thousands 3 thousands 7 tens 2 ones = fifty-three thousand, seventy-two 5 3 0 7 2 5 3 0 7 2 g. 8,397 < eighty thousand, three hundred ninety-seven 8 3 9 7 8 0 3 9 7 A STORY OF UNITS – TEKS EDITION Lesson 12 Problem Set 3 2 Lesson 12: Comparing numbers based on the meaning of the digits using , or = to 146 record the comparison. © 2020 Great Minds PBC TEKS Edition | greatminds.org/texas Name __________________________________________ Date _____________________ 3. The information in the chart is based on the Cities in Texas Population in 2010 2010 census. Baytown 71,802 Use the information to list the populations in order Bryan 76,201 from greatest to least. Then, name the city that had Edinburg 77,100 the lowest population in 2010. Mission 77,058 78,817 people Pharr 70,400 77,100 people Sugar Land 78,817 77,058 people 76,201 people 71,802 people In 2010, Pharr had the lowest population of the Texas cities 70,400 people in the chart at 70,400 people. 4. The planets in the chart are listed in order from Planet Name Diameter the planet closest to the sun to the planet farthest from the sun. The diameter of each planet is given. Mercury 3,032 miles Venus 7,521 miles a. List the names of the planets in order according Earth 7,926 miles to their diameters from least to greatest. Mars 4,221 miles Mercury 3,032 miles Jupiter 88,846 miles Mars 4,221 miles Saturn 74,897 miles Venus 7,521 miles Uranus 31,763 miles Earth 7,926 miles Neptune 30,775 miles Neptune 30,775 miles Uranus 31,763 miles Saturn 74,897 miles Jupiter 88,846 miles b. Does the planet farthest from the sun have the greatest diameter? Explain your reasoning. The planet farthest from the sun does not have the greatest diameter. Neptune is last in the chart, so it is farthest from the sun, but Jupiter has the greatest diameter at 88,846 miles. Lesson 12: Comparing numbers based on the meaning of the digits using , or = to record the comparison. 147 © 2020 Great Minds PBC TEKS Edition | greatminds.org/texas Lesson 12: Compare numbers based on the meaning of the digits using , or = to 144 record the comparison. © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 Problem Set 3 2 Name Date Lesson 12 Problem Set 1. L abel the units in the place value chart. Draw dots to represent each number in the place value chart. Use , or = to compare the two numbers. Write the correct symbol in the circle. a. 40,603 4,087 b. 67,902 63,546 Lesson 12: Compare numbers based on the meaning of the digits using , or = to record the comparison. 145 © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 Problem Set 3 2 Name ___________________________________________ Date ______________________ 2.  Compare the two numbers by using the symbols , or =. Write the correct symbol in the circle. a. 5,842 40,441 b. 92,340 98,000 c. 75,311 75,199 d. 32,014 2 ten thousands 8 hundreds 7 tens 6 ones e. 20,000 + 8,000 + 9 (2 × 10,000) + (8 × 100) + (9 × 1) f. 5 ten thousands 3 thousands 7 tens 2 ones fifty-three thousand, seventy-two g. 8,397 eighty thousand, three hundred ninety-seven Lesson 12: Compare numbers based on the meaning of the digits using , or = to 146 record the comparison. © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 Problem Set 3 2 Name ___________________________________________ Date ______________________ 3. The information in the chart is based on the Cities in Texas Population in 2010 2010 census. Baytown 71,802 Use the information to list the populations in order Bryan 76,201 from greatest to least. Then, name the city that had Edinburg 77,100 the lowest population in 2010. Mission 77,058 Pharr 70,400 Sugar Land 78,817 4. T he planets in the chart are listed in order from Planet Name Diameter the planet closest to the sun to the planet farthest from the sun. The diameter of each planet is given. Mercury 3,032 miles Venus 7,521 miles a. List the names of the planets in order according Earth 7,926 miles to their diameters from least to greatest. Mars 4,221 miles Jupiter 88,846 miles Saturn 74,897 miles Uranus 31,763 miles Neptune 30,775 miles b. Does the planet farthest from the sun have the greatest diameter? Explain your reasoning. Lesson 12: Compare numbers based on the meaning of the digits using , or = to record the comparison. 147 © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 Exit Ticket 3 2 Lesson 12 Exit Ticket Name ___________________________________________ Date ______________________ 1. A  family is buying a used car. They are choosing among four car models. Use the information in the chart to order the car prices from least to greatest. Then name the car model with the lowest price. Used Car Model Price Model A $19,600 Model B $20,195 Model C $19,499 Model D $19,998 2. U  se each of the digits 5, 6, 7, 8, and 9 exactly once to create a five-digit number that makes the comparison true. 80,000 + 9,000 + 200 + 10 + 4 < __________________ Lesson 12: Compare numbers based on the meaning of the digits using , or = to 148 record the comparison. © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 Homework 3 2 Lesson 12 Homework Name ___________________________________________ Date ______________________ 1. L abel the units in the place value chart. Draw place value disks to represent each number in the place value chart. Use , or = to compare the two numbers. Write the correct symbol in the circle. a. 1,823 10,023 b. 83,042 81,342 Lesson 12: Compare numbers based on the meaning of the digits using , or = to record the comparison. 149 © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 Homework 3 2 2. Compare the two numbers by using the symbols , or =. Write the correct symbol in the circle. a. 20,084 2,584 b. 73,000 71,499 c. 45,622 45,266 d. 60,352 6 ten thousands 3 hundreds 5 tens 2 ones e. (9 × 10,000) + (6 × 100) + (3 × 1) 90,000 + 600 + 3 f. 3 ten thousands 2 thousands 7 tens 4 ones fifteen thousand, forty-seven g. 4,125 forty thousand, one hundred twenty-five Lesson 12: Compare numbers based on the meaning of the digits using , or = to 150 record the comparison. © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson 12 Homework 3 2 3. A  group of friends will participate in a 5-kilometer Name Number of Steps walk to raise money for a local charity. The chart Camila 43,098 shows the total number of steps they each walked during the week before the 5-kilometer walk. Emily 42,199 Jasmine 43,100 List the numbers of steps in order from greatest to least. Then, name the person who took the Lanelle 44,005 fewest steps that week. Mia 42,250 4. T he chart lists all the Texas counties where the number People Under the Age of people under the age of 18 was between 50,000 and County in Texas of 18 in 2010 100,000 during the 2010 census. Bell 88,117 a. List the names of the counties in order from least Brazoria 86,985 to greatest according to the number of people Galveston 74,167 under the age of 18. Jefferson 60,398 Lubbock 67,862 McLennan 59,745 Nueces 88,255 Smith 53,796 Webb 88,158 b. Kim made a list of the counties in order from least to greatest according to the total population in 2010 is as follows: Smith, McLennan, Webb, Jefferson, Lubbock, Galveston, Bell, Brazoria, Nueces. Does Kim’s list match the order in Part (a)? Why or why not? Lesson 12: Compare numbers based on the meaning of the digits using , or = to record the comparison. 151 © Great Minds PBC TEKS Edition | greatminds.org/Texas  A STORY OF UNITS – TEKS EDITION Lesson Lesson12 2 Template 3 2 Lesson 2 Template unlabeled hundred thousands place value chart Lesson 12: Compare numbers based on the meaning of the digits using , or = to 152 record the comparison. © Great Minds PBC TEKS Edition | greatminds.org/Texas