# Reading and Writing Large Numbers

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2 Getting Started Mathematical Practices SMP1, SMP2, SMP4, SMP7 Content Standards 6.SP.4, 6.SP.5c, 6.SP.5d Mental Math and Reflexes Students write numbers from dictation and record numbers that are times as great. Suggestions: Write 9,0. Write the number that is times as great. 90,0 Write 150,0. Write the number that is times as great. 1,50 Write 30,0,000. Write the number that is times as great. 300,0,000 Write 701,0,0. Write the number that is times as great. 7,0, Refer back to the above problems during discussions of place-value chart patterns. Math Message Complete the Math Message on journal page Teaching the Lesson Math Message Follow-Up (Math Journal 1, p. 45) SOLVING WHOLE-CLASS DISCUSSION Interactive whiteboard-ready epresentations are available at to help you teach the lesson. Ask students to share the methods they used to record the number 9,500,000,000,000 in the place-value chart. Some students may have entered digits from right to left, moving from ones to s. Others may have used the commas to organize their digit entries. The number 9,500,000,000,000 is written in standard notation the most familiar way of representing whole numbers and decimal numbers. In standard notation, digits are written in specified places. Most students should be able to read and write large numbers in standard notation. Have pairs of students look for patterns in the place-value chart and share the patterns they find. Patterns include: Each place is times the place to its right. Each period or group is divided into three places ones, tens, and hundreds. Each period or group is separated by a comma. Ask students to write on their slates or on the board the number that is: times as great as 9,500,000,000, ,000,000,000,000 1_ times as great as 9,500,000,000, ,000,000,000 Math Message Reading and Writing Large Numbers A light-year is a unit of distance. A light-year is the distance that light travels in one year. One light-year is roughly 9,500,000,000,000 kilometers. 1. Write the number 9,500,000,000,000 in the blank squares of the place-value chart. 0,000,000,000,000,000,000,000,000,000 s s s s ones 0,000,000,000,000,000,000 0,000,000,000,000 0,000, , 5 0 0, 0 0 0, 0 0 0, Write each of the following numbers in standard notation. 2. one hundred twenty 120,000,000,000 5,878,000,000, five, eight hundred seventy-eight 4. fifty-seven, three hundred forty-six, five hundred three, four hundred nineteen Write the following number in expanded notation. Example: 9,763 = (9 ) + (7 0) + (6 ) + (3 1) 1 57,346,503, ,062 (4,000) + (7 ) + (6 ) + (2 1) 6. 68,250,000 (6,000,000) + (8 ) + (2 0,000) + (5,000) Math Journal 1, p. 45 EM3MJ1_G6_U02_45_81.indd 45 Lesson 3

3 Name 0,000,000,000,000,000,000,000,000,000 Teaching Aid Master 15-Digit Place-Value Charts s s s s ones 0,000,000,000,000,000,000 0,000,000,000,000 0,000,000 0 Math Masters, p. 409 Number-and-Word Notation Convert the numbers given in standard notation to number-and-word notation. Example: SeaWorld Adventure Park in Orlando, Florida, is the second most visited aquarium in the United States. Each year, approximately 5,0,000 people visit this attraction. 1. Disneyland Paris, the fourth most popular amusement park in the world, has about 12,800,000 visitors annually. 2. Approximately 8,700,000,000 one-dollar bills are in circulation in the United States. 1 people 12.8 visitors 8.7 dollar bills 3. Ross, the tenth closest star to Earth, is approximately 61,0,000,000,000 miles away miles Convert the numbers given in number-and-word notation to standard notation. Example: The Andromeda galaxy is 2.3 light-years away. 2,300,000 light-years 4. The Library of Congress in Washington, D.C., contains more than 128 items. 5. Bill Gates purchased one of Leonardo da Vinci s notebooks for 30.8 dollars. 6. The tuition, books, and living expenses for 4 years of college can be as much as a quarter of 1 dollars ,000,000 30,800,000 items dollars 250,000 dollars Interpreting Expanded Notation for Large Numbers (Math Journal 1, p. 45; Math Masters, p. 409; Transparency of Math Masters, p. 409) 0,000,000,000,000 s s s s ones,000,000,000,000,000 0,000,000,000,000,000,000 0,000,000,000,000 0,000,000 0 WHOLE-CLASS Display a transparency of Math Masters, page 409 and give one copy of the same page to each student. Ask students to write the number 235 in the place-value chart at the top half of the page. They will convert this number from standard notation into expanded notation. In expanded notation, a number is written as the sum of the values of its digits. For example, in the number 235, the place of the digit 2 is hundreds, so its value is 2 0. The value of the digit 3 is 3. The value of the digit 5 is 5 1. So, in expanded notation, 235 is written as: (2 0) + (3 ) + (5 1). Help students see how they can apply their extended multiplication facts to write numbers in expanded notation. The diameter of the Sun is about 863,706 miles. Ask students to record this number in their place-value charts. Suggest they use the place-value chart to convert this number from standard notation to expanded notation. When students have finished, ask a volunteer to share his or her work. 863,706 = (8 0,000) + (6,000) + (3 ) + (7 0) + (6 1) Pose additional problems such as the following: Write 68,250,000 in expanded notation. (6,000,000) + (8 ) + (2 0,000) + (5,000) Write 2,703,9 in expanded notation. (2 ) + (7 0,000) + (3 ) + (1 0) + (9 1) Have students work independently to complete journal page 45. When most students have finished, go over the answers. Ongoing Assessment: Recognizing Student Achievement 1 Journal Page 45 Problems 2 4 Use journal page 45, Problems 2 4 to assess students ability to write whole numbers to s. Students are making adequate progress if they are able to successfully complete Problems 2 4. Some students may be able to complete Problems 5 and 6. Math Journal 1, p. 46 EM3MJ1_G6_U02_45_81.indd 46 4 Unit 2 Operations with Whole Numbers and Decimals

5 Math Boxes 1. Circle the value of the underlined digit in the number 193,247,056,825. A. 900,000,000,000 B. 90,000,000,000 C. 9,000,000,000 D. 900,000, Use the stem-and-leaf plot to find the following landmarks. a. maximum 258 Stems Leaves (0s and s) (1s) b. minimum c. median d. mode Complete the What s My Rule? table. Rule: Multiply by. in out ,030 39, , ,925 45,021 Math Journal 1, p. 47 EM3MJ1_G6_U02_45_81.indd Convert the numbers given in standard notation to number-and-word notation. a. The Milky Way galaxy is about 150,000 light-years across. 150 light-years b. The greatest distance that Neptune is from Earth is about 2,920,000,000 miles miles Solve. Marta s mother is 5 times as old as Marta. Marta s mother is 25 years old. a. How old is Marta? 5 years old b. In 5 years, Marta s mother will be 3 times as old as Marta. How old will Marta be then? years old 240 Ongoing Assessment: Informing Instruction Watch for students who have not developed an effective strategy for entering numbers into the place-value template. Encourage those students to enter digits from right to left. 2. Convert number-and-word notation to standard notation. Write on the board. Point out that the decimal point represents the comma named by the word. So, in 32.65, the decimal point represents the s comma. Show students how to use the comma to position the nonzero digits. Then insert zeros to complete the conversion to standard notation. (See margin.) Pose additional problems such as the following: Convert 125 to standard notation. 125,000,000 Convert 27.5 to standard notation. 27,500 Convert 140 to standard notation. 140,000,000,000 Have students complete journal page 46. decimal point in number-and-word notation 32, 650, 000 H T O H T O H T O Adjusting the Activity Have students use the place-value templates (Math Masters, p. 409) as they work on the journal pages, Math Boxes, and Study Link for this lesson. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Name STUDY LINK 2 1 Large Numbers 1. Write the digit in each place of the number 6,812,507,439. a. s b. hundred s c. ten s d. s e. hundred s f. ten s 2. Write each of the following numbers in standard form. a. four hundred thirty b. ninety, one hundred five c. one hundred seventy, sixty-five d. nine, five hundred, two hundred forty-three 3. Write each number in expanded form. Example: 235 = (2 º 0) + (3 º ) + (5 º 1) a. 32 b. 7,300,000,000,000 c. 2,5,709 Study Link Master Use extended facts to complete the following. a. 1 5 º b. 1 5 º c. 1 5 º 430,000 90,5, ,000,065 9,500,243,000 (3 º 0,000) + (2 º,000) + (1 º ) (7 º,000) + (3 º 0,000,000,000) (2 º ) + (5 º 0,000) + (1 º,000) + (7 º 0) + (9 º 1) Math Masters, p Ongoing Learning & Practice Line Plots and Box Plots (Math Journal 1, pp. 47A and 47B) INDEPENDENT Students practice constructing box plots and finding data landmarks and measures of spread. They consider the advantages of displaying data in box plots and in line plots. Math Boxes (Math Journal 1, p. 47) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 2-3. The skills in Problems 4 and 5 preview Unit 3 content. Writing/Reasoning Have students write a response to the following: Explain how you solved Problem 5a. Sample answer: I divided Marta s mother s age by 5 to get Marta s age. 6 Unit 2 Operations with Whole Numbers and Decimals

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