Reading and Writing Large Numbers


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1 Reading and Writing Large Numbers Objective To read and write large numbers in standard, expanded, and numberandword notations. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Apply placevalue concepts to read, write, and interpret large numbers. Convert between standard and expanded notations. Apply extended facts and order of operations to express the value of digits in a number. [Operations and Computation Goal 2] Key Activities Students read and write numbers to s in standard notation, expanded notation, and numberandword notation and convert between these notations. Ongoing Assessment: Recognizing Student Achievement Use journal page 45. Ongoing Assessment: Informing Instruction See page 6. Key Vocabulary standard notation expanded notation numberandword notation Materials Math Journal 1, pp. 45 and 46 Math Masters, p. 409 transparency of Math Masters, p. 409 Line Plots and Box Plots Math Journal 1, pp. 47A and 47B Students practice constructing box plots and finding data landmarks and measures of spread. Math Boxes Math Journal 1, p. 47 Students practice and maintain skills through Math Box problems. Study Link Math Masters, pp. 41 and 42 Students practice and maintain skills through Study Link activities. READINESS Playing Number TopIt Math Masters, pp. 463, 464, and 478 per partnership: scissors, tape, 4 each of number cards 0 9 (from the Everything Math Deck, if available) Students apply placevalue concepts to read, write, and compare numbers through s. ENRICHMENT Walking Away with a Billion Dollars Math Masters, p. 43 Students apply placevalue concepts and extended multiplication and division facts to solve a multistep problem. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p.131 Students add the terms expanded notation, standard notation, and numberandword notation to their Math Word Banks. Advance Preparation Allow three days to complete Lessons and 2 2. Make at least one copy of Math Masters, page 409 per student. Teacher s Reference Manual, Grades 4 6 pp Unit 2 Operations with Whole Numbers and Decimals
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 placevalue chart patterns. Math Message Complete the Math Message on journal page Teaching the Lesson Math Message FollowUp (Math Journal 1, p. 45) SOLVING WHOLECLASS DISCUSSION Interactive whiteboardready 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 placevalue 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 placevalue 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 lightyear is a unit of distance. A lightyear is the distance that light travels in one year. One lightyear is roughly 9,500,000,000,000 kilometers. 1. Write the number 9,500,000,000,000 in the blank squares of the placevalue 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 seventyeight 4. fiftyseven, three hundred fortysix, 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 15Digit PlaceValue 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 NumberandWord Notation Convert the numbers given in standard notation to numberandword 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 onedollar 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 numberandword notation to standard notation. Example: The Andromeda galaxy is 2.3 lightyears away. 2,300,000 lightyears 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 WHOLECLASS 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 placevalue 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 placevalue charts. Suggest they use the placevalue 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
4 Interpreting Numberand Word Notation for Large Numbers (Math Journal 1, p. 46; Math Masters, p. 409; Transparency of Math Masters, p. 409) On the board, draw and label five sets of three dashed lines, separated by commas, or use an overhead and show the transparency of Math Masters, page 409. WHOLECLASS Line Plots and Box Plots The line plot below shows the total attendance (in s, rounded to the nearest 0.1 ) in 2009 at each of the 30 Major League Baseball stadiums. X X X X X X X X X X X 2009 Attendance at MLB Stadiums X X X X X X X X X X X X X X X X Millions of People 1. Use the data in the line plot to create a box plot Attendance at MLB Stadiums X X X Numberandword notation consists of the significant digits of a large number followed by a word for the place value. Examples include 27 and 8.5. Use the template to practice converting between standard and numberandword notations. 1. Convert standard notation to numberandword notation. Write 27,000,000 on the placevalue template Millions of People 2. Find the following data landmarks and measures of spread: a. Minimum: 1.4 e. Range: 2.4 b. Maximum: 3.8 f. Lower quartile: 1.9 c. Mode: 1.9 g. Upper quartile: 3.1 d. Median: 2.35 h. Interquartile range: Look at the line plot. What are some advantages to displaying data in a line plot? Sample answer: Each data point is represented. It is easy to see the spread of the data, where data points are clumped, and whether there are outliers. 4. Look at the box plot. What are some advantages to displaying data in a box plot? Sample answer: It is easy to see the median of the data. A box plot shows how the data are distributed and whether or not the data are bunched in a particular quartile. Math Journal 1, p. 47A EM3MJ1_G6_U02_45_81.indd 47A 27, 000, 000 H T O H T O H T O 27 Numberandword notation depends on the largest period. Because the digits 2 and 7 are in the s period, the numberandword notation of 27,000,000 is 27. Now write 8,500,000,000 on the placevalue template. 8, 500, 000, 000 H T O H T O H T O H T O 8.5 The digit 8 is in the s period and 5 is in the s period. Billions is the largest period, so the numberandword notation should be in terms of s. Since 500,000,000 is 0.5, = 8.5. Pose additional problems such as the following: Convert 46,750,000 to numberandword notation Convert 203,600,000,000 to numberandword notation Convert 900,000 to numberandword notation. 900, or 0.9 Line Plots and Box Plots continued The box plots below show the total attendance (in s, rounded to the nearest 0.1 ) in 2009 at the 16 National League stadiums and the 14 American League stadiums Attendance at MLB Stadiums (by league) National League American League Millions of People 5. Find the following data landmarks and measures of spread for the National League data: a. Minimum: 1.5 e. Lower quartile: 1.85 b. Maximum: 3.8 f. Upper quartile: 3.2 c. Median: 2.6 g. Interquartile range: 1.35 d. Range: Find the following data landmarks and measures of spread for the American League data: a. Minimum: 1.4 e. Lower quartile: 1.9 b. Maximum: 3.7 f. Upper quartile: 2.6 c. Median: 2.2 g. Interquartile range: 0.7 d. Range: Use the box plots, landmarks, and measures of spread to compare the attendance data for the National League and American League baseball stadiums. Sample answer: The leagues have similar ranges of data, but the American League data have a smaller median and a much smaller interquartile range. This means that the middle half of the American League data is a lot more bunched than the middle half of the National League data. Math Journal 1, p. 47B 45_81_EMCS_S_G6_MJ1_U02_ indd 47B 3/6/12 1:33 PM Lesson 5
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 stemandleaf 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 numberandword notation. a. The Milky Way galaxy is about 150,000 lightyears across. 150 lightyears 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 placevalue template. Encourage those students to enter digits from right to left. 2. Convert numberandword 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 numberandword notation 32, 650, 000 H T O H T O H T O Adjusting the Activity Have students use the placevalue 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, sixtyfive d. nine, five hundred, two hundred fortythree 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 23. 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
6 Study Link (Math Masters, pp. 41 and 42) INDEPENDENT Home Connection Students apply placevalue concepts to large numbers. They practice writing large numbers in standard, expanded, and numberandword notation. Study Link Master Name STUDY LINK 2 1 Large Numbers continued Because the orbits of the planets are elliptical in shape, the distance between two planets changes over time. The least distances of Mercury, Venus, Saturn, and Neptune from Earth appear in the table at the right. The distances are approximations. Least Distance from Earth Planet Distance (in miles) Mercury 48,000,000 Venus 25,700,000 Saturn 850,000,000 Neptune 2,680,000,000 3 Differentiation Options READINESS Playing Number TopIt (Math Masters, pp. 463, 464, and 478) PARTNER Min 5. Write each planet s least distance from Earth in numberandword notation. 48 miles 25.7 miles 850 miles 2.68 miles a. Mercury b. Venus c. Saturn d. Neptune 6. Write the following numbers in standard notation. 44,300,000,000 6,500,000,000, , a b. 6.5 c. 0.9 d. 0.7 hundred Practice Round each number to the given place ,254; hundreds ,989; ten s 416, , ,857,000; hundred s. 6,593,278; s 1,900,000 7,000,000 To provide experience applying placevalue concepts, have students play Number TopIt. Give each pair of players a copy of Math Masters, pages 463, 464, and 478, scissors, tape, and number cards. After students have assembled their placevalue mats, have them read the game directions. Ask them to record the results for each round of play on page 478. Math Masters, p. 42 ENRICHMENT INDEPENDENT Walking Away with a Billion Dollars (Math Masters, p. 43) 5 15 Min Students apply their knowledge of placevalue concepts and extended multiplication and division facts to solve a multistep problem and explain their solution strategies. ELL SUPPORT INDEPENDENT Building a Math Word Bank (Differentiation Handbook, p. 131) 5 15 Min To provide language support for number notations, have students use the Word Bank template found on Differentiation Handbook, page 131. Ask students to write the terms expanded notation, standard notation, and numberandword notation, draw pictures representing each term, and write other related words. See the Differentiation Handbook for more information. Name 2 1 Walking Away with a Billion Dollars Suppose you inherit one dollars. The bank pays you the entire amount of money in $0 bills. About how much will your payment weigh in tons? Use the information below to solve the problem. You can cover a sheet of paper with about six $0 bills. There are 500 sheets in a ream of paper. There are reams in 1 carton of paper. One ream of paper weighs about 5 pounds. One ton equals 2,000 pounds. Teaching Master Show all your work. Write an explanation that is clear and easy to follow. Sample answer: One sheet of paper is worth about $600, so one ream of paper is worth about $600 º 500, or $300,000. One carton of paper is worth º $300,000, or $3,000,000, and weighs 50 pounds. So, every 3 dollars weighs about 50 pounds. There are about 333 sets of 3 dollars in 1 dollars, so 1 dollars will weigh about 333 º 50 16,650 pounds. 16,650 / 2, tons. My payment will weigh about 8 tons. Math Masters, p. 43 Lesson 7
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