Reading Writing Small Numbers Objective To read write small numbers in stard exped notations wwweverydaymathonlinecom epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Stards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts Skills Apply place-value concepts to read, write, interpret numbers less than [Number Numeration Goal ] Convert between stard exped notations [Number Numeration Goal ] Apply extended facts order of operations to express the value of digits in a number [Operations Computation Goal 2] Key Activities Students read write numbers to in stard notation exped notation They also convert between these notations Key Vocabulary stard notation exped notation Materials Math Journal, pp 48 5 Study Link 2 Math Masters, p 4 transparency of Math Masters, p 4 4 2 3 Playing High-Number Toss (Decimal Version) Student Reference Book, p 324 Math Masters, p 455 per partnership: 4 each of number cards 9 (from the Everything Math Deck, if available), calculator (optional) Students practice reading, writing, comparing numbers through Ongoing Assessment: Recognizing Student Achievement Use Math Masters, p 455 [Number Numeration Goal 6] Math Boxes Math Journal, p 5 Students practice maintain skills through Math Box problems Study Link Math Masters, pp 44 45 Students practice maintain skills through Study Link activities READINESS Modeling Comparing Decimals Math Masters, pp 46 4 43 scissors Students use base- grids to model compare decimals through ENRICHMENT Decimals between Decimals Students explore the infinite number of decimals between any two given decimal numbers Advance Preparation Allow three days for Lessons 2 Make at least one copy of Math Masters, page 4 per student Teacher s Reference Manual, Grades 4 6 pp 94 98 8 Unit 2 Operations with Whole Numbers Decimals
Getting Started Mathematical Practices SMP, SMP3, SMP4, SMP6, SMP7 Content Stards 6NS6c, 6NS7a Mental Math Reflexes Students divide numbers by record their answers on slates or dry-erase boards $ / $ $ / $ $3 / $3 / / / Refer to the above problems during discussions of place-value chart patterns Math Message Complete the Math Message on journal page 48 Study Link 2 Follow-Up Briefly review answers Teaching the Lesson Math Message Follow-Up (Math Journal, pp 48 49) WHOLE-CLASS DISCUSSION In the previous lesson, students used their knowledge of place-value concepts to read write whole numbers In this lesson, they will apply similar place-value concepts to read write fractional quantities The number 6 that students recorded in the chart is written in stard notation Stard notation is a base-ten placevalue numeration Ask students to look at 6 identify the digits in the following places: ten- 6 SOLVING Ask students to generate a few sentences using the different meanings of tenth For example, Mary finished in tenth place; A dime is a tenth of a dollar Have students work in pairs to look for patterns in the place-value chart Then ask them to share the patterns they found Patterns include: Each place is _ the value of the place to its left times the value of the place to its right The value of each place in the place-value chart is a power of The value of each place to the left of the decimal point is a product of s, for example, = The value of each place to the right of the decimal point is a product of _ (or s), for example, = _ _ = NOTE Multiplying a number by _ is the same as dividing the number by s Math Message Reading Writing Numbers between A grain of salt is about 6 millimeter long Write the number 6 in the place-value chart below Adjusting the Activity 6 Write each of the following numbers in stard form four 4 2 twenty-three 23 3 seventy-five 75 4 one hundred nine ten- 9 5 eight 8 6 one fifty-four 54 7 twenty-four fifty-six 2456 8 Write the word name for the following decimal numbers ten- hundred- a 6 Sixteen hundred- b One millionth ELL Have students highlight each th ending in the place-value chart on journal page 48 Discuss the difference between tenth as an ordinal number tenth as a fractional part AUDITORY KINESTHETIC TACTILE VISUAL 28 Math Journal, p 48 EM3MJ_G6_U2_45_8indd 48 // 5:33 PM Lesson 9
Reading Writing Small Numbers Complete the following sentences Example: A grain of salt is about 4, or four, of an inch long A penny weighs about, or one tenth, of an ounce 2 A dollar bill weighs about 35, or thirty-five, of an ounce 3 On average, fingernails grow at a rate of about 28, or twenty-eight ten-, of a centimeter per day 4 Toenails, on average, grow at a rate of about 7, or seven ten-, of a centimeter per day 5 It takes about 5, or five, of a second for a smell to transfer from the nose to the brain 6 A baseball thrown by a major-league pitcher takes about, or one hundredth, of a second to cross home plate 7 A flea weighs about 7, or seventeen hundred-, of an ounce 8 A snowflake weighs about 4, or four hundred-, of an ounce Try This 9 About how many times heavier is a penny than a dollar bill? About 3 times as heavy About how many times faster do fingernails grow than toenails? About 4 times as fast Math Journal, p 49 45_8_EMCS_S_G6_MJ_U2_576388indd 49 28 2/5/ 2:57 PM To read a small number such as 6, underline the final digit identify its place value 6, ten- Then read the number (ignoring the decimal point any leading zeros) followed by the place value One thous sixteen ten- Writing the number as a fraction or a mixed number can also help students read it For example, 6738 as a mixed number is 6 _ 738, is read six seven hundred thirty-eight To write a small number, such as three hundred fifty-nine ten-, in stard notation, the last digit of the decimal number should be in the place value named Ten- Draw a decimal point mark spaces up to including the place identified Write the number in the spaces so the final digit is written in the last space at the right 3 5 9 Fill any blank spaces with zeros 3 5 9 NOTE In Everyday Mathematics, a zero appears to the left of the decimal point in any number greater than less than This makes it easier to order decimal numbers, to draw attention to the decimal point, to correspond with the display on most calculators Have students complete journal pages 48 49 Exped Notation for Small Numbers Write each of the following numbers in exped notation Example: 596 ( 5 ) + ( 9 ) + ( 6 ) 847 (8 ) + (4 ) + (7 ) 2 393 (3 ) + (9 ) + (3 ) 3 253 (2 ) + (5 ) + (3 ) Give the value of the underlined digit in each number below Example: 2354 5, or 5 4 969665 5 59994 6 236273 6 7 3 8, Six seven hundred thirty-eight 3 5 5, or 5 ten- 9, or 9 3, or 3 hundred- 7 3872946 2, or 2 Write each number as a fraction or mixed number _ 735 3 _ 4 Example : 735, Example 2: 34 8 73 9 23575 543 9 ten- Three hundred fifty-nine ten ten- hundred- _, 7 3_ 235 75_, 543 Adjusting the Activity Have students use the place-value template (Math Masters, p 4) as they work on the journal pages, Math Boxes, 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 Interpreting Exped Notation for Small Numbers (Math Journal, p 5; Math Masters, p 4; Transparency of Math Masters, p 4) 4 9 5 ten- hundred- WHOLE-CLASS Display a transparency of Math Masters, page 4 distribute one copy of the same page to each student Ask students to write the number 495 in the place-value chart Students will apply skills they used in the previous lesson to write this decimal number in exped notation (4 ) + (9 ) + (5 ) Have students work independently to complete journal page 5 Use extended facts to complete the following 5 a tenth = b hundredth = c thousth = Math Journal, p 5 EM3MJ_G6_U2_45_8indd 5 2// :58 AM Unit 2 Operations with Whole Numbers Decimals
2 Ongoing Learning & Practice Playing High-Number Toss (Decimal Version) (Student Reference Book, p 324; Math Masters, p 455) Divide the class into pairs distribute four each of number cards 9 to each pair, as well as a game record sheet (Math Masters, p 455) Students may need to play a practice game At the end of each round when finding the total score, allow students to use calculators, if needed Ongoing Assessment: Recognizing Student Achievement PARTNER Math Masters Page 455 Use Math Masters, page 455 to assess students ability to compare decimals through Students are making adequate progress if they are able to identify the larger number Some students may not need a calculator to find the difference between scores [Number Numeration Goal 6] Math Boxes Write each of the following numbers using digits a five fifty-five 555 b one hundred eight 8 c two hundred six nineteen ten- 269 26 27 2 Write each number in exped form a 5378 b 942 3 This line graph shows the average monthly rainfall in Jacksonville, Florida Rainfall (in inches) (5 ) + (3 ) + (7 ) + (8 ) (9 ) + (4 ) + (2 ) Which conclusion can you draw from the graph? Average Monthly Rainfall Fill in the circle next to the best answer in Jacksonville, Florida 8 A At least months of the year, the 7 average rainfall is less than 35 inches 6 5 B The average rainfall increases from 4 June through December 3 2 C The average rainfall for May November is about the same Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec D Jacksonville gets more rain on average than Tampa Month 4 Janessa is 3 years older than her brother Lamont EM3MJ_G6_U2_45_8indd 5 a If Janessa is 8 years old, how old is Lamont? 5 years old b How old is Janessa when she is twice as old as Lamont? 6 years old Math Journal, p 5 5 Find the perimeter of the square if s = 43 cm Use the formula P = 4 s, where s represents the length of one side P = 72 cm s 22 5 // 5:33 PM Math Boxes (Math Journal, p 5) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 2-4 The skills in Problems 4 5 preview Unit 3 content Writing/Reasoning Have students write a response to the following: Explain why each of the other three answers for Problem 3 is not the best choice Sample answer: A is not correct because only 5 months have an average rainfall less than 35 inches B is incorrect because the average rainfall is very low from October to December D is not correct because there is no way to know what the average rainfall is for Tampa Study Link Master Name STUDY LINK 2 2 Writing Decimals Build a numeral Write: 2 Build a numeral Write: 9 in the place, 3 in the place, 4 in the place, 6 in the ten- place, 8 in the place, 4 in the place, 3 in the place, in the place, 6 in the place in the place 26 28 Study Link (Math Masters, pp 44 45) Home Connection Students practice place-value skills write small numbers in stard exped notations INDEPENDENT Answer: Answer: 38 469 346 Write the following numbers in words 3 8 4 95 5 5 6 67 7 482 Write a decimal place value in each blank space eight- ninety-five five- sixty-seven four eight hundred two ten- hundred- 8 Bamboo grows at a rate of about 4, or four, kilometer per hour 9 The average speed that a certain br of catsup pours from the mouth of the bottle is about 3, or three, mile per hour A three-toed sloth moves at a speed of about 68 to 98, or sixty-eight to ninety-eight, mile per hour Math Masters, p 44 Lesson
Name STUDY LINK 2 2 Writing Decimals continued Write each of the following numbers in exped notation Example: 2756 (2 º ) (7 º ) (5 º ) (6 º ) 3 2 93527 3 Using the digits, 3, 6, 8, write the greatest decimal number possible 863 4 Using the digits, 3, 6, 8, write the least decimal number possible 368 Try This ten- hundred- (º ) (3 º ) ( º ) (9 º ) (3 º ) (5 º ) (2 º ) (7 º ) C A D B 6 65 7 Name the point on the number line that represents each of the following numbers D A C B 63 5 66 6 6299 7 6 8 695 9 Refer to the number line above Round 6299 to the nearest hundredth Practice Study Link Master 68 742 2 6 8 2 7 4 2 459 58 22 4 5 9 23 5 8 Math Masters, p 45 NOTE Collect store students base- grids for future use 2 r 2 Teaching Master Name 46 Modeling Comparing Decimals One way to compare decimals is to model them with base- grids The flat is the whole, or The long is worth Another way to compare decimals is to draw pictures The flat is the whole, or The cube is worth The fractional part of the cube is worth Use decimal models to complete the following = = = Model the decimal numbers in each pair Draw a picture to record each model Then compare the decimal numbers using <, >, or = 2 3 3 4 56 562 4 5 Model record a decimal number that is between 4 42 Sample answer: > 2 25 The long is worth The cube is worth The fractional part of the cube is worth > < Math Masters, p 46 48 4 < < 42 3 Differentiation Options READINESS Modeling Comparing Decimals (Math Masters, pp 46, 4 43) PARTNER 5 5 Min To provide experience comparing decimals, have students use base- grids Provide each pair with one copy of Math Masters, page 46, two copies of page 4, one copy of pages 42 43, scissors Review the worth of the flat, long, unit, fractional parts of the unit, as shown on Math Masters, page 46 After students have prepared their base- grids, ask them to record their models compare the given decimal numbers using <, >, or = ENRICHMENT PARTNER Decimals between Decimals 5 5 Min Between any two decimal numbers, there is always another decimal number Help students explore this concept by asking them to list 2 or more decimal numbers between a given pair of decimals Suggested decimal pairs include: 2; 33 34; 256 2562 Have students describe any patterns or strategies they used to generate their lists Continue the discussion by asking students to comment about the relative positions of their answers on the number line Ask questions such as the following: If a number is between 33 34, is it greater than or less than 33? Greater than 33 Should the number be to the left of 33 or to the right of 33 on the number line? To the right of 33 If a number is between 33 34, is it greater than or less than 34? Less than 34 Should the number be to the left of 34 or to the right of 34 on the number line? To the left of 34 Choose two of your decimal numbers between 256 2562 Which number would be farther to the right on a number line? Answers vary Encourage students to sketch number lines plot the decimal numbers to verify their relative positions Have students make a general statement about the relative positions of two numbers on a number line Sample answer: A greater number will be farther to the right on a number line EM3cuG6MM_U2_4-7indd 46 /7/ 3:38 PM 2 Unit 2 Operations with Whole Numbers Decimals