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1 Slide 1 / 192 Slide 2 / 192 New Jersey enter for Teaching and Learning Progressive Mathematics Initiative 5th Grade This material is made freely available at and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others. ecimal oncepts lick to go to website: Slide 3 / 192 Slide 4 / 192 Table of ontents lick on a topic to go to that section. What is a ecimal? The charts have 4 parts. 1 Factor Vocab Word Identify Place Values whole number that can divide into another number with no remainder. Read and Write ecimals whole number that multiplies with another number to make a third number. ompare & Order ecimals 15 Numbers to esignated Place Values 3 3 Examples/ ounterexamples Slide 5 / 192 (s it is used in the lesson.) 5 R is a factor of 15 Glossary 2 Its meaning 3 x 5 = 15 3 is not a factor of 16 3 and 5 are factors of 15 4 ack to Link to return to the instructional page. Instruction Slide 6 / 192 Vocabulary words are identified with a dotted underline. Sometimes when you subtract the fractions, you find that you can't because the first numerator is smaller than the second! When this happens, you need to regroup from the whole number. (lick on the dotted underline.) What is a ecimal? How many thirds are in 1 whole? How many fifths are in 1 whole? How many ninths are in 1 whole? The underline is linked to the page in the presentation's glossary containing the vocab chart. Return to Table of ontents

2 Slide 7 / 192 Slide 8 / 192 Where do we see decimals being used? lick on the photo to find out! What is a decimal number? In baseball, batting averages are in decimals. Miguel abrera has a batting average of In races to show speed. The women's record for the fastest 100 meter dash is seconds. ecimal Number (based on the number 10, tenth parts, and powers of ten) contains a ecimal Point. lick to find out! Music Stations that show their radio frequency in decimals. With money to show dollars and change. This shows $6.91. nd many other places! Slide 9 / 192 Slide 10 / 192 ecimals are used in situations when more precision is needed. Lets take a look at decimals on a number line. lick on the picture below for an interactive number line. Teacher Notes Why do we need decimals? For instance, when two people cross the finish line, someone will win by a fraction of a second. We show those fractions as decimals. If you are spending money, many things are not worth an exact dollar amount. Slide 11 / 192 Slide 12 / 192 Our place value chart is almost like a mirror image, with a line between the ones place and the decimal point. Identify Place Values thousands hundreds tens ones. tenth hundredth thousandths Return to Table of ontents Everything to the left ends in "s" and everything to the right ends in "ths"

3 Slide 13 / 192 Slide 14 / 192 Place Value hart 987, Teacher Notes 1 What digit is in the thousandths place? Slide 14 () / What digit is in the thousandths place? 2 What digit is in the tenths place? 987, , Slide 15 () / What digit is in the hundredths place? 2 What digit is in the tenths place? 987, Slide 16 / , Slide 15 / 192

4 Slide 16 () / 192 Slide 17 / , Yellow Rod How many yellow rods are needed to fill the blue block? click 1 What is the value of a yellow rod? one-tenth (0.1) click 2 lue lock One Unit (1) Slide 17 () / 192 Slide 18 / 192 Teacher Notes Tenths Think of it in terms of money. How many dimes does it take to make a dollar? Yellow Rod Use this page for students to gain an How many yellow rods understanding of are what needed to fill the blue tenths and hundredths look like. block? dimes = 1 dollar 10 click What is the value of a yellow rod? one-tenth (0.1) click lue lock One Unit (1) So, a dime is one tenth of a whole dollar. Slide 19 / 192 Slide 19 () / 192 Hundredths Hundredths Yellow Rod Yellow Rod Red lock Red lock How many red blocks are needed to fill the blue block? 100 (Hint: Fill a yellow rod with red blocks) How many red blocks are needed to fill the blue block? 100 (Hint: Fill a yellow rod with red blocks) click lue lock One Unit (1) Use this page for students to gain an understanding What is the value of aof red what tenths and one-hundredth (0.01) hundredths look like. click lue lock One Unit (1) Teacher Notes What is the value of a red block? one-hundredth (0.01) click Teacher Notes click block? Teacher Notes Tenths 3 What digit is in the hundredths place?

5 Slide 20 / 192 Slide 21 / 192 So a dollar is a whole. Think of it in terms of money. dime is a tenth. How many pennies does it take to make a dollar? nd a penny is a hundredth. pennies = 1 dollar one. tenth hundredth What if we had a coin that was smaller than a penny? So, a penny is one hundredth of a whole dollar. How many times smaller than a penny do you think it would be? What would you call it? Slide 22 / 192 Slide 23 / yellow rods = 0.3 three tenths 23 red blocks = 0.23 twenty three hundredths lue = One Unit lue = One Unit Slide 24 / 192 Slide 24 () / 192 Interactive Number Grid - Use to Show ecimals Interactive Number Grid - Use to Show ecimals Teacher Notes lick to Go to Interactive Site Teacher Notes lick to Go to Interactive Site This site requires Flash 5 Plugin

6 Slide 25 / 192 If the square equals one whole, what does the shaded area represent? If the square equals one whole, what does the shaded area represent? 4 4 Slide 25 () / Slide 26 / 192 If the square equals one whole, what does the shaded area represent? If the square equals one whole, what does the shaded area represent? 5 5 Slide 26 () / If the square equals one whole, what does the shaded area represent? 6 6 Slide 27 () / 192 If the square equals one whole, what does the shaded area represent? Slide 27 /

7 Slide 28 / 192 If the square equals one whole, what does the shaded area represent? If the square equals one whole, what does the shaded area represent? 7 7 Slide 28 () / Slide 29 / 192 If the square equals one whole, what does the shaded area represent? If the square equals one whole, what does the shaded area represent? 8 8 Slide 29 () / Slide 30 / 192 Slide 31 / 192 Lets look at place value using money again. thousands hundreds tens ones. tenth hundredth dime penny pennies = 1 dime dimes = 1 dollar bill 1 dollar bills = 1 ten dollar bill ten dollar bills = 1 hundred dollar bill What do you notice about place value? Place Value s you look at the place value chart, how many times does the value of the number decrease as you go to the right? Each place has a value that is one tenth of the value of its place its left. lick to to reveal

8 Slide 32 / 192 Slide 33 / 192 Lets look at place value using money again. Lets take a closer look at what happens as we move to the left on the place value chart. tens ones. Teacher Notes 10 tens = 1 hundred 10 ones = ten thousands hundreds tenth hundredth dime penny hundred dollars is times as much as ten dollars ten dollars is times as much as a dollar dollar is times as much as a dime dime is times as much as a penny one x 10 = ten x 10 = 1 hundred x 10 = 1 thousand... What do you notice about place value? Slide 34 / 192 Slide 35 / 192 Place Value 1 hundred 10 = ten ten 10 = one s you look at the place value chart, how many times does the value of the number increase as you go to the left? Each place has a value that is 10 times the value of its lick place to the right. to reveal 1 thousand Slide 36 / 192. Lets use place value to compare decimal #s. standard form word form expanded form. hundredths 33 thirty-three hundredths The 3 in the tenths place is ten times as much as the 3 in the hundredths place. Teacher Notes. tenths 10 = 1 hundred. standard form word form expanded form 10 = ten Slide 37 / 192 tenths hundredths 44 forty-four hundredths The 4 in the hundredths place is one tenth the 4 in the tenths place. 10 = 1 Teacher Notes Lets take a closer look at what happens as we move to the right on the place value chart.

9 Slide 38 / 192 Slide 38 () / In the number 3.33, the digit in the tenths place is one tenth of the digit in the hundredths place. True False False True 9 In the number 3.33, the digit in the tenths place is one tenth of the digit in the hundredths place. False Slide 39 / 192 Slide 39 () / In the number , the digit in the thousandths place is one tenth of the digit in the place. ones tenths tenths ones hundredths hundredths 10 In the number , the digit in the thousandths place is one tenth of the digit in the place. Slide 40 / 192 Slide 40 () / digit in the ones place is 100 times as much as a digit in the place. 11 digit in the ones place is 100 times as much as a digit in the place. hundredths tenths hundredths tenths ones ones

10 Slide 41 / 192 Slide 41 () / 192 1/ times 10 times 12 The value of the 6 in is the value of the 6 in /10 12 The value of the 6 in is the value of the 6 in /10 1/ times 100 times From PR sample test From PR sample test Slide 42 / 192 Slide 42 () / The value of the 3 in is the value of the 3 in /10 13 The value of the 3 in is the value of the 3 in / times 1/ times 10 times 1/ times From PR sample test From PR sample test Slide 43 / 192 Slide 44 / ecimals on the number line 3 What does each line, between the whole numbers 2 and 3, represent on this number line? Label the number line. Teacher Notes ecimals on the number line What does each line, between the whole numbers 32 and 33, represent on this number line? Label the number line.

11 Slide 45 / 192 Slide 46 / 192 ecimals on the number line ecimals on the number line What does each line, between the decimal numbers 4.3 and 4.4, represent on this number line? What does each line, between the decimal numbers 0.63 and 0.64, represent on this number line? Label the number line. Label the number line. Slide 47 / 192 Slide 48 / 192 National Library of Virtual Manipulatives 14 lick to go to web site. hange Places to "ecimals" at the bottom left. Which letter corresponds to the number 4.4 on this number line? 10 0 Zoom in to drag the dot more precisely. Slide 48 () / Which letter corresponds to the number 6.8 on this number line? 0 10 Which letter corresponds to the number 4.4 on this number line? 14 Slide 49 / 192

12 Slide 49 () / Which letter corresponds to the number 0.8 on this number line? 0 1 Which letter corresponds to the number 6.8 on this number line? 15 Slide 50 / 192 Slide 50 () / Which letter corresponds to the number 7.2 on this number line? Which letter corresponds to the number 0.8 on this number line? 16 Slide 51 / 192 Slide 51 () / Which letter corresponds to the number 19.3 on this number line? Which letter corresponds to the number 7.2 on this number line? 17 Slide 52 / 192

13 Slide 52 () / Which letter corresponds to the number on this number line? Which letter corresponds to the number 19.3 on this number line? 18 Slide 53 / 192 Slide 53 () / 192 Which letter corresponds to the number 5.35 on this number line? Which letter corresponds to the number on this number line? 4 19 Slide 54 / 192 Slide 54 () / Which letter corresponds to the number 1.08 on this number line? Not plotted on this number line Which letter corresponds to the number 5.35 on this number line? 20 Slide 55 / 192

14 Slide 55 () / [This object is a pull tab] Not plotted on this number line Which letter corresponds to the number 6.23 on this number line? Not plotted on this number line Slide 56 () / 192 Which letter corresponds to the number 6.23 on this number line? Slide 57 () / Which letter corresponds to the number 17.4 on this number line? Not plotted on this number line Slide 58 / 192 Which letter corresponds to the number 17.4 on this number line? Slide 57 / 192 Not plotted on this number line Not plotted on this number line 1 22 Read & Write ecimals Return to Table of ontents Which letter corresponds to the number 1.08 on this number line? 21 Slide 56 / 192

15 Slide 59 / 192 Slide 60 / 192 Word Form In this unit, we will be working with numbers written in standard, word and expanded form. Word form is simply the number written using words instead of digits, commas, and a period when needed ones 3 2 Lets review each tenths and and and ,000 hundredths thousandths Word Form three and four hundredths two and three hundred fifty-one thousandths eight tenths Slide 62 / 192 ndth andth o u sa ten th redth thous hund an d tenth one an d red ten hund thous o u sa o u sa red th n ten th hund millio To read decimal numbers we: nd nd Slide 61 / 192 9, 8 7 5, Read the number to the left of the decimal 2. Say "and" for the period 3. Read the number to the right of the decimal 4. State the place value of the last digit. This number is read: Nine million, eight hundred seventy-five thousand, six hundred ten N four hundred seventy-nine thousandths Remember the place values after the decimal point start with tenths Slide 64 / s andth thous s hund redth tenth tens 5 an d 3 4 o n es 2 s reds hund an d s thous lick on the the dice, and then read the number. Teacher Notes Slide 63 / 192 an you read the number?

16 Slide 64 () / 192 Teacher Notes lick on the the dice, and then read the number. lick on the double arrows for the first dice and fill in whole numbers. Then click on the double arrows for the second dice and fill in decimal numbers. Slide 65 / 192 How do you write a decimal in words? 1. Look to see if there is a number to the left of the decimal; if so write it out. If there is no number to the left of the decimal, skip to step Write an and for the decimal point. 3. Write the number in the decimal part. 4. Write the word for the place value of the rightmost digit. Write in words Thirteen and twenty-four lick to reveal hundredths The numbers twenty-one through lickalways to reveal ninety-nine are hyphenated. Slide 66 / 192 Slide 67 / 192 How does a comma help when writing a decimal number? Write the decimal in words The place value before the comma is always stated. 1) 5.04 Five and four hundredths For example: 2) One hundred forty-six and four hundred fifty-seven thousandths 1,547 is written One THOUSN, five hundred forty-seven 3).0009 Nine ten-thousandths 4) 6, Six thousand, three hundred forty-five and one hundred forty-nine thousand ths Slide 68 / 192 Slide 69 / 192 Teacher Notes 6,547,100 is written 6 MILLION, five hundred forty-seven THOUSN, one hundred

17 Slide 70 / four and thirty-six four and thirty-six tenths four, thirty-six What is 4.36 in word form? four and thirty-six What is 4.36 in word form? 24 Slide 70 () / 192 four and thirty-six tenths four, thirty-six four and thirty-six hundreths four and thirty-six hundreths Slide 71 / What is in word form? What is in word form? sixty-three and sixty-seven hundredths sixty-three and sixty-seven thousandths sixty-three and sixty-seven thousandths sixty-three and sixty-seven sixty-three and sixty-seven hundredths 25 Slide 71 () / 192 sixty-three and sixty-seven sixty-three, sixty-seven thousandths sixty-three, sixty-seven thousandths 26 What is in word form? zero and four hundred nineteen four hundred nineteen hundredths four hundred nineteen thousandts four one nine 26 Slide 72 () / 192 What is in word form? zero and four hundred nineteen Slide 72 / 192 four hundred nineteen hundredths four hundred nineteen thousandts four one nine

18 Slide 73 / What is 0.09 in Slide 73 () / word form? word form? nine hundredths nine and nine hundredths nine and nine nine and nine What is 0.09 in nine hundredths nine and nine hundredths nine and zero nine tenths nine and zero nine tenths Slide 74 / word form? four zero seven zero two one What is in word form? four zero seven zero two one four hundred seven twenty-one four hundred seven and twenty-one thousandths four hundred seven and twenty-one hundredths four hundred seven twenty-one What is in 28 Slide 74 () / 192 four hundred seven and twenty-one thousandths four hundred seven and twenty-one hundredths Slide 75 / 192 Standard Form Standard form is the way we usually see numbers written, using digits, commas and a period when needed. Standard Form Slide 76 / 192 Standard Form 1. If there is a ths, there will be a decimal 2. If there is an and, there will be a whole number to the left of the decimal 3. Note the ending - this is the place where the decimal number will end 4. Use the decimal chart to help you!

19 Slide 77 / 192 Slide 78 / 192 s Teacher Notes andth thous s redth hund s tenth an d o n es tens red s hund thous an d s Use the chart as a guide to write the decimal numbers in standard form. 1. two hundred sixteen and 2 tenths 2. thirty-two and nine thousandths 3. four thousand, five hundred six and twenty-four hundredths 4. nine hundred and eight hundredths Slide 79 / 192 What is fifty-two and eighteen hundredths? 52,18 52, What is fifty-two and eighteen hundredths? 29 Slide 79 () / Slide 80 / 192 What is five thousand, fifty and five hundredths? , , , , , , What is five thousand, fifty and five hundredths? 30 Slide 80 () / 192

20 Slide 81 / 192 What is six hundred three and four thousandths? What is six hundred three and four thousandths? 31 Slide 81 () / 192 Slide 82 / 192 What is thirty-four hundredths? What is thirty-four hundredths? 32 Slide 82 () / 192 Slide 83 / 192 What is four hundred ninety-five thousandths? What is four hundred ninety-five thousandths? 33 Slide 83 () / 192

21 Slide 84 / 192 Slide 85 / 192 Expanded Form Place value charts make it easy to write numbers in expanded form, because it helps us see the value of each digit ones tenths and and and ,000 hundredths thousandths Expanded Form Slide 86 / 192 Slide 87 / 192 This interactive game will help you practice writing numbers in expanded form. s a class, select the correct building blocks for each place value, then write the number in expanded form. heck your work as a class Slide 88 / 192 Slide 88 () / What is in standard form? 34 What is in standard form? Teacher Notes To write a number in expanded form, the number is written as a sum of the value of each digit.

22 Slide 89 / 192 Slide 89 () / What is in standard form? 35 What is in standard form? Slide 90 / 192 Slide 90 () / Which is equivalent to 30.53? Which is equivalent to 30.53? Slide 91 / Which is equivalent to 0.873? Slide 91 () / Which is equivalent to 0.873?

23 Slide 92 / 192 Slide 92 () / 192 eight tenths 38 Which number is equivalent to 0.08? eight hundredths eight tenths Which number is equivalent to 0.08? eight hundredths Slide 93 / 192 Slide 93 () / Which number is equivalent to three hundred four thousandths Which number is equivalent to three hundred four thousandths Slide 94 / 192 Slide 94 () / Which number is equivalent to sixteen hundredths? 40 Which number is equivalent to sixteen hundredths?

24 Slide 95 / 192 Slide 96 / 192 There are two symbols we use to compare numbers when they are not equal. We call these number sentences inequalities. > (greater than) < (less than) ompare & Order ecimals One number goes on the left of the symbol and another number goes on the right of the symbol. Return to Table of ontents The number on the left of the ">" shows the larger number. For example: 2>1 2 is "greater than" 1 The number on the left of the "<" shows the smaller number. For example: 1<2 1 is "less than" 2 Slide 97 / 192 Slide 98 / 192 omparing ecimals Symbols and Words to remember when comparing numbers SYMOL WORS > greater than/largest < = less than/ smallest equal Slide 99 / 192 Slide 100 / 192 ompare and 0.21 Line up the decimal points Put zeros in wherever digits are missing ompare the digits, from left to right The largest digit, having the same place value, names the largest number Line up the decimal points Put zeros in wherever digits are missing ompare the digits, from left to right The largest digit, having the same place value, names the largest number < 0.21 lick to reveal ompare 0.36 and put zero on the end ompare left to right. 2 is greater than 0, so 0.21 is greatest. Line up the decimal points Put zeros in wherever digits are missing ompare the digits, from left to right The largest digit, having the same place value, names the largest number 0.36lick>to0.312 reveal put zero on the end ompare left to right. 6 is greater than 1, so 0.36 is greatest.

25 Slide 101 / 192 Slide 102 / 192 ecimal Squares Interactive Games ompare and 0.02 Line up the decimal points Put zeros in wherever digits are missing ompare the digits, from left to right The largest digit, having the same place value, names the largest number put zero on the end ompare left to right. 2 is greater than 0, so 0.02 is greatest < 0.02 lick to reveal Slide 103 / 192 Slide 103 () / 192 hoose the correct symbol. > < = hoose the correct symbol. > < 41 In this game the robot won, because is greater than Game could also be played with two students having a spinner and writing down their decimal number. = lick for link Slide 104 / > < = 42 three hundred eleven thousandths hoose the correct symbol > < = three hundred eleven thousandths hoose the correct symbol. 42 Slide 104 () / 192

26 Slide 105 / 192 hoose the correct symbol. > hoose the correct symbol. > < < 43 = 43 Slide 105 () / 192 = 0.05 Slide 106 / Slide 106 () / 192 hoose the correct symbol. > < hoose the correct symbol. > twenty-four hundredths < twenty-four hundredths = = Slide 107 / 192 > < = forty-six hundredths 45 hoose the correct symbol. > 0.6 < = forty-six hundredths hoose the correct symbol. 45 Slide 107 () /

27 Slide 108 / 192 Slide 108 () / 192 Marcel 46 In a paper airplane contest, Marcel's plane travels meters. Salvador's plane travels 3.35 meters. ased on the measurements, whose plane traveled the farthest distance? On your paper, explain you know. If youhow have struggling students, this is a good opportunity to utilize Marcel "think, pair, share." Salvador Salvador (erived from ( (erived from Slide 109 / 192 Slide 110 / 192 Ordering ecimals 47 Line up all of the decimal points ompare the digits, from left to right names the largest number Example: What digit tells us this is the largest number? click ompare the digits 1 Slide 110 () / The number with the least value is: Slide 111 / The number with the least value is: The largest digit, having the same place value, The number with the least value is: Put zeros in wherever digits are missing Why is this the smallest number? This will provide students with a platform to learn [This object is a pull tab] from each other. ( 46 In a paper airplane contest, Marcel's plane travels meters. Salvador's plane travels 3.35 meters. ased on the measurements, whose plane traveled the farthest distance? On your paper, explain how you know.

28 Slide 111 () / 192 The number with the greatest value is: The number with the least value is: 48 Slide 112 / Slide 112 () / The number with the greatest value is: The number with the greatest value is: 49 Slide 113 / 192 Slide 113 () / How much money would you like to win? 0.67 $ $ $ $ The number with the greatest value is: 50 Slide 114 / 192

29 Slide 114 () / 192 How much money would you like to win? 52 Using the following digits, create the largest number you can between 0 and 1. $ $ $ $ , 7, 0, 2 51 Slide 115 / 192 Slide 115 () / Using the following digits, create the largest number you can between 0 and 1. Slide 116 / Using the following digits, create the smallest number you can between 0 and 1. 1, 7, 0, 2 1, 7, 0, Slide 116 () / 192 Slide 117 / 192 Ordering ecimals 53 Using the following digits, create the smallest number you can between 0 and 1. Order the numbers from least to greatest. Move the numbers to put them in order. 1, 7, 0,

30 Slide 118 / 192 Slide 119 / 192 Ordering ecimals 54 Order the numbers from greatest to least. Move the numbers to put them in order. Which of the following is ordered least to greatest? 0.3, 0.03, 0.33, , 0.33, 0.3, Slide 119 () / Which of the following is ordered least to greatest? Slide 120 / Which of the following is ordered least to greatest? 0.3, 0.03, 0.33, , 0.06, , 0.3, 0.33, , 0.06, , 0.33, 0.3, , 0.3, 0.33, , 0.5, Slide 120 () / Which of the following is ordered greatest to least? 0.008, 0.06, , 0.008, 0.087, , 0.06, , 0.087, 0.87, , 0.5, , 0.87, 0.087, Which of the following is ordered least to greatest? 55 Slide 121 / 192

31 Slide 121 () / Which of the following is not correct? 8.07, 0.008, 0.087, > 0.08 > , 0.087, 0.87, > > , 0.87, 0.087, Which of the following is ordered greatest to least? 56 Slide 122 / < 0.08 < 0.23 Slide 122 () / Which of the following is correct? 0.23 > 0.08 > < 0.32 < 0.41 < > > > > 0.41 > < 0.08 < 0.23 Which of the following is not correct? 57 Slide 123 / > 0.41 > > 0.8 Which of the following is correct? 0.8 < 0.32 < 0.41 < > > 0.41 > > 0.41 > > In a paper airplane contest, Marcel's plane travels meters. Salvador's plane travels 3.35 meters. Jennifer's plane travels 3.3 meters. ased on the measurements, who won the contest? On your paper, explain your answer. Marcel Salvador Jennifer (erived from ( 58 Slide 124 / 192 Slide 123 () / 192

32 Slide 124 () / 192 Slide 125 / In a paper airplane contest, Marcel's plane travels meters. Salvador's plane travels 3.35 meters. Jennifer's plane travels 3.3 meters. ased on the measurements, who won the contest? If you have struggling On your paper, explain your answer. students, this is a good opportunity to utilize Marcel "think, pair, share." Numbers to esignated Place Values Jennifer This will provide students with a platform to learn from each other. [This object is a pull tab] (erived from Return to Table of ontents ( Salvador Slide 126 / 192 Slide 127 / 192 Number Line Investigation 0 10 Instructions for the next slide: 1. Roll the die. 2. lick the yellow arrow to pop out the number. 3. Move the number to the correct place on the number line. 4. etermine whether the number is closer to 0 or 10. The dotted line shows the halfway mark between 0 and 10. Think, Pair, Share: This can be repeated six times. What rule can you use to determine whether any given number is closer to 0 or to 10? Slide 128 / 192 Slide 129 / 192 ing 8,749 to the nearest ten. 1. Put your pencil point under the digit in the tens place. Look to the right. ing makes numbers easier to work with in your head. ed numbers are only approximate. n exact answer generally can not be obtained using rounded numbers. Use rounding to get an answer that is close and does not have to be exact. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit? Increases by 1 OR remains the same 4. What happens to everything to the left of the tens place? Those digits always remain the same. 5. What happens to everything to the right of the tens place? Those digits become zero. Teacher Notes Review

33 Slide 129 () / 192 8,749 to the nearest ten. 2. Is the digit 5 or more? Yes OR No Teacher Notes 1. Put your pencil point under the digit in the tens place. Look to the right. Move pencil under the digit that is being rounded to Slide 130 / 192 Review 8,749 to the nearest hundred. 1. Put your pencil point under the digit in the tens place. Look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit? 3. What happens to the digit? Increases by 1 OR remains the same Teacher Notes Review Increases by 1 OR remains the same 4. What happens to everything to the left of the tens place? Those digits always remain the same. 5. What happens to everything to the right of the tens place? Those digits become zero. 4. What happens to everything to the left of the hundreds place? Those digits always remain the same. 5. What happens to everything to the right of the hundreds place? Those digits become zero. Slide 130 () / 192 Slide 131 / 192 Review 8,749 to the nearest hundred to the nearest ten. Move pencil under the digit that is being rounded to 2. Is the digit 5 or more? Yes OR No Teacher Notes 1. Put your pencil point under the digit in the tens place. Look to the right. 3. What happens to the digit? Increases by 1 OR remains the same 4. What happens to everything to the left of the hundreds place? Those digits always remain the same. 5. What happens to everything to the right of the hundreds place? Those digits become zero. Slide 131 () / to the nearest ten ,561 to the nearest hundred. 60 Slide 132 / 192

34 Slide 132 () / 192 Slide 133 / ,561 to the nearest hundred. 564,012 to the nearest hundred thousand. 61 4,600 Slide 133 () / Slide 134 / ,399 to the nearest thousand. 564,012 to the nearest hundred thousand. 600,000 Slide 134 () / ,399 to the nearest thousand. 7,000 63,752 to the nearest hundred. 63 Slide 135 / 192

35 Slide 135 () / 192 Slide 136 / 192 What happens in this case? 64 63, to the nearest ten. to the nearest hundred. 63,800 The 7 to the right of the 9 tells us to increase the 9 by 1. What happens? Slide 137 / 192 Slide 137 () / ,972 to the nearest hundred. 3,972 to the nearest hundred. 4,000 Slide 138 / 192 Slide 138 () / to the nearest ten. 98 to the nearest ten

36 Slide 139 / 192 Slide 139 () / to the nearest 399,238 ten thousand. 399,238 ten thousand. to the nearest ,000 Slide 140 / 192 Slide 140 () / ,521 to the nearest thousand. 9,521 to the nearest thousand. 10,000 Slide 141 / 192 Slide 141 () / ,983 to the nearest hundred. 9,983 to the nearest hundred ,000

37 Slide 142 / 192 Slide 143 / 192 Number Line Investigation 1 2 Instructions for the next slide: 1. Roll the die. 2. lick the yellow arrow to pop out the number. 3. Position the number in the correct place on the number line. 4. etermine whether the number is closer to 1 or 2. The dotted line shows the halfway mark between 1 and 2. This can be repeated six times. Think, Pair, Share: What rule can you use to determine whether any given number is closer to 1 or to 2? Slide 144 / 192 ing ecimals Let's learn how to round decimals using the following examples: to the nearest tenths place. When rounding decimals, put your pencil point under the place value that you are rounding to O NOT MOVE IT Slide 145 / to the nearest tenth. 1. Put your pencil point under the digit in the tenths place. Look to the right. 2. Is the digit 5 or more? Yes OR No 3. What happens to the digit? Increases by 1 OR remains the same 4. What happens to everything to the left of the tenths place? Those digits always remain the same. Slide 146 / What happened to the digits to the right of the tenths place? Slide 147 / to the hundredths place. Remember, we are rounding. 1. Put your pencil point under the digit in the hundredths place. Look to the right. The place values to the right of the tenths place have zero value, so now the digits 6 and 8 become zeroes. 2. Is the digit 5 or more? Yes OR No = What happens to the digit? Increases by 1 OR remains the same However we leave the zeros off when they are at the end of a number to the right of the decimal point. 4. What happens to everything to the left of the hundredths place? Those digits always remain the same. 5. What happens to everything to the right of the hundredths place? Those digits become zero (and we leave them off since they are to the right of the decimal).

38 Slide 148 / 192 Slide 149 / 192 Which of the decimals round to 0.02? Try this: to the nearest hundredths place : lick to reveal 0.02 Slide 150 / 192 Slide 150 () / to the nearest hundredth. to the nearest hundredth Slide 151 / to the nearest ten. to the nearest ten Slide 151 () /

39 Slide 152 / to the nearest hundred. to the nearest hundred Slide 152 () / 192 6,900 Slide 153 / to the nearest tenth. to the nearest tenth Slide 153 () / Slide 154 / to the nearest thousand. to the nearest thousand Slide 154 () / 192 7,000

40 Slide 155 / 192 Slide 155 () / to the nearest thousandth to the nearest thousandth Slide 156 / 192 When rounding to a specific place, your answer MUST have a digit in that place Example: to the nearest tenth to the nearest tenth. : 24.0 There must be a digit in the tenths place, since we were to round to the tenths place. Slide 157 () / 192 Slide 158 / to the nearest tenth. to the nearest hundredth aution! Slide 157 / 192

41 Slide 158 () / to the nearest hundredth. to the nearest tenth Slide 159 / 192 Slide 159 () / to the nearest tenth. to the nearest thousandth Slide 160 / 192 Slide 160 () / to the nearest thousandth. to the nearest tenth Slide 161 / 192

42 Slide 161 () / Slide 162 / decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is What is the maximum possible value of this decimal? On your paper, use words and the number line to explain your reasoning to the nearest tenth. (Problem derived from Slide 163 / decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is What is the minimum possible value of this decimal? On your paper, use words and the number line to explain your reasoning. 81 decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is What is the maximum possible value of this decimal? On your paper, use words and the number line to explain your reasoning. ( Slide 162 () / ( (Problem derived from Slide 163 () / 192 Slide 164 / Jules reads that one pint is equivalent to liters. He asks his teacher how many liters there are in a pint. His teacher responds that there are about 0.47 liters in a pint. He asks his parents, and they say there are about 0.5 liters in a pint. Who is correct? On your paper, explain your answer. 82 decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is What is the minimum possible value of this decimal? On your paper, use words and the number line to explain your reasoning. His teacher His parents oth of them ( (Problem derived from (Problem derived from ( ( (Problem derived from

43 Slide 164 () / 192 Slide 165 / 192 Or have them choose a corner of the room (assign a letter to each of 3 His parents corners) and justify their answer. Students can then persuade each [This object is a pull tab] at the correct answer. oth of themother to arrive (Problem derived from cm cm cm Slide 165 () / 192 Slide 166 / Rainfall collected in a rain gauge was found to be 3.4 cm when rounded to the nearest tenth of a centimeter. Select all the measurements below that could be the actual measurement of the rainfall cm cm 85 nnual rainfall total for cities in New York are listed below. Rochester Ithaca 0.97 meters meters Saratoga Springs New York ity 1.5 meters meters the smallest total rainfall to the nearest tenth cm cm (erived from Slide 166 () / 192 rag and rop nnual rainfall total for cities in New York are listed below. Ithaca 0.97 meters Rochester rag and drop one number into each box. When you are finished, the number inside each box should match the number below the box when rounded to the nearest hundredth meters Saratoga Springs New York ity 1.5 meters 0.9 meters meters the smallest total rainfall[this toobject the nearest tenth. is a pull tab] (erived from ( 85 Slide 167 / 192 From PR sample test ( cm ( group, before discussing it as a class. His teacher 84 Rainfall collected in a rain gauge was found to be 3.4 cm when rounded to the nearest tenth of a centimeter. Select all the measurements below that could be the actual measurement of the rainfall. 83 Jules reads that one pint is equivalent to liters. He asks his teacher how many liters there are in a there are about 0.47 pint. His teacher responds that liters in a pint. He asks having his parents, onsider studentsand write they their say explanations, their answers, there are about 0.5 liters insubmit a pint. Who is correct? then pair-share a partner or their On your paper, explain your with answer.

44 Use rounding to estimate answers to problems. t a restaurant, a burger is $5.99, fries are $3.85 and a small drink is $1.29. to the nearest dollar to estimate the cost to purchase all three items. ost Estimate $5.99 $6 $3.85 $4 $1.29 $1 Slide 169 / the following items, to the nearest dollar, to figure out the approximate cost if all of the items were bought. pens $2.99 pencils $2.20 book bag $15.75 Slide 168 / 192 It would cost about $11 to purchase all three items. 86 the following items, to the nearest dollar, to figure out the approximate cost if all of the items were bought. pens $2.99 pencils $2.20 book bag $15.75 $3+$2+$16 =$21.00 Slide 170 / the following items to the nearest dollar to figure out the approximate cost if all of the items were bought. jeans $24.99 t-shirt $6.79 hat $12.31 Slide 169 () / the following items to the nearest dollar to figure out the approximate cost if all of the items were bought. jeans $24.99 t-shirt $6.79$25+$7+$12 hat $12.31 =$44.00 Slide 171 / the following items to the nearest dollar to figure out the approximate cost if all of the items were bought. milk $3.79 bread $2.15 juice $2.40 Slide 170 () / 192

45 88 the following items to the nearest dollar to figure out the approximate cost if all of the items were bought. milk $3.79 bread $2.15 juice $2.40 $4+$2+$2 = $8 Slide 172 / the following items to the nearest half dollar to figure out the approximate cost if all of the items were bought. chicken $8.60 potatoes $2.45 peas $0.99 Slide 171 () / the following items to the nearest half dollar to figure out the approximate cost if all of the items were bought. chicken $8.60 potatoes $2.45 peas$9.00+$2.50+$1.00 $0.99 Slide 173 / the following items to the nearest half dollar to figure out the cost if all of the items were bought. apples $4.60 bananas $1.90 oranges $3.10 =$12.50 Slide 172 () / the following items to the nearest half dollar to figure out the cost if all of the items were bought. apples $4.60 bananas $1.90 oranges $3.10 $5.00+$ = $10.00 Slide 174 / the following items to the nearest ten dollars to figure out the approximate cost if all of the items were bought. sneakers $36.21 sweatshirt $13.99 socks $6.00 Slide 173 () / 192

46 Slide 174 () / 192 Slide 175 / the following items to the nearest ten dollars to figure 92 the following items to the nearest hundred dollars to figure out the approximate cost if all of the items were bought. computer$ printer $ desk $ sneakers $36.21 sweatshirt $13.99 $40.00+$10.00+$10.00= socks $6.00 $60.00 out the approximate cost if all of the items were bought. Slide 175 () / 192 Slide 176 / the following items to the nearest hundred dollars to figure out the approximate cost if all of the items were bought. Glossary computer$ printer $700+$200+$200= $ desk $ $1100 Return to Table of ontents Slide 177 / 192 Slide 178 / 192 ecimal Number Expanded Form ecimal Number (based on the number 10, tenth parts, and powers of ten) contains a ecimal Point. When a number is written as a sum of the value of each digit = ack to ack to Instruction Instruction

47 Slide 179 / 192 Slide 180 / 192 Greater Than Hundredths symbol that shows that the number on the left is larger than the number on the right. part of one whole that has been divided into 100 equal parts. lso, a part of one tenth that has been divided into 10 equal parts. the alligator eats the bigger number.4 > four tenths is greater than two tenths ack to ack to 0.01 Instruction Slide 181 / 192 Instruction Slide 182 / 192 Inequality Less Than number statement that shows that two numbers are not equal. symbol that shows that the number on the left is smaller than the number on the right..2 =.4.4 >.2 four tenths is greater than two tenths.2 <.4 two tenths is less than four tenths two tenths is not equal to four tenths the alligator will not eat the smaller # ack to.2 <.4 two tenths is less than four tenths Instruction ack to Instruction Slide 183 / 192 Slide 184 / 192 Place Value Standard Form The value of a digit depending on its position in a number. Standard form is the way we usually see numbers written, using digits, commas and a period when needed ack to Instruction ack to Instruction

48 Slide 185 / 192 Slide 186 / 192 Tenths Thousandths part of one whole that has been divided into 10 equal parts. part of one whole that has been divided into 1,000 equal parts. lso, a part of one tenth that has been divided into 100 equal parts, and a part of one hundredth that has been divided into 10 equal parts ack to ack to Instruction Instruction Slide 187 / 192 Slide 188 / 192 Word Form Unit Word form is a number written using words instead of digits, commas, and a period when needed. unit is used to describe one of something. In place value, a unit is the ones place. $2.99 for 16 oz $ for 1 oz three dollars and forty-four cents Unit (1 unit) :24pm three and forty-five hundredths Eight twenty-four pm ack to ack to Instruction Instruction Slide 189 / 192 Slide 190 / 192 ack to ack to Instruction Instruction

49 Slide 191 / 192 Slide 192 / 192 ack to ack to Instruction Instruction

Gap Closing. Representing and Comparing Decimals. Junior / Intermediate Student Book

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