Slide 30 / 192 Representing Units Lets take a closer look at what happens as we move to the left on the place value chart. Teacher Notes 10 tens = 1 hundred 10 ones = ten one x 10 = ten x 10 = 1 hundred x 10 = 1 thousand... Slide 31 / 192 Money and Decimals Lets look at place value using money again. . ones tens thousands hundreds tenth hundredth dime penny A hundred dollars is ____ times as much as ten dollars A ten dollars is ____ times as much as a dollar A dollar is ____ times as much as a dime A dime is ____ times as much as a penny What do you notice about place value? Slide 31 (Answer) / 192 Money and Decimals Lets look at place value using money again. . tens ones thousands hundreds tenth hundredth MP.4 - Model with mathematics. penny dime For this standard, students should Math Practice solve real life & society related questions and represent real life A hundred dollars is ____ times as much as ten dollars scenarios mathematically. A ten dollars is ____ times as much as a dollar Using money to solve problems comparing place value gives A dollar is ____ times as much as a dime students an opportunity to do this. [This object is a pull tab] A dime is ____ times as much as a penny What do you notice about place value?
Slide 32 / 192 Place Value As 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 place to the right. Click to reveal Slide 33 / 192 Representing Units Lets take a closer look at what happens as we move to the right on the place value chart. 1 hundred 10 = ten ten 10 = one 1 thousand 10 = 1 hundred 10 = ten 10 = 1 Slide 33 (Answer) / 192 Representing Units Teacher Notes Use the moveable Lets take a closer look at what happens as we pieces to show that move to the right on the place value chart. ten is "one tenth" of 100, and one is "one 1 hundred 10 = ten ten 10 = one tenth" of ten. [This object is a pull tab] 1 thousand 10 = 1 hundred 10 = ten 10 = 1
Slide 34 / 192 Place Value . Lets use place value to compare decimal #s. tenths hundredths 33 . standard form word form thirty-three hundredths 0.3 + 0.03 expanded form The 3 in the tenths place is ten times as much as the 3 in the hundredths place. Slide 34 (Answer) / 192 Place Value . Lets use place value to compare decimal #s. Writing numbers in word, standard and expanded tenths hundredths Teacher Notes form has been addressed 33 previously. Take note if you have students who . need extra instruction/ standard form practice with this skill. The words are also linked to vocabulary slides. [This object is a pull tab] word form thirty-three hundredths expanded form 0.3 + 0.03 The 3 in the tenths place is ten times as much as the 3 in the hundredths place. Slide 35 / 192 Place Value . tenths hundredths 44 . standard form forty-four hundredths word form 0.4 + 0.04 expanded form The 4 in the hundredths place is one tenth the 4 in the tenths place.
Slide 36 / 192 9 In the number 3.33, the digit in the tenths place is one tenth of the digit in the hundredths place. True False Slide 36 (Answer) / 192 9 In the number 3.33, the digit in the tenths place is one tenth of the digit in the hundredths place. True False Answer False [This object is a pull tab] Slide 37 / 192 10 In the number 11.111, the digit in the thousandths place is one tenth of the digit in the ________ place. A ones B tenths C hundredths
Slide 37 (Answer) / 192 10 In the number 11.111, the digit in the thousandths place is one tenth of the digit in the ________ place. A ones Answer B tenths C C hundredths [This object is a pull tab] Slide 38 / 192 11 A digit in the ones place is 100 times as much as a digit in the ______ place. A ones B tenths C hundredths Slide 38 (Answer) / 192 11 A digit in the ones place is 100 times as much as a digit in the ______ place. A ones Answer C B tenths C hundredths [This object is a pull tab]
Slide 39 / 192 12 The value of the 6 in 26.495 is _______________ the value of the 6 in 17.64. A 1/10 B 10 times C 1/100 D 100 times From PARCC EOY sample test #18 Slide 39 (Answer) / 192 12 The value of the 6 in 26.495 is _______________ the value of the 6 in 17.64. A Answer A 1/10 B 10 times C 1/100 [This object is a pull tab] D 100 times From PARCC EOY sample test #18 Slide 40 / 192 13 The value of the 3 in 0.931 is _______________ the value of the 3 in 0.384 A 1/10 B 10 times C 1/100 D 100 times From PARCC EOY sample test #18
Slide 40 (Answer) / 192 13 The value of the 3 in 0.931 is _______________ the value of the 3 in 0.384 A 1/10 A Answer B 10 times C 1/100 D 100 times [This object is a pull tab] From PARCC EOY sample test #18 Slide 41 / 192 Decimals on the Number Line 3 2 What does each line, between the whole numbers 2 and 3, represent on this number line ? Label the number line. Slide 41 (Answer) / 192 Decimals on the Number Line Use the interactive Teacher Notes number line if further 3 2 exploration is needed. What does each line, between the whole numbers 2 and 3, represent on this number line ? [This object is a pull tab] Label the number line.
Slide 42 / 192 Decimals on the Number Line 33 32 What does each line, between the whole numbers 32 and 33, represent on this number line ? Label the number line. Slide 43 / 192 Decimals on the Number Line 4.4 4.3 What does each line, between the decimal numbers 4.3 and 4.4, represent on this number line ? Label the number line. Slide 44 / 192 Decimals on the Number Line 0.63 0.64 What does each line, between the decimal numbers 0.63 and 0.64, represent on this number line? Label the number line.
Slide 45 / 192 National Library of Virtual Manipulatives Click to go to web site. Change Places to "Decimals" at the bottom left. Zoom in to drag the dot more precisely. Slide 46 / 192 14 Which letter corresponds to the number 4.4 on this number line? A B C D 0 10 Slide 46 (Answer) / 192 14 Which letter corresponds to the number 4.4 on this number line? A B C D 0 10 Answer C [This object is a pull tab]
Slide 47 / 192 15 Which letter corresponds to the number 6.8 on this number line? 0 10 A B C D Slide 47 (Answer) / 192 15 Which letter corresponds to the number 6.8 on this number line? Answer 0 A B C D 10 C [This object is a pull tab] Slide 48 / 192 16 Which letter corresponds to the number 0.8 on this number line? 0 A B C D 1
Slide 48 (Answer) / 192 16 Which letter corresponds to the number 0.8 on this number line? Answer 0 A B C D 1 C [This object is a pull tab] Slide 49 / 192 17 Which letter corresponds to the number 7.2 on this number line? A B C D 7 8 Slide 49 (Answer) / 192 17 Which letter corresponds to the number 7.2 on this number line? 7 A B C D 8 Answer B [This object is a pull tab]
Slide 50 / 192 18 Which letter corresponds to the number 19.3 on this number line? 19 A B C D 20 Slide 50 (Answer) / 192 18 Which letter corresponds to the number 19.3 on this number line? 19 A B C D 20 Answer C [This object is a pull tab] Slide 51 / 192 19 Which letter corresponds to the number 324.5 on this number line? A B C D 4 325 2 3
Slide 51 (Answer) / 192 19 Which letter corresponds to the number 324.5 on this number line? A B C D 4 325 2 3 Answer B [This object is a pull tab] Slide 52 / 192 20 Which letter corresponds to the number 5.35 on this number line? 5.3 A B C D 5.4 Slide 52 (Answer) / 192 20 Which letter corresponds to the number 5.35 on this number line? 5.3 5.4 A B C D Answer C [This object is a pull tab]
Slide 53 / 192 21 Which letter corresponds to the number 1.08 on this number line? 1 1.1 A B C Not plotted on this number line D Slide 53 (Answer) / 192 21 Which letter corresponds to the number 1.08 on this number line? Answer B 1 B C 1.1 A Not plotted on this number line D [This object is a pull tab] Slide 54 / 192 22 Which letter corresponds to the number 6.23 on this number line? 6.2 6.3 A B C D Not plotted on this number line
Slide 54 (Answer) / 192 22 Which letter corresponds to the number 6.23 on this number line? 6.2 6.3 A B C Answer B Not plotted on this number line D [This object is a pull tab] Slide 55 / 192 23 Which letter corresponds to the number 17.4 on this number line? 17.1 C 17.2 A B Not plotted on this number line D Slide 55 (Answer) / 192 23 Which letter corresponds to the number 17.4 on this number line? 17.1 Answer 17.2 A B C D [This object is a pull tab] D Not plotted on this number line
Slide 56 / 192 Read & Write Decimals Return to Table of Contents Slide 57 / 192 In this unit, we will be working with numbers written in standard, word, and expanded form. Lets review each. Slide 58 / 192 Word Form Word form is simply the number written using words instead of digits, commas, and a period when needed. . 1 1 10 1 1 100 10 1,000 ones tenths hundredths thousandths 3 0 4 and 2 3 5 1 and 8 and Word Form three and four hundredths two and three hundred fifty-one thousandths eight tenths
Slide 59 / 192 Reading Decimals To read decimal numbers we: 1. 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. Slide 60 / 192 Reading Decimals hundred thousand ten thousandth ten thousand thousandth hundredth thousand hundred million tenth one and ten 9, 8 7 5, 6 1 0 . 4 7 9 This number is read: Nine million, eight hundred seventy-five thousand, six hundred ten AND four hundred seventy-nine thousandths Remember the place values after the decimal point start with tenths Can You Read the Number? Slide 61 / 192 thousandths hundredths thousands hundreds tenths ones tens and 0 . 0 7 5 4 6 . 2 5 9 8 . 3 0 . 8 9 0 . 0 1 1 2 3 5 . 6 4 9 . 7
Slide 62 / 192 Dice Reading Click on the the dice, and then read the number. Slide 62 (Answer) / 192 Dice Reading Click on the the dice, and then read the number. Teacher Notes Click 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. [This object is a pull tab] Slide 63 / 192 Writing Decimals 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 3. 2. 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 13.24 in words Thirteen and twenty-four hundredths Click to reveal The numbers twenty-one through ninety-nine are always hyphenated. Click to reveal
Slide 64 / 192 Writing Decimals How does a comma help when writing a decimal number? The place value before the comma is always stated. For example: 1,547 is written One THOUSAND, five hundred forty-seven 6,547,100 is written 6 MILLION, five hundred forty-seven THOUSAND, one hundred Slide 65 / 192 Write the Decimal in Words 1) 5.04 Five and four hundredths 2) 146.457 One hundred forty-six and four hundred fifty-seven thousandths 3) .0009 Nine ten-thousandths 4) 6,345.149 Six thousand, three hundred forty-five and one hundred forty-nine thousandths Slide 65 (Answer) / 192 Write the Decimal in Words MP.1 - Make sense of problems and persevere in solving them. Some students may not know where to Math Practice begin. Sketching a place value chart, and 1) 5.04 Five and four hundredths using comas and the decimal point as benchmarks may help. 2) 146.457 One hundred forty-six and four hundred fifty-seven thousandths Ask: How could you start this problem? How could you make it easier to solve? What are you having trouble with? 3) .0009 Nine ten-thousandths To guide them to using these strategies. [This object is a pull tab] 4) 6,345.149 Six thousand, three hundred forty-five and one hundred forty-nine thousandths
Slide 66 / 192 Slide 67 / 192 Web Site Practice Slide 67 (Answer) / 192 Web Site Practice Practice I gives a decimal in standard form, and has the students identify the Teacher Notes word form. Practice II gives the decimal number verbally, and has the students identify the number given. (This can be saved for the next set of practice problems) To use responders with these problems, start a multiple- choice instant question. [This object is a pull tab]
Slide 68 / 192 24 What is 4.36 in word form? four and thirty-six A four and thirty-six tenths B four, thirty-six C four and thirty-six hundredths D Slide 68 (Answer) / 192 24 What is 4.36 in word form? four and thirty-six A four and thirty-six tenths B Answer D C four, thirty-six four and thirty-six hundredths D [This object is a pull tab] Slide 69 / 192 25 What is 63.067 in word form? sixty-three and sixty-seven hundredths A sixty-three and sixty-seven thousandths B sixty-three and sixty-seven C sixty-three, sixty-seven thousandths D
Slide 69 (Answer) / 192 25 What is 63.067 in word form? sixty-three and sixty-seven hundredths A sixty-three and sixty-seven thousandths B Answer B sixty-three and sixty-seven C sixty-three, sixty-seven thousandths D [This object is a pull tab] Slide 70 / 192 26 What is 0.419 in word form? zero and four hundred nineteen A four hundred nineteen hundredths B four hundred nineteen thousandths C four one nine D Slide 70 (Answer) / 192 26 What is 0.419 in word form? zero and four hundred nineteen A Answer C four hundred nineteen hundredths B four hundred nineteen thousandths C four one nine D [This object is a pull tab]
Slide 71 / 192 27 What is 0.09 in word form? A nine and nine B nine hundredths C nine and nine hundredths D nine and zero nine tenths Slide 71 (Answer) / 192 27 What is 0.09 in word form? A nine and nine B nine hundredths C nine and nine hundredths Answer B D nine and zero nine tenths [This object is a pull tab] Slide 72 / 192 28 What is 407.021 in word form? four zero seven zero two one A four hundred seven twenty-one B C four hundred seven and twenty-one thousandths four hundred seven and twenty-one hundredths D
Slide 72 (Answer) / 192 28 What is 407.021 in word form? four zero seven zero two one A B four hundred seven twenty-one Answer C four hundred seven and twenty-one thousandths C D four hundred seven and twenty-one hundredths [This object is a pull tab] Slide 73 / 192 Standard Form Standard form is the way we usually see numbers written, using digits, commas and a period when needed. Standard Form 10.88 0.387 92.3 6.91 Slide 74 / 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!
Slide 75 / 192 Standard Form Chart Use the chart as a guide to write the decimal numbers in standard form. thousandths hundredths thousands hundreds tenths ones tens and 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 76 / 192 Web Site Practice Slide 76 (Answer) / 192 Web Site Practice Practice I gives a decimal in standard form, and has the students identify the Teacher Notes word form. Practice II gives the decimal number verbally, and has the students identify the number given. (This can be saved for the next set of practice problems) To use responders with these problems, start a multiple- choice instant question. [This object is a pull tab]
Slide 77 / 192 29 What is fifty-two and eighteen hundredths? A 52,18 B 52.018 C 52.18 D 52.0018 Slide 77 (Answer) / 192 29 What is fifty-two and eighteen hundredths? A 52,18 B 52.018 C 52.18 Answer C D 52.0018 [This object is a pull tab] Slide 78 / 192 30 What is five thousand, fifty and five hundredths? 550.5 A B 5,050.5 5,050.05 C 5,500.05 D
Slide 78 (Answer) / 192 30 What is five thousand, fifty and five hundredths? 550.5 A 5,050.5 B Answer C 5,050.05 C 5,500.05 D [This object is a pull tab] Slide 79 / 192 31 What is six hundred three and four thousandths? 603.4 A 603.004 B 603.04 C 603.0004 D Slide 79 (Answer) / 192 31 What is six hundred three and four thousandths? 603.4 A 603.004 B Answer C 603.04 B 603.0004 D [This object is a pull tab]
Slide 80 / 192 32 What is thirty-four hundredths? 340 A B 34 0.34 C 0.034 D Slide 80 (Answer) / 192 32 What is thirty-four hundredths? 340 A 34 B Answer C 0.34 C D 0.034 [This object is a pull tab] Slide 81 / 192 33 What is four hundred ninety-five thousandths? A 495 B 495.000 C 0.0495 D 0.495
Slide 81 (Answer) / 192 33 What is four hundred ninety-five thousandths? A 495 B 495.000 C 0.0495 Answer D D 0.495 [This object is a pull tab] Slide 82 / 192 Expanded Form To write a number in expanded form, the number is written as a sum of the value of each digit. Place value charts make it easy to write numbers in expanded form, because it helps us see the value of each digit. 1 . 1 10 1 1 100 10 1,000 ones tenths hundredths thousandths 3 0 4 and 1 2 3 5 and 8 and Expanded Form 3 + 0.04 2 + 0.3 + 0.04 + 0.001 0.8 Slide 83 / 192 2 0.008 0.03 0.5
Slide 83 (Answer) / 192 Use this tool as a place value visual to model Teacher Notes 2 expanded form to the 0.008 0.03 0.5 students. (Pull the numbers apart.) Show how it breaks down to 2 + 0.5 + 0.03 + 0.008 [This object is a pull tab] Slide 84 / 192 Decimal Place Value Game This interactive game will help you practice writing numbers in expanded form. As a class, select the correct building blocks for each place value, then write the number in expanded form. Check your work as a class. 100 + 20 + 9 + 0.2 + 0.04 Slide 85 / 192
Slide 86 / 192 34 What is 80 + 0.2 + 0.03 in standard form? Slide 86 (Answer) / 192 34 What is 80 + 0.2 + 0.03 in standard form? Answer 80.23 [This object is a pull tab] Slide 87 / 192 35 What is 0.5 + 0.004 in standard form?
Slide 87 (Answer) / 192 35 What is 0.5 + 0.004 in standard form? Answer 0.504 [This object is a pull tab] Slide 88 / 192 36 Which is equivalent to 30.53? A 30+0.5+0.3 B 3+0.05+0.03 C 0.3+0.05+0.003 D 30+0.05+0.003 Slide 88 (Answer) / 192 36 Which is equivalent to 30.53? A 30+0.5+0.3 B 3+0.05+0.03 Answer C C 0.3+0.05+0.003 D 30+0.05+0.003 [This object is a pull tab]
Slide 89 / 192 37 Which is equivalent to 0.873? A 0.8+0.07+0.03 B 8+0.7+0.3 C 0.8+0.07+0.3 D 0.8+0.07+0.003 Slide 89 (Answer) / 192 37 Which is equivalent to 0.873? A 0.8+0.07+0.03 B 8+0.7+0.3 Answer D C 0.8+0.07+0.3 D 0.8+0.07+0.003 [This object is a pull tab] Slide 90 / 192 38 Which number is equivalent to 0.08? A eight tenths B 0.8 + 0.08 C eight hundredths
Slide 90 (Answer) / 192 38 Which number is equivalent to 0.08? A eight tenths Answer B 0.8 + 0.08 C C eight hundredths [This object is a pull tab] Slide 91 / 192 39 Which number is equivalent to 0.3 + 0.004 A 3.04 B 0.34 C three hundred four thousandths Slide 91 (Answer) / 192 39 Which number is equivalent to 0.3 + 0.004 A 3.04 B 0.34 Answer C C three hundred four thousandths [This object is a pull tab]
Slide 92 / 192 40 Which number is equivalent to sixteen hundredths? A 0.016 B .1 + 0.06 C .01 + 0.06 Slide 92 (Answer) / 192 40 Which number is equivalent to sixteen hundredths? A 0.016 B .1 + 0.06 Answer B C .01 + 0.06 [This object is a pull tab] Slide 93 / 192
Slide 93 (Answer) / 192 Slide 94 / 192 Compare & Order Decimals Return to Table of Contents Slide 95 / 192 Inequalities There are two symbols we use to compare numbers when they are not equal. We call these number sentences inequalities . > ( greater than ) < ( less than ) One number goes on the left of the symbol and another number goes on the right of the symbol. 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 96 / 192 Inequality Symbols Symbols and Words to remember when comparing numbers SYMBOL WORDS greater than/largest > less than/ smallest < equal = Slide 97 / 192 Comparing Decimals · Line up the decimal points · Put zeros in wherever digits are missing · Compare the digits, from left to right · The largest digit, having the same place value, names the largest number Slide 98 / 192 Comparing Decimals Compare 0.045 and 0.21 0.045 · Line up the decimal points put zero 0.21 0 · Put zeros in wherever digits are missing on the end · Compare the digits, from left to right · The largest digit, having the same place value, Compare left to right. names the largest number 2 is greater than 0, so 0.21 is greatest. 0.045 < 0.21 Click to reveal
Slide 99 / 192 Comparing Decimals Compare 0.36 and 0.312 put zero 0.36 0 · Line up the decimal points on the end 0.312 · Put zeros in wherever digits are missing · Compare the digits, from left to right · The largest digit, having the same place value, Compare left to right. names the largest number 6 is greater than 1, so 0.36 is greatest. 0.36 > 0.312 Click to reveal Slide 100 / 192 Comparing Decimals Compare 0.009 and 0.02 0.009 · Line up the decimal points put zero 0.02 0 · Put zeros in wherever digits are missing on the end · Compare the digits, from left to right · The largest digit, having the same place value, Compare left to right. names the largest number 2 is greater than 0, so 0.02 is greatest. 0.009 < 0.02 Click to reveal Slide 101 / 192 Decimal Squares Interactive Games Click for link. In this game the robot Game could also be won, because 0.7950 is played with two students greater than 0.5021. having a spinner and writing down their decimal number.
Slide 102 / 192 42 Choose the correct symbol. A > 0.41 0.049 B < C = Slide 102 (Answer) / 192 42 Choose the correct symbol. A > 0.41 0.049 B < C = Answer A [This object is a pull tab] Slide 103 / 192 43 Choose the correct symbol. 0.301 three hundred eleven thousandths A > B < C =
Slide 103 (Answer) / 192 43 Choose the correct symbol. 0.301 three hundred eleven thousandths Answer A > B B < = C [This object is a pull tab] Slide 104 / 192 44 Choose the correct symbol. A > 0.007 0.05 B < C = Slide 104 (Answer) / 192 44 Choose the correct symbol. > A 0.007 0.05 < B Answer B C = [This object is a pull tab]
Slide 105 / 192 45 Choose the correct symbol. > A < 0.179 twenty-four hundredths B C = Slide 105 (Answer) / 192 45 Choose the correct symbol. A > < 0.179 twenty-four hundredths B Answer C = B [This object is a pull tab] Slide 106 / 192 46 Choose the correct symbol. > A forty-six hundredths 0.6 B < C =
Slide 106 (Answer) / 192 46 Choose the correct symbol. A > forty-six hundredths 0.6 < B C = Answer B [This object is a pull tab] Slide 107 / 192 47 Select from the choices to correctly complete the comparison. 4.408 four and forty-eight thousanths > A < B C = From PARCC PBA sample test #3 Slide 107 (Answer) / 192 47 Select from the choices to correctly complete the comparison. 4.408 four and forty-eight thousanths Answer A > A B < = C [This object is a pull tab] From PARCC PBA sample test #3
Slide 108 / 192 48 Select from the choices to correctly complete the comparison. six hundred ninety-one and five hundredths > A 6 x 100 + 9 x 10 + 1 + 8 x 11,000 < B C = From PARCC PBA sample test #3 Slide 108 (Answer) / 192 48 Select from the choices to correctly complete the comparison. six hundred ninety-one and five hundredths Answer A > 6 x 100 + 9 x 10 + 1 + 8 x 11,000 B B < = C [This object is a pull tab] From PARCC PBA sample test #3 Slide 109 / 192 Teacher Note Teachers: Use this Mathematical Practice Pull Tab for the next slide.
Slide 109 (Answer) / 192 Teacher Note MP.3 - Construct viable arguments and critique the reasoning of others. If the answer is not unanimous, give the students Teachers: an opportunity to justify their response and Use this Mathematical Practice Pull Tab for the next slide. Math Practice evaluate the reasoning of others. Ensure that they are listening to and questioning other students. Ask: How was your answer different than some of your classmates? How did you reach that conclusion? Why is that true? Who would like to share a different way of [This object is a pull tab] answering the problem? Slide 110 / 192 49 In a paper airplane contest, Marcel's plane travels 3.345 meters. Salvador's plane travels 3.35 meters. Based on the measurements, whose plane traveled the farthest distance? On your paper, explain how you know. A Marcel B Salvador ( ( Derived from Slide 110 (Answer) / 192 49 In a paper airplane contest, Marcel's plane travels 3.345 meters. Salvador's plane travels 3.35 meters. Based on the measurements, whose plane traveled the farthest B distance? On your paper, explain how you know. If you have struggling students, this is a good Answer opportunity to utilize "think, pair, share." A Marcel This will provide students B Salvador with a platform to learn from each other. [This object is a pull tab] ( ( Derived from
Slide 111 / 192 Ordering Decimals · Line up all of the decimal points · Put zeros in wherever digits are missing · Compare the digits, from left to right · The largest digit, having the same place value, names the largest number Example: Why is 910.800 this the 085.007 smallest number? 910.801 What digit tells us this is the 911.900 largest number? 085.070 1 click Compare the digits Slide 112 / 192 50 The number with the least value is: 61.005 A 61.3 B 61.05 C 61.04 D Slide 112 (Answer) / 192 50 The number with the least value is: 61.005 A 61.3 B Answer A 61.05 C 61.04 D [This object is a pull tab]
Slide 113 / 192 51 The number with the least value is: A 0.005 0.5 B 0.05 C 0.0005 D Slide 113 (Answer) / 192 51 The number with the least value is: 0.005 A 0.5 B Answer D 0.05 C D 0.0005 [This object is a pull tab] Slide 114 / 192 52 The number with the greatest value is: 9.888 A 9.8 B C 9.008 D 9.088
Slide 114 (Answer) / 192 52 The number with the greatest value is: A 9.888 B 9.8 Answer A 9.008 C 9.088 D [This object is a pull tab] Slide 115 / 192 53 The number with the greatest value is: 0.67 A B 0.067 0.0067 C 0.00067 D Slide 115 (Answer) / 192 53 The number with the greatest value is: 0.67 A 0.067 B Answer A 0.0067 C 0.00067 D [This object is a pull tab]
Slide 116 / 192 54 How much money would you like to win? $150.59 A $140.99 B $150.82 C $140.50 D Slide 116 (Answer) / 192 54 How much money would you like to win? $150.59 A $140.99 B Answer $150.82 C C $140.50 D [This object is a pull tab] Slide 117 / 192 55 Using the following digits, create the largest number you can between 0 and 1. 1 0 2 7 , , ,
Slide 117 (Answer) / 192 55 Using the following digits, create the largest number you can between 0 and 1. 1 0 7 2 , , , Answer .7210 [This object is a pull tab] Slide 118 / 192 56 Using the following digits, create the smallest number you can between 0 and 1. 1 7 0 2 , , , Slide 118 (Answer) / 192 56 Using the following digits, create the smallest number you can between 0 and 1. 1 0 2 7 , , Answer , .0127 [This object is a pull tab]
Slide 119 / 192 Ordering Decimals Order the numbers from least to greatest. Move the numbers to put them in order. 15 0 1.5 0.015 0.15 Slide 119 (Answer) / 192 Ordering Decimals MP.5 - Use appropriate tools strategically. Order the numbers from least to greatest. Move the numbers to put them in order. Ask students to share their method Math Practice for comparing the numbers. Did they use mental math, a place value chart, lining up the decimals 15 0 1.5 0.015 0.15 without needing a chart. Ask: What strategy did you use? [This object is a pull tab] Could you do this mentally? Slide 120 / 192 Ordering Decimals Order the numbers from greatest to least. Move the numbers to put them in order. 0.709 0.009 0.68 0.08 0.07
Slide 121 / 192 57 Which of the following is ordered least to greatest? A 0.3, 0.03, 0.33, 3.3 B 0.03, 0.3, 0.33, 3.3 C 0.03, 0.33, 0.3, 3.3 Slide 121 (Answer) / 192 57 Which of the following is ordered least to greatest? A 0.3, 0.03, 0.33, 3.3 0.03, 0.3, 0.33, 3.3 B 0.03, 0.33, 0.3, 3.3 Answer C B [This object is a pull tab] Slide 122 / 192 58 Which of the following is ordered least to greatest? 0.008, 0.06, 0.5 A B 0.5, 0.06, 0.008 C 0.06, 0.5, 0.008
Slide 122 (Answer) / 192 58 Which of the following is ordered least to greatest? 0.008, 0.06, 0.5 A 0.5, 0.06, 0.008 B Answer A 0.06, 0.5, 0.008 C [This object is a pull tab] Slide 123 / 192 59 Which of the following is ordered greatest to least? 8.07, 0.008, 0.087, 0.87 A 0.008, 0.087, 0.87, 8.07 B 8.07, 0.87, 0.087, 0.008 C Slide 123 (Answer) / 192 59 Which of the following is ordered greatest to least? A 8.07, 0.008, 0.087, 0.87 B 0.008, 0.087, 0.87, 8.07 Answer C 8.07, 0.87, 0.087, 0.008 C [This object is a pull tab]
Slide 124 / 192 60 Which of the following is not correct? 0.23 > 0.08 > 0.009 A 0.23 > 0.009 > 0.08 B C 0.009 < 0.08 < 0.23 Slide 124 (Answer) / 192 60 Which of the following is not correct? A 0.23 > 0.08 > 0.009 B 0.23 > 0.009 > 0.08 Answer 0.009 < 0.08 < 0.23 C B [This object is a pull tab] Slide 125 / 192 61 Which of the following is correct? A 0.8 < 0.32 < 0.41 < 0.701 B 0.8 > 0.701 > 0.41 > 0.32 C 0.32 > 0.41 > 0.701 > 0.8
Slide 125 (Answer) / 192 61 Which of the following is correct? A 0.8 < 0.32 < 0.41 < 0.701 B 0.8 > 0.701 > 0.41 > 0.32 0.32 > 0.41 > 0.701 > 0.8 Answer C B [This object is a pull tab] Slide 126 / 192 62 In a paper airplane contest, Marcel's plane travels 3.345 meters. Salvador's plane travels 3.35 meters. Jennifer's plane travels 3.3 meters. Based on the measurements, who won the contest? On your paper, explain your answer. A Marcel B Salvador C Jennifer ( ( Derived from Slide 126 (Answer) / 192 62 In a paper airplane contest, Marcel's plane travels 3.345 meters. Salvador's plane travels 3.35 meters. Jennifer's plane travels 3.3 meters. Based on the measurements, B who won the contest? On your paper, explain your answer. If you have struggling students, this is a good Answer opportunity to utilize A Marcel "think, pair, share." B Salvador This will provide students with a platform to learn C Jennifer from each other. [This object is a pull tab] ( ( Derived from
Slide 127 / 192 Round Numbers to Designated Place Values Return to Table of Contents Slide 128 / 192 Number Line Investigation Instructions for the next slide: 1. Roll the die. 2. Click the yellow arrow to pop out the number. 3. Move the number to the correct place on the number line. 4. Determine whether the number is closer to 0 or 10. The dotted line shows the halfway mark between 0 and 10. This can be repeated six times. Slide 129 / 192 Number Line Investigation 0 10
Slide 129 (Answer) / 192 Number Line Investigation MP.8 - Look for and express 0 10 regularity in repeated reasoning. Student think, pair, share. Math Practice Ask: What rule can you use to determine whether any given number is closer to 0 or 10? After share-out. Ask: How can you use this to tackle [This object is a pull tab] similar problems? Slide 130 / 192 Rounding Rounding makes numbers easier to work with in your head. Rounded numbers are only approximate. · An 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. Slide 131 / 192 Review Round 8,749 to the nearest ten. 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? 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.
Slide 131 (Answer) / 192 Review Round 8,749 to the nearest ten. Teacher Notes 1. Put your pencil point under the digit in the tens place. Move pencil under the Look to the right. digit that is being rounded to 2. Is the digit 5 or more? Yes OR No [This object is a pull tab] 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. Slide 132 / 192 Review Round 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? 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 132 (Answer) / 192 Review Round 8,749 to the nearest hundred. 1. Put your pencil point under the digit in the tens place. Look to the right. Teacher Notes Move pencil under the 2. Is the digit 5 or more? Yes OR No digit that is being rounded to 3. What happens to the digit? Increases by 1 OR remains the same [This object is a pull tab] 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 133 / 192 63 Round 143 to the nearest ten. Slide 133 (Answer) / 192 63 Round 143 to the nearest ten. Answer 140 [This object is a pull tab] Slide 134 / 192 64 Round 4,561 to the nearest hundred.
Slide 134 (Answer) / 192 64 Round 4,561 to the nearest hundred. Answer 4,600 [This object is a pull tab] Slide 135 / 192 65 Round 564,012 to the nearest hundred thousand. Slide 135 (Answer) / 192 65 Round 564,012 to the nearest hundred thousand. Answer 600,000 [This object is a pull tab]
Slide 136 / 192 66 Round 7,399 to the nearest thousand. Slide 136 (Answer) / 192 66 Round 7,399 to the nearest thousand. Answer 7,000 [This object is a pull tab] Slide 137 / 192 67 Round 63,752 to the nearest hundred.
Slide 137 (Answer) / 192 67 Round 63,752 to the nearest hundred. Answer 63,800 [This object is a pull tab] Slide 138 / 192 Rounding What happens in this case? Round 697 to the nearest ten. The 7 to the right of the 9 tells us to increase the 9 by 1. What happens? Answer ____________ Slide 139 / 192 68 Round 3,972 to the nearest hundred.
Slide 139 (Answer) / 192 68 Round 3,972 to the nearest hundred. Answer 4,000 [This object is a pull tab] Slide 140 / 192 69 Round 98 to the nearest ten. Slide 140 (Answer) / 192 69 Round 98 to the nearest ten. Answer 100 [This object is a pull tab]
Slide 141 / 192 70 Round 399,238 to the nearest ten thousand. Slide 141 (Answer) / 192 70 Round 399,238 to the nearest ten thousand. Answer 400,000 [This object is a pull tab] Slide 142 / 192 71 Round 9,521 to the nearest thousand.
Slide 142 (Answer) / 192 71 Round 9,521 to the nearest thousand. Answer 10,000 [This object is a pull tab] Slide 143 / 192 72 Round 9,983 to the nearest hundred. Slide 143 (Answer) / 192 72 Round 9,983 to the nearest hundred. Answer 10,000 [This object is a pull tab]
Slide 144 / 192 Number Line Investigation Instructions for the next slide: 1. Roll the die. 2. Click the yellow arrow to pop out the number. 3. Position the number in the correct place on the number line. 4. Determine 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. Slide 145 / 192 Number Line Investigation 1 2 Think, Pair, Share: What rule can you use to determine whether any given number is closer to 1 or to 2? Slide 146 / 192 Rounding Decimals Let's learn how to round decimals using the following examples: Round 687.268 to the nearest tenths place. When rounding decimals, put your pencil point under the place value that you are rounding to DO NOT MOVE IT 687.268
Slide 147 / 192 Round 687.268 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 148 / 192 Rounding Decimals 5. What happened to the digits to the right of the tenths place? Remember, we are rounding. The place values to the right of the tenths place have zero value, so now the digits 6 and 8 become zeroes. 687.300 = 687.3 However we leave the zeros off when they are at the end of a number to the right of the decimal point. Slide 149 / 192 Round 8.73258 to the hundredths place. 1. Put your pencil point under the digit in the hundredths 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 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).
Slide 150 / 192 Slide 151 / 192 Rounding Practice Try this: Round 687.4953 to the nearest hundredths place Answer: 687.50 Click to reveal Slide 152 / 192 73 Round 6874.6479 to the nearest hundredth.
Slide 152 (Answer) / 192 73 Round 6874.6479 to the nearest hundredth. Answer 6874.65 [This object is a pull tab] Slide 153 / 192 74 Round 6874.6479 to the nearest ten. Slide 153 (Answer) / 192 74 Round 6874.6479 to the nearest ten. Answer 6870 [This object is a pull tab]
Slide 154 / 192 75 Round 6874.6479 to the nearest hundred. Slide 154 (Answer) / 192 75 Round 6874.6479 to the nearest hundred. Answer 6,900 [This object is a pull tab] Slide 155 / 192 76 Round 6874.6479 to the nearest tenth.
Slide 155 (Answer) / 192 76 Round 6874.6479 Answer to the nearest tenth. 6874.6 [This object is a pull tab] Slide 156 / 192 77 Round 6874.6479 to the nearest thousand. Slide 156 (Answer) / 192 77 Round 6874.6479 Answer to the nearest thousand. 7,000 [This object is a pull tab]
Slide 157 / 192 78 Round 6874.6479 to the nearest thousandth. Slide 157 (Answer) / 192 78 Round 6874.6479 to the nearest thousandth. Answer 6874.648 [This object is a pull tab] Slide 158 / 192 Caution! When rounding to a specific place, your answer MUST have a digit in that place. Example: Round 23.97 to the nearest tenth Answer: 24.0 There must be a digit in the tenths place, since we were to round to the tenths place.
Slide 159 / 192 79 Round 678.97 to the nearest tenth. Slide 159 (Answer) / 192 79 Round 678.97 to the nearest tenth. Answer 679.0 [This object is a pull tab] Slide 160 / 192 80 Round 6.304 to the nearest hundredth.
Slide 160 (Answer) / 192 80 Round 6.304 Answer to the nearest hundredth. 6.30 [This object is a pull tab] Slide 161 / 192 81 Round 5.03 to the nearest tenth. Slide 161 (Answer) / 192 81 Round 5.03 to the nearest tenth. Answer 5.0 [This object is a pull tab]
Slide 162 / 192 82 Round 0.3497 to the nearest thousandth. Slide 162 (Answer) / 192 82 Round 0.3497 Answer to the nearest thousandth. 0.350 [This object is a pull tab] Slide 163 / 192 83 Round 84.951 to the nearest tenth.
Slide 163 (Answer) / 192 83 Round 84.951 to the nearest tenth. Answer 85.0 [This object is a pull tab] Slide 164 / 192 84 A decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is 18.6. What is the maximum possible value of this decimal? On your paper, use words and the number line to explain your reasoning. ( ( Problem derived from Slide 164 (Answer) / 192 84 A decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is 18.6. What is the maximum possible value of this decimal? On your paper, use words and the number line to explain your reasoning. Answer 18.64 [This object is a pull tab] ( ( Problem derived from
Slide 165 / 192 85 A decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is 18.6. What is the minimum possible value of this decimal? On your paper, use words and the number line to explain your reasoning. ( ( Problem derived from Slide 165 (Answer) / 192 85 A decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is 18.6. What is the minimum possible value of this decimal? On your paper, use words and the number line to explain your reasoning. Answer 18.55 [This object is a pull tab] ( ( Problem derived from Slide 166 / 192 86 Jules reads that one pint is equivalent to 0.473 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. A His teacher B His parents C Both of them ( ( Problem derived from
Slide 166 (Answer) / 192 86 Jules reads that one pint is equivalent to 0.473 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 A pint. He asks his parents, and they say there are about 0.5 liters in a pint. Who is correct? On your paper, Consider having students write their explanations, submit their answers, explain your answer. then pair-share with a partner or their Answer group, before discussing it as a A His teacher class. Or have them choose a corner of the B His parents room (assign a letter to each of 3 corners) and justify their answer. Students can then persuade each C Both of them other to arrive at the correct answer. [This object is a pull tab] ( ( Problem derived from Slide 167 / 192 87 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. A 3.251 cm B 3.349 cm C 3.352 cm D 3.295 cm Slide 167 (Answer) / 192 87 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. A 3.251 cm Answer C B 3.349 cm C 3.352 cm D 3.295 cm [This object is a pull tab]
Slide 168 / 192 88 Annual rainfall total for cities in New York are listed below. Rochester 0.97 meters Ithaca 0.947 meters Saratoga Springs 1.5 meters New York City 1.268 meters Round the smallest total rainfall to the nearest tenth. ( ( Derived from Slide 168 (Answer) / 192 88 Annual rainfall total for cities in New York are listed below. Rochester 0.97 meters Answer Ithaca 0.947 meters 0.9 meters Saratoga Springs 1.5 meters New York City 1.268 meters Round the smallest total rainfall to the nearest tenth. [This object is a pull tab] ( ( Derived from Slide 169 / 192 Drag and Drop Drag 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. From PARCC EOY sample test #6
Slide 170 / 192 Estimating Answers Use rounding to estimate answers to problems. At a restaurant, a burger is $5.99, fries are $3.85 and a small drink is $1.29. Round to Cost Estimate the nearest dollar to estimate the cost to $5.99 $6 purchase all three items. $3.85 $4 $1.29 $1 It would cost about $11 to purchase all three items. Slide 171 / 192 89 Round 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 171 (Answer) / 192 89 Round 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 Answer book bag $15.75 $3+$2+$16 =$21.00 [This object is a pull tab]
Slide 172 / 192 90 Round 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 172 (Answer) / 192 90 Round the following items to the nearest dollar to figure out the approximate cost if all of the items were bought. jeans $24.99 $25+$7+$12 t-shirt $6.79 Answer hat $12.31 =$44.00 [This object is a pull tab] Slide 173 / 192 91 Round 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 173 (Answer) / 192 91 Round 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 Answer juice $2.40 $4+$2+$2 = $8 [This object is a pull tab] Slide 174 / 192 92 Round 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 174 (Answer) / 192 92 Round 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 Answer $9.00+$2.50+$1.00 peas $0.99 =$12.50 [This object is a pull tab]
Slide 175 / 192 93 Round 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 Slide 175 (Answer) / 192 93 Round 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 Answer $5.00+$2.00+3.00= $10.00 [This object is a pull tab] Slide 176 / 192 94 Round 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 176 (Answer) / 192 94 Round 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 Answer $40.00+$10.00+$10.00= socks $6.00 $60.00 [This object is a pull tab] Slide 177 / 192 95 Round the following items to the nearest hundred dollars to figure out the approximate cost if all of the items were bought. computer$688.23 printer $213.50 desk $175.89 Slide 177 (Answer) / 192 95 Round the following items to the nearest hundred dollars to figure out the approximate cost if all of the items were bought. computer$688.23 $700+$200+$200= printer Answer $213.50 desk $1100 $175.89 [This object is a pull tab]
Slide 178 / 192 96 Which numbers show 1,034.17 rounded correctly to different place values? Select the three correct answers. A 1,000 B 1,030 C 1,035 D 1,100 E 1,034.1 F 1.034.2 From PARCC PBA sample test #12 Part B Slide 178 (Answer) / 192 96 Which numbers show 1,034.17 rounded correctly to different place values? Select the three correct answers. A 1,000 Answer B 1,030 A, B, F C 1,035 D 1,100 [This object is a pull tab] E 1,034.1 F 1.034.2 From PARCC PBA sample test #12 Part B Slide 179 / 192 Glossary & Standards Return to Table of Contents
Slide 179 (Answer) / 192 Glossary & Standards Vocabulary Words are bolded Teacher Notes in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it. [This object is a pull tab] Return to Table of Contents Slide 180 / 192 Standards for Mathematical Practices MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. Click on each standard to bring you to an example of how to meet this standard within the unit. Slide 181 / 192 Decimal Number A Decimal Number ( based on the number 10, tenth parts, and powers of ten ) contains a Decimal Point. Back to Instruction
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