6th Grade. Slide 1 / 215. Slide 2 / 215. Slide 3 / 215. Fraction & Decimal Computation. Fraction and Decimal Computation

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1 Slide 1 / 215 Slide 2 / 215 6th Grade Fraction & Decimal Computation Fraction and Decimal Computation Slide 3 / 215 Fraction Division Long Division Review Adding Decimals Subtracting Decimals Distributive Property & Product of Decimals Multiplying Decimals Dividing Decimals Glossary & Standards Click on the topic to go to that section

2 Fraction and Decimal Computation Slide 3 () / 215 Click on the topic to go to that section Fraction Division Long Division Review Adding Decimals Subtracting Decimals Vocabulary Words are bolded Distributive Property in the & presentation. Product of Decimals The text Multiplying Decimals box the word is in is then Dividing Decimals linked to the page at the end Glossary & Standards of the presentation with the word defined on it. Teacher Notes Slide 4 / 215 Fraction Division Return to Table of Contents Recall from 5th grade: Modeling Division Slide 5 / 215 When we are dividing, we are breaking apart into equal groups. Dividend Divisor = Quotient The model below represents: 8 4 = 2 2 groups of 4

3 Applying to Fractions The previous example used whole numbers and grouped the dividend according to the divisor. Slide 6 / 215 The same strategy can be applied when dividing with fractions. Use the model below to demonstrate: 8 1 = The pink rectangle represents 1. 2 See how many you can fit in the 8 squares. Applying to Fractions The previous example used whole numbers and grouped the dividend according to the divisor. Slide 6 () / 215 The same strategy can be applied when dividing with fractions. The "half" square is infinitely cloned and students should Use the model below to demonstrate: "fill" the 8 squares 1 = with 16 half squares 2 to show 8 Teacher Notes 8 / 0.5 = The pink rectangle represents 1. 2 See how many you can fit in the 8 squares. Example Use the model below to demonstrate 2 1 = 3 Slide 7 /

4 1 Evaluate the following problem using the model below. Slide 8 / = Evaluate the following problem using the model below. Slide 8 () / = Evaluate the following problem using the model below. 5 1 = 2 Slide 9 /

5 2 Evaluate the following problem using the model below. 5 1 = 2 Slide 9 () / Visual Model A fraction can be divided by a whole number using the following visual model. 3/ Slide 10 / 215 Divide into 4 groups Visual Model A fraction can be divided by a whole number using the following visual model. 3/ Slide 10 () / 215 Divide into 4 groups 3/5 4 = 3/20

6 Word Problem Slide 11 / 215 The previous expression can be represented by the following word problem: How much will each person receive if 4 friends share a 3/5 pound bag of popcorn? Each friend will receive 3/20 lb. of popcorn. Slide 12 / 215 Slide 12 () / 215

7 Slide 13 / 215 Slide 13 () / 215 Slide 14 / 215

8 Slide 15 / 215 Slide 16 / 215 Slide 17 / 215

9 Slide 17 () / 215 Slide 18 / 215 Slide 18 () / 215

10 Vocabulary Review Slide 19 / 215 Complex Fraction: A fraction with another fraction in the numerator, denominator or both. Reciprocal: The inverse of a number/fraction. Original Number 4 Reciprocal 2 Patterns Slide 20 / 215 Do you notice a pattern between the division of fractions and their solution? Patterns Slide 20 () / 215 Do you notice a pattern between the division of fractions and their solution? Teacher Notes Discuss Patterns either from model or number sentence.

11 Slide 21 / 215 If you think about it, we are dividing by a fraction which creates a complex fraction. You need to eliminate the fraction in the denominator in order to solve the problem. To do this, multiply the numerator and denominator of the complex fraction by the reciprocal of the denominator (making the denominator = 1). You can then simplify the fraction by rewriting it without the denominator of 1 and solve the new multiplication problem. Example Slide 22 / = = x 3 2 x 3 2 = 1 2 x = 1 2 x 3 2 Original Problem Complex Fraction Multiply by Reciprocal Simplify Denominator Rewrite Without 1 There are rules that can be applied to fraction division problems to eliminate steps from this lengthy procedure. source - Dividing Fractions Algorithm Slide 23 / 215 Algorithm Step 1: Leave the first fraction the same. Step 2: Multiply the first fraction by the reciprocal of the second fraction. Step 3: Simplify your answer = 5 x 2 1 = 1 x 2 5 x 1 = 2 5

12 Dividing Fractions Algorithm Slide 24 / 215 Some people use the saying " Keep Change Flip" to help them remember the algorithm. Change Keep Flip Changed Kept Flipped = 3 5 x 8 7 = 3 x 8 5 x 7 = Slide 25 / 215 Checking Your Slide 26 / 215 To check your answer, use your knowledge of fact families = = x is 7 8 of 24 35

13 Slide 27 / ) = 5 4 x 8 10 True False Slide 27 () / ) = 5 4 x 8 10 True False FALSE Slide 28 / ) = True False

14 Slide 28 () / ) = True False FALSE Slide 29 / ) = A 1 B C Slide 29 () / ) = A 1 B C A

15 10 ) Slide 30 / ) Slide 30 () / ) Slide 31 / 215

16 Slide 31 () / 215 Simplify Slide 32 / 215 Sometimes you can cross simplify prior to multiplying. without cross simplifying with cross simplifying Can this problem be cross simplified? Slide 33 / 215 Yes No

17 12 Can this problem be cross simplified? Slide 33 () / 215 Yes No YES 13 Can this problem be cross simplified? Slide 34 / 215 Yes No 13 Can this problem be cross simplified? Slide 34 () / 215 Yes No NO

18 14 Can this problem be cross simplified? Slide 35 / 215 Yes No 14 Can this problem be cross simplified? Slide 35 () / 215 Yes No NO 15 Can this problem be cross simplified? Slide 36 / 215 Yes No

19 15 Can this problem be cross simplified? Slide 36 () / 215 Yes No YES 16 ) Slide 37 / ) Slide 37 () / 215

20 17 ) Slide 38 / ) Slide 38 () / ) Slide 39 / 215

21 18 ) Slide 39 () / ) Slide 40 / ) Slide 40 () / 215

22 Visual Model A mixed number can be divided by a mixed number using the following visual model. Slide 41 / 215 First find the least common denominator (LCD) which is 6. If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit? Visual Model A mixed number can be divided by a mixed number using the following visual model. Slide 41 () / First find the least common denominator (LCD) which is 6. If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed [This numbers object is a pull tab] fit? Visual Model Slide 42 / 215 Since our LCD is 6, every 6 lines is considered a whole. 1 1/2 is equivalent to 9 sections on the number line. 1 1/ /3 2 2/3 is equivalent to 16 sections on the number line. So 1 1/2 2 2/3 = 9/16

23 Visual Model Slide 43 / 215 What if the problem were written as? 2 2/ /2 1 1/2 How many times does 1 1/2 divide into 2 2/3? Dividing Mixed Numbers Algorithm Slide 44 / 215 Step 1: Rewrite the Mixed Number(s) as an improper fraction(s). (write whole numbers / 1) Step 2: Follow the same steps for dividing fractions = = 6 x 2 = 12 = Example Slide 45 / 215 Evaluate: = = 5 3 x 2 7 = 10 21

24 Slide 46 / ) = Slide 46 () / ) = Slide 47 / ) =

25 Slide 47 () / ) = Slide 48 / ) = Slide 48 () / ) =

26 Slide 49 / ) = Slide 49 () / ) = Application Problem Slide 50 / 215 Winnie needs pieces of string for a craft project. How many 1/6 yd pieces of string can she cut from a piece that is 2/3 yd long? x 6 1 = 12 3 = pieces or x 6 1 = = 4 pieces

27 Application Problem Slide 51 / 215 One student brings 1/2 yd of ribbon. If 3 students receive an equal length of the ribbon, how much ribbons will each student receive? x 1 3 = 1 6 yards of ribbon Application Problem Slide 52 / 215 Kristen is making a ladder and wants to cut ladder rungs from a 6 ft board. Each rung needs to be 3/4 ft long. How many ladder rungs can she cut? x 4 3 = = = 1 8 rungs Application Problem Slide 53 / 215 A box weighing 9 1/3 lb contains toy robots weighing 1 1/6 lb apiece. How many toy robots are in the box? x = 8 1 = 8 robots

28 24 Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion? Slide 54 / 215 A 8 pounds B 4 1/2 pounds C 2/5 pounds D 1/8 pound 24 Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion? Slide 54 () / 215 A 8 pounds B 4 1/2 pounds C 2/5 pounds D 1/8 pound D 25 A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel? Slide 55 / 215 A 84 miles B 62 miles C 42 miles D 38 miles

29 25 A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel? Slide 55 () / 215 A 84 miles B 62 miles C 42 miles D 38 miles D 26 One tablespoon is equal to 1/16 cup. It is also equal to 1/2 ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use? Slide 56 / 215 A 48 tablespoons B 24 tablespoons C 12 tablespoons D 6 tablespoons 26 One tablespoon is equal to 1/16 cup. It is also equal to 1/2 ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use? Slide 56 () / 215 A 48 tablespoons B 24 tablespoons C 12 tablespoons D 6 tablespoons C

30 27 A bookstore packs 6 books in a box. The total weight of the books is 14 2/5 pounds. If each book has the same weight, what is the weight of one book? Slide 57 / 215 A 5/12 pound B 2 2/5 pounds C 8 2/5 pounds D 86 2/5 pounds 27 A bookstore packs 6 books in a box. The total weight of the books is 14 2/5 pounds. If each book has the same weight, what is the weight of one book? Slide 57 () / 215 A 5/12 pound B 2 2/5 pounds C 8 2/5 pounds D 86 2/5 pounds B 28 There is gallon of distilled water in the Slide 58 / 215 class science supplies. If each pair of students doing an experiment uses gallon of distilled water, there will be gallon left in the supplies. How many students are doing the experiments?

31 28 There is gallon of distilled water in the Slide 58 () / 215 class science supplies. If each pair of students doing an experiment uses gallon of distilled water, there will be gallon left in the supplies. How many students are doing the experiments? 29 Carol makes cups of snack mix. She Slide 59 / 215 puts all the snack mix into plastic bags. She puts cup of the snack mix in each bag. How many plastic bags does Carol need? Enter your answer in the box. bags From PARCC EOY sample test non-calculator #9 29 Carol makes cups of snack mix. She Slide 59 () / 215 puts all the snack mix into plastic bags. She 14 bags puts cup of the snack mix in each bag. & Math Practice How many plastic MP 4bags does Carol need? Word problems allow students to Enter your answer recognize in the math box. in everyday like and use the math they know to solve problems. bags From PARCC EOY sample test non-calculator #9

32 30 Part A A group of hikers buy 8 bags of trail mix. Slide 60 / 215 Each bag contains cups of trail mix. The trail mix is shared evenly among 12 hikers. How many cups of trail mix will each hiker receive? Show your work or explain your answer. From PARCC PBA sample test calculator #10 30 Part A A group of hikers buy 8 bags of trail mix. Slide 60 () / 215 Each bag contains cups of trail mix. The trail mix is shared evenly among 12 hikers. How many cups of trail mix will each hiker receive? Show your work or explain your answer. From PARCC PBA sample test calculator #10 31 Part B The hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout. Determine the total distance each hiker will hike. Show your work or explain your answer. Slide 61 / 215 From PARCC PBA sample test calculator #10

33 31 Part B The hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout. Determine the total distance each hiker will hike. Show your work [This object or explain is a pull tab] your answer. Slide 61 () / 215 From PARCC PBA sample test calculator #10 32 Part B (continued) Determine the total number of gallons of water each hiker will bring. Show your work or explain your answer. Slide 62 / 215 From PARCC PBA sample test calculator #10 32 Part B (continued) Determine the total number of gallons of water each hiker will bring. Show your work or explain your answer. Slide 62 () / 215 From PARCC PBA sample test calculator #10

34 33 This diagram shows a number line. Slide 63 / 215 Part A James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long. How many pieces can James cut from the board? Explain how James can use the number line diagram to determine the number of pieces he can cut from the board. From PARCC PBA sample test calculator #8 33 This diagram shows a number line. Slide 63 () / 215 The number line diagram show segments marked that are spaces 1/8 unit apart. I know James' Part A board is 3/4 foot long. I counted James has a board the number that is of 3/4 1/8 foot units long. until He I got wants to cut to 3/4 on the number line. There the board into pieces that are each 1/8 foot long. How are 6 of these. So James can cut a many pieces can total James of 6 pieces cut from from the the board? board. Explain how James can use the number line diagram to determine the number of pieces he can cut from the board. From PARCC PBA sample test calculator #8 34 Part B Write an equation using division that represents how James can find the number of pieces he can cut from the board. Slide 64 / 215 From PARCC PBA sample test calculator #8

35 34 Part B Write an equation using division that represents how James can find the number of pieces he can cut from the board. Slide 64 () / 215 From PARCC PBA sample test calculator #8 Slide 65 / 215 Long Division Review Return to Table of Contents Some division terms to remember... The number to be divided into is known as the dividend The number which divides the other number is known as the divisor Slide 66 / 215 The answer to a division problem is called the quotient 20 5 = 4 divisor 5 4 quotient 20 dividend 20 5 = 4

36 When we are dividing, we are breaking apart into equal groups Slide 67 / 215 EXAMPLE 1 Find Step 1: Can 3 go into 1, no so can Click for step 1 3 go into 13, yes Step 2: Bring down the 2. Can 3 Click for step 2 go into 12, yes x 4 = = 1 Compare 1 < 3 3 x 4 = = 0 Compare 0 < 3 Step 3: Check your answer. Slide 68 / x Estimating Your Before any calculations, estimate your answer to make sure you are on the right track. Slide 69 / What place value should we round to? Round to the largest place value. 357 rounds to 15 rounds to Our answer should approximately be... 20

37 EXAMPLE 2 (change pages to see each step) Slide 70 / 215 Step 1: Can 15 go into 3, no so can 15 go into 35, yes x 2 = = 5 Compare 5 < 15 EXAMPLE 2 (change pages to see each step) Slide 71 / 215 Step 2 : Bring down the 7. Can 25 go into 207, yes x 3 = =12 Compare 12 < 15 EXAMPLE 2 (change pages to see each step) Slide 72 / 215 Step 3: You need to add a decimal and a zero since the division is not complete. Bring the zero down and continue the long division x 8 = = 0 Compare 0 < 15 Is our answer close to our estimate?

38 Check your answer. Slide 73 / x Estimate the following problems. Discuss your answers with your group. Slide 74 / Now solve the following problems. Discuss your answers with your group. Slide 75 /

39 35 Estimate the quotient. Slide 76 / Estimate the quotient. Slide 76 () / Compute. Slide 77 / =

40 36 Compute. Slide 77 () / = Estimate the quotient. Slide 78 / 215 1, Estimate the quotient. Slide 78 () / 215 1, Approximately 33

41 38 Compute. Slide 79 / 215 1, = 38 Compute. Slide 79 () / 215 1, = Estimate the quotient. Slide 80 / 215 1,288 35

42 39 Estimate the quotient. Slide 80 () / 215 1, Compute. Slide 81 / 215 1, = 40 Compute. Slide 81 () / 215 1, = 36.8

43 41 The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row. Slide 82 / The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row. Slide 82 () / The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row? Slide 83 / 215

44 42 The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row? Slide 83 () / Compute. Slide 84 / = 43 Compute. Slide 84 () / = 45.25

45 44 The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day? Slide 85 / The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day? Slide 85 () / Compute. Slide 86 / =

46 45 Compute. Slide 86 () / = Compute. Slide 87 / = 46 Compute. Slide 87 () / = 53.5

47 47 Enter your answer in the box. Slide 88 / , = From PARCC EOY sample test non-calculator #18 47 Enter your answer in the box. Slide 88 () / , = 432 From PARCC EOY sample test non-calculator #18 Slide 89 / 215 Adding Decimals Return to Table of Contents

48 Adding Decimals Slide 90 / 215 If you know how to add whole numbers then you can add decimals. Just follow these few steps. Step 1: Step 2: Step 3: Put the numbers in a vertical column, aligning the decimal points. Add each column of digits, starting on the right and working to the left. Place the decimal point in the answer directly below the decimal points that you lined up in Step 1. Adding Decimals Slide 91 / 215 When adding or subtracting decimals, always remember to align the decimals vertically Adding Decimals Slide 91 () / 215 When adding or subtracting decimals, always remember to align the decimals vertically... MP 5 Math Practice Students who struggle to line up the digits correctly for an addition of decimals problem may find it useful to 0.25 line them up using graph paper. This 0.25 will help them to choose to use graph paper as a tool 0.25to help them solve problems

49 Estimating Your Before any calculations, estimate your answer to make sure you are on the right track. Slide 92 / What place value should we round to? Round to the nearest whole number. 5.1 rounds to 1.25 rounds to 0.04 rounds to 1.99 rounds to Our answer should approximately be... 8 Adding Decimals Slide 93 / 215 Now, try this - Don't forget - LINE THEM UP You can add a zero as a place holder to help line your numbers up TRY THESE. Estimate the following sums in your notebook. Check with the rest of your group. Slide 94 / 215 1) ) = = 24 3) ) = = 18

50 TRY THESE. Complete in your notebook then check with the rest of your group. Slide 95 / 215 1) ) ) ) TRY THESE. Complete in your notebook then check with the rest of your group. Slide 95 () / 215 1) ) MP Remind students to compare their estimates to their + exact 9. answers to see if their exact answers make sense. Math Practice 3) ) Add the following: Slide 96 / = A 6.1 B C 1.15 D 0.16

51 48 Add the following: Slide 96 () / = A 6.1 B C 1.15 D 0.16 C 49 Joanne and Peter are working together to solve the problem Joanne says that the sum should be approximately 2. Peter disagrees and says the sum should be approximately 0. Who is correct? Why? Slide 97 / 215 A Joanne B Peter 49 Joanne and Peter are working together to solve the problem Joanne says that the sum should be approximately 2. Peter disagrees and says the sum should be approximately 0. Who is correct? Why? Slide 97 () / 215 A Joanne B Peter Joanne is correct because 0.6 rounds to 1 and 0.55 rounds to 1. So the estimation is 2. Peter only looked at the whole number and did not round the decimals.

52 50 Find the sum. Slide 98 / = 50 Find the sum. Slide 98 () / = Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $ Estimate how much Franco spent on the video games. Slide 99 / 215

53 51 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $ Estimate how much Franco spent on the video games. Slide 99 () / 215 $66 52 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $ How much did he spend on video games? Slide 100 / Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $ How much did he spend on video games? Slide 100 () / 215 $65.85

54 53 What is the sum of Slide 101 / and ? A B C D What is the sum of Slide 101 () / and ? A B C B D Estimate the sum. Slide 102 / A 20 B 21 C 22 D 23

55 54 Estimate the sum. Slide 102 () / A 20 B 21 C 22 D 23 B 55 Find the sum. Slide 103 / = A B C D Find the sum. Slide 103 () / = A B C D C

56 56 Five students collected paper to be recycled. Shelly's stack was.008 cm. thick; Ken's stack was.125 cm. thick; Joe's stack was.150 cm. thick; Betty's stack was.185 cm. thick; Mary's stack was.005 cm. thick. What was the thickness of the papers collected to be recycled? A.561 cm. B.452 cm. C.480 cm. D.473 cm. Slide 104 / Five students collected paper to be recycled. Shelly's stack was.008 cm. thick; Ken's stack was.125 cm. thick; Joe's stack was.150 cm. thick; Betty's stack was.185 cm. thick; Mary's stack was.005 cm. thick. What was the D thickness of the papers collected to be recycled? A.561 cm. B.452 cm. C.480 cm. D.473 cm. Slide 104 () / Find the sum. Slide 105 / =

57 57 Find the sum. Slide 105 () / = What is the sum of and 2.67? Slide 106 / 215 Enter your answer in the box. From PARCC EOY sample test non-calculator #19 58 What is the sum of and 2.67? Slide 106 () / 215 Enter your answer in the box From PARCC EOY sample test non-calculator #19

58 Web Link Slide 107 / 215 Let's go to Cool Math and practice addition. Cool Math Link Slide 108 / 215 Subtracting Decimals Return to Table of Contents Subtracting Decimals If you know how to subtract whole numbers then you can subtract decimals. Just follow these few steps. Slide 109 / 215 Step 1: Step 2: Step 3: Put the numbers in a vertical column, aligning the decimal points Subtract the numbers from right to left using the same rules as whole numbers Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.

59 Estimating Your Before any calculations, estimate your answer to make sure you are on the right track. Slide 110 / What place value should we round to? Round to the nearest whole number rounds to 8.21 rounds to Our answer should approximately be Subtracting Decimals Slide 111 / 215 What do we do if there aren't enough decimal places when we subtract? Don't forget...line Them Up! What goes here? TRY THESE. Estimate the following differences in your notebook. Then check with the rest of your group. Slide 112 / 215 1) ) = = 3 3) ) = = 5

60 TRY THESE. Complete in your notebook then check with the rest of your group. Slide 113 / 215 1) ) ) ) TRY THESE. Complete in your notebook then check with the rest of your group. Slide 113 () / 215 1) ) MP Remind students - to compare their estimates to their exact answers to see if their exact answers make sense. 3) ) Math Practice [This object is a pull tab] ) = Slide 114 / 215

61 59 ) = Slide 114 () / ) = Slide 115 / ) = Slide 115 () /

62 61 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. What is the estimate of Sally's profit? Slide 116 / 215 A $20 B $18 C $13 D $12 61 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. What is the estimate of Sally's profit? Slide 116 () / 215 A $20 B $18 C $13 D $12 D 62 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. How much profit? did Sally actually make as a Slide 117 / 215 A $37.57 B $12.43 C $13.57 D $12.00

63 62 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. How much profit? did Sally actually make as a Slide 117 () / 215 A $37.57 B $12.43 C $13.57 D $12.00 B 63 ) = Slide 118 / ) = Slide 118 () /

64 64 The Johnson twins raced each other in the 200-meter dash. Jordan finished in seconds, and Max finished in seconds. How much faster was Jordan than Max? Slide 119 / The Johnson twins raced each other in the 200-meter dash. Jordan finished in seconds, and Max finished in seconds. How much faster was Jordan than Max? Slide 119 () / seconds 65 Timothy is working on the problem He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4.1 and 0.1 to estimate the answer. Is he correct in doing so? Why or why not? Yes No Slide 120 / 215

65 65 Timothy is working on the problem He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4.1 and 0.1 to estimate the answer. Is he correct in doing so? Why or why not? Yes No Timothy is correct but he still has to use decimals instead of whole numbers. He would get the same estimate for this problem if he rounded to the nearest whole number. Slide 120 () / ) = Slide 121 / ) = Slide 121 () /

66 67 ) = Slide 122 / ) = Slide 122 () / Which problem below would give you two different estimates when you either round to the nearest whole or round to the nearest tenths? Slide 123 / 215 A B C D

67 68 Which problem below would give you two different estimates when you either round to the nearest whole or round to the nearest tenths? Slide 123 () / 215 A B C D D 69 If you buy two movie tickets for $8.25 each, what will your change be from $20? Slide 124 / If you buy two movie tickets for $8.25 each, what will your change be from $20? Slide 124 () / 215 $3.50

68 Web Link Slide 125 / 215 Let's go to Cool Math and practice subtraction. Cool Math Link Slide 126 / 215 The Distributive Property and the Product of Decimals Return to Table of Contents Multiplication Slide 127 / 215 If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps. Step 1: Ignore the decimal points. Step 2: Multiply the numbers using the same rules as whole numbers. Step 3: Count the total number of digits to the right of the decimal point. Put that many digits to the right of the decimal point in your answer.

69 Distributive Property Slide 128 / 215 Evaluate 200 x ,300 We can also use the distributive property to calculate the product. Separate 41.5 into an addition expression with two addends Apply the distributive property Apply the order of operations 200 x x ( ) (200 x 41) + (200 x 0.5) 8, = 8,300 Distributive Property Slide 128 () / 215 Evaluate 200 x 41.5 MP 7 8,300 The use of the distributive property will help students to see the structure of the problem. Math Practice We can also use the distributive property to calculate the product. Separate 41.5 into an addition expression with two addends 200 x x ( ) Apply the distributive property Apply the order of operations (200 x 41) + (200 x 0.5) 8, = 8,300 Distributive Property Slide 129 / 215 Evaluate 400 x x ( + ) (400 x ) + (400 x ) + = 7332 This method is known as partial products.

70 Distributive Property Slide 130 / 215 How can we use partial products to calculate the area of the rectangle shown below? ft ft 0.6 ft 200 x ft ft 200 x ( + ) (200 x ) + (200 x ) + = 11,720 Click to reveal Distributive Property Slide 130 () / 215 How can we use partial products to calculate the area of the rectangle shown below? Click on the yellow box to ft ft show the visual 0.6 ft representation of partial 200 x 58.6 products. 200 ft ft Teacher Notes 200 x ( + ) (200 x [This object is a pull ) tab] + (200 x ) + = 11,720 Click to reveal 70 ) 12(43) = 12(40) x 12(3) Slide 131 / 215 True False

71 70 ) 12(43) = 12(40) x 12(3) Slide 131 () / 215 True False FALSE 71 Use the distributive property to rewrite the expression. Slide 132 / 215 3(76.8) Students type their answers here 71 Use the distributive property to rewrite the expression. Slide 132 () / 215 3(76.8) Students type their answers here 3( )

72 72 Calculate the product using partial products. Slide 133 / 215 5(48) 72 Calculate the product using partial products. Slide 133 () / 215 5(48) Calculate the product using partial products. Slide 134 / (5.2)

73 73 Calculate the product using partial products. Slide 134 () / (5.2) Calculate the product using partial products. Slide 135 / (7.4) 74 Calculate the product using partial products. Slide 135 () / (7.4) 2,220

74 75 Calculate the product using partial products. Slide 136 / (6.5) 75 Calculate the product using partial products. Slide 136 () / (6.5) 1, Calculate the area of the rectangle using partial products. Slide 137 / units 43.9 units

75 76 Calculate the area of the rectangle using partial products. Slide 137 () / units 13, units Slide 138 / 215 Multiplying Decimals Return to Table of Contents Multiplication Slide 139 / 215 Convert the following decimal numbers into fractions. 0.7 x 0.09 What is the product? We multiplied seven tenths by nine hundredths. What place value will the last digit in the product be in if we convert it into a decimal number? Thousandths

76 Try These! Slide 140 / 215 What place value will the last digit be in for the following problems? Don't forget to convert them to fractions first. Fractions Product Place Value 1) 0.3 x 0.7 2) 0.2 x ) 0.08 x Multiplication Slide 141 / 215 Do you notice a pattern for multiplying decimals? 3.5 x x x Where does the decimal point go? Drag the decimal point Multiplication Slide 142 / 215 If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps. Step 1: Step 2: Step 3: Ignore the decimal points. Multiply the numbers using the same rules as whole numbers. Count the total number of digits to the right of the decimal points in both numbers. Put that many digits to the right of the decimal point in your answer.

77 Multiplication Slide 143 / x.04 } 2 digits } 2 digits.1284 There are a total of four digits to the right of the decimal points. There must be four digits to the right of the decimal point in the answer. Estimate Your Before any calculations, estimate your answer to make sure you are on the right track. Slide 144 / x 4.04 What place value should we round to? Round to the nearest whole number rounds to 4.04 rounds to Our answer should approximately be Exact 23.2 x } 1 digit } 2 digits Slide 145 / 215 There are a total of three digits to the right of the decimal points. There must be three digits to the right of the decimal point in the answer. Estimating helps us recognize where the decimal point belongs!

78 Estimate Your Estimate your answer for the following problem by rounding the numbers to the nearest whole number. Slide 146 / x rounds to What is your estimate? 0.05 rounds to For problems like these, use your number sense! You are multiplying 9.5 by 0.05 which means you are taking a part (fraction) of 9.5. So your answer must be smaller than 9.5! TRY THESE. Estimate the following products in your notebook then check with the rest of your group. Slide 147 / 215 1) ) 8.31 x 4.21 x x 4 = 60 8 x 1 = 8 3) ) x 5.2 x x 5 = 35 smaller than TRY THESE. Complete in your notebook then check with the rest of your group. Slide 148 / 215 1) ) 8.31 x 4.21 x ) ) x 5.2 x

79 TRY THESE. Complete in your notebook then check with the rest of your group. Slide 148 () / 215 1) ) 8.31 x 4.21 MP 1 x Remind students 0000 to compare their estimates to their exact answers to see if their exact answers make sense ) ) x 5.2 x Math Practice 77 Estimate the product. Slide 149 / x A The product will be less than 1 B The product will be equal to 1 C The product will be greater than 1 77 Estimate the product. Slide 149 () / x A The product will be less than 1 B The product will be equal to 1 C The product will be greater than 1 A

80 78 The product of 0.42 x will have 4 digits to the right of the decimal point. True False Slide 150 / The product of 0.42 x will have 4 digits to the right of the decimal point. True False Slide 150 () / 215 False 79 Multiply 0.42 x Slide 151 / 215

81 79 Multiply 0.42 x Slide 151 () / Multiply x 2.1 Slide 152 / Multiply x 2.1 Slide 152 () /

82 81 You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money? Slide 153 / 215 Estimate to determine your answer. Do not solve. Yes No 81 You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money? Slide 153 () / 215 Estimate to determine your answer. Do not solve. Yes No NO 82 You need to buy 6 notebooks that cost $0.87 each. How much will this cost? Slide 154 / 215

83 82 You need to buy 6 notebooks that cost $0.87 each. How much will this cost? Slide 154 () / 215 $ Multiply x Slide 155 / Multiply x Slide 155 () /

84 84 The regular price of a pair of jeans is $ Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $ Slide 156 / 215 What would the total cost be of four pairs of jeans on sale? A $ B $90.00 C $86.00 D $ The regular price of a pair of jeans is $ Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $ Slide 156 () / 215 What would the total cost be of four pairs B of jeans on sale? A $ B $90.00 C $86.00 D $ How many digits will be to the right of decimal point the product for the problem x 7.8? A 2 B 3 C 4 D 5 Slide 157 / 215

85 85 How many digits will be to the right of decimal point the product for the problem x 7.8? A 2 B 3 C 4 D 5 D Slide 157 () / Multiply x 7.8 Slide 158 / Multiply x 7.8 Slide 158 () /

86 87 Multiply x 0.21 Slide 159 / Multiply x 0.21 Slide 159 () / Enter your answer in the box. Slide 160 / x 4.39 = From PARCC EOY sample test non-calculator #7

87 88 Enter your answer in the box. Slide 160 () / x 4.39 = From PARCC EOY sample test non-calculator #7 89 Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 at a school event. Slide 161 / 215 How much profit, in dollars, will Thomas earn if he sells all the bottles of water? Enter your answer in the box. $ From PARCC EOY sample test non-calculator #17 89 Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 $22.31 at a school event. Slide 161 () / 215 How much profit, in dollars, will Thomas earn if he sells all MP the 2 bottles of water? Make sure to also check that the Enter your answer students in the have box. used good reasoning habits and can show an $ understandable representation of the problem solved. & Math Practice From PARCC EOY sample test non-calculator #17

88 Slide 162 / 215 Dividing Decimals Return to Table of Contents Divide Decimals by Whole Numbers Slide 163 / 215 Step 1: Step 2: Use long division. Bring the decimal point up into the quotient Try This! Slide 164 / =

89 Try This! Slide 164 () / = The Power of Ten Multiplying by a power of ten makes dividing by decimals easier! Slide 165 / 215 1) 13 x 10 = 2) 94 x 100 = 3) 28 x 1000 = 4) 6.2 x 10 = 5) 4.78 x 100 = 6) x 1000 = Do you see a pattern for multiplying by a power of ten? The decimal point moves to the right depending on the number of zeros Click in the to power of ten! Reveal 10 The Power of Ten Multiplying by a power of ten makes dividing by decimals easier! Slide 165 () / 215 Math Practice MP 8 Noticing the pattern when multiplying by 1) 13 x 10 = a power of ten will help 4) 6.2 students x 10 = to understand the algorithm for 2) 94 x 100 = 5) 4.78 x 100 = multiplication of decimals. 3) 28 x 1000 = 6) x 1000 = Do you see a pattern for multiplying by a power of ten? The decimal point moves to the right depending on the number of zeros Click in the to power of ten! Reveal

90 Divide by Decimals Slide 166 / 215 Step 1: Change the divisor to a whole number by multiplying by a power of 10. Step 2: Multiply the dividend by the same power of 10. Step 3: Step 4: Use long division. Bring the decimal point up into the quotient. Divisor Quotient Dividend Power of Ten Slide 167 / 215 Try rewriting these problems so you are ready to divide! Multiply by 10, so that 15.6 becomes must also be multiplied by Multiply by 1000, so that.234 becomes must also be multiplied by 1000 Power of Ten Slide 168 / 215 Rewrite each problem after multiplying by a power of 10. 1) ) ) )

91 Estimating Your Before any calculations, estimate your answer to make sure you are on the right track. Slide 169 / What place value should we round to? Round to the nearest whole number rounds to 4.04 rounds to Our answer should approximately be... 5 Try This! Be sure to round your answer to the thousandths. Slide 170 / Estimate Slide 171 / 215 Estimate your answer for the following problem by rounding the numbers to the nearest whole number rounds to What is your estimate? 0.05 rounds to For problems like these, use your number sense! If you are dividing 9.5 by 0.05, then does that mean the quotient will be smaller than 9.5 or greater than 9.5? Your answer must be greater than 9.5!

92 Estimate Slide 171 () / 215 Estimate your answer for the following problem by rounding the numbers to the nearest whole number. Math Practice MP This standard is addressed when you 9.5 rounds to ask the students if What they will is your get a estimate? quotient smaller or greater than rounds to For problems like these, use your number sense! If you are dividing 9.5 by 0.05, then does that mean the quotient will be smaller than 9.5 or greater than 9.5? Your answer must be greater than 9.5! 90 Divide Slide 172 / = 90 Divide Slide 172 () / = 39

93 91 Use estimation to figure out if the quotient will be Slide 173 / 215 A less than B around C greater than Use estimation to figure out if the quotient will be Slide 173 () / 215 A less than B around C C greater than Slide 174 /

94 92 Slide 174 () / ) 10 divided by 0.25 = Slide 175 / ) 10 divided by 0.25 = Slide 175 () /

95 94 ) = Slide 176 / ) = Slide 176 () / Slide 177 /

96 95 Slide 177 () / Estimate Slide 178 / Estimate Slide 178 () /

97 97 Evaluate = Slide 179 / Evaluate = Slide 179 () / Estimate Slide 180 / 215

98 98 Estimate Slide 180 () / Evaluate = Slide 181 / Evaluate = Slide 181 () /

99 100 Enter your answer in the box = Slide 182 / 215 From PARCC EOY sample test #2 non-calculator 100 Enter your answer in the box = Slide 182 () / From PARCC EOY sample test #2 non-calculator Terminating and Repeating Slide 183 / 215 There are two types of decimals - terminating and repeating. A terminating decimal is a decimal that ends. All of the examples we have completed so far are terminating. A repeating decimal is a decimal that continues forever with one or more digits repeating in a pattern. To denote a repeating decimal, a line is drawn above the numbers that repeat. However, with a calculator, the last digit is rounded.

100 Terminating or Repeating Slide 184 / 215 Let's consider the following... Click to Reveal Terminating or Repeating Slide 184 () / 215 Let's consider the following... Teacher Notes Explain how this is a repeating decimal and how we put a Click bar over to Reveal the numbers that repeat. Repeating Example Slide 185 / Click 36 to Reveal

101 Repeating Example Slide 186 / Click to Reveal ) Slide 187 / ) Slide 187 () / 215

102 102 ) = Slide 188 / ) = Slide 188 () / You need to put some gas in your car. Regular gasoline is $3.59 per gallon. You only have a $20 bill on you. How many gallons can you buy? Slide 189 / 215

103 103 You need to put some gas in your car. Regular gasoline is $3.59 per gallon. You only have a $20 bill on you. How many gallons can you buy? Slide 189 () / gallons 104 ) = Slide 190 / 215 A 2.27 B C 22.7 D ) = Slide 190 () / 215 A 2.27 B C 22.7 D D

104 105 Slide 191 / Slide 191 () / If 6 people are on an elevator and together they weigh pounds, find the average weight of each person. Slide 192 / 215

105 106 If 6 people are on an elevator and together they weigh pounds, find the average weight of each person. Slide 192 () / pounds 107 ) = Slide 193 / ) = Slide 193 () / 215

106 108 Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag? Slide 194 / Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag? Slide 194 () / lbs 109 Slide 195 / 215

107 109 Slide 195 () / ) = Slide 196 / ) = Slide 196 () / 215

108 111 Texas suffered through a heat wave in August The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, and What was the average temperature for those four days? Slide 197 / Texas suffered through a heat wave in August The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, and What was the average temperature for those four days? Slide 197 () / o F 112 For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.10 on one pattern and $8.40 on another. How much does one yard cost? Slide 198 / 215

109 112 For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.10 on one pattern and $8.40 on another. How much does one yard cost? Slide 198 () / 215 $ ) Slide 199 / 215 A 40.9 B C D ) Slide 199 () / 215 A 40.9 B C D 40.9 B

110 Slide 200 / 215 Glossary & Standards Return to Table of Contents Slide 200 () / 215 Teacher Notes Vocabulary Words are bolded in Glossary the presentation. The text box the word is in is then & Standards linked to the page at the end of the presentation with the word defined on it. Return to Table of Contents Algorithm Slide 201 / 215 A step-by-step process to find a solution. How to... Step 1: Step 2: Step 3: = Add the ones then add the tens It's like a cooking recipe for mathematics. Back to Instruction

111 Average The value/amount of each item when the total is distributed across each item equally. Slide 202 / = 9 = 9 3 = 3 Back to Instruction Complex Fraction Slide 203 / 215 A fraction whose numerator or denominator or both contain fractions = = Must be written as a fraction. Back to Instruction Cross Simplify Slide 204 / 215 Used to make operations with fractions easier. Divide the numerator of one fraction and the denominator of another fraction by their GCF GCF of 5 and 15 is = Back to Instruction

112 Distributive Property Multiplying a sum by a number is the same as multiplying each addend in the sum by the same number and then adding the products. Slide 205 / (3 + 2) 3x5=3(3+2) (3+4)= (2x3)+(2x4) also applies to subtraction a(b-c)=ab-ac a(b+c)=ab+ac Back to Instruction Dividend Slide 206 / 215 The number being divided in a division equation Dividend 24 8 = 3 Dividend Dividend 24 8 = 3 Back to Instruction Divisor The number the dividend is divided by. A number that divides another number without a remainder. Slide 207 / Divisor 24 8 = 3 Divisor 25 8 = 3 R1 Must divide evenly. Back to Instruction

113 Power of 10 Slide 208 / 215 Any integer powers of the number ten. (Ten is the base, the exponent is the power.) 10 = 10x10 = 10x10x10 = 10 1 = = = 1,000 Back to Instruction Profit Slide 209 / 215 The difference between the amount earned and the amount spent. Earned - Spent Profit $30 Washing Cars $12 - Supplies $18 Profit Back to Instruction Quotient Slide 210 / 215 The number that is the result of dividing one number by another = 4 Quotient 12 Quotient = Quotient 4 Back to Instruction

114 Reciprocal Slide 211 / 215 One of two numbers whose product is one. 1 x 1 = 1 1 is the reciprocal of 1. Number 2 x 1 2 = 1 Reciprocal r x r = 1 Back to Instruction Repeating Decimal Slide 212 / 215 A decimal with a digit or group of digits that repeats endlessly = =.21 ( ) Back to Instruction Terminating Decimal Slide 213 / 215 A decimal that ends and doesn't go on forever. 1/2 =.5 3/8 = Back to Instruction

115 Vertical Slide 214 / 215 In an up-down position. vertical horizontal diagonal Back to Instruction Standards for Mathematical Practice Slide 215 / 215 MP1: Making sense of problems & persevere in solving them. MP2: Reason abstractly & 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 & make use of structure. MP8: Look for & express regularity in repeated reasoning. Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used. If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab. Standards for Mathematical Practice Slide 215 () / 215 MP1: Making sense of problems & persevere in solving them. MP2: Reason abstractly & 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 & make use of structure. MP8: Look for & express regularity in repeated reasoning. Math Practice Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used. If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.

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