Slide 1 / 215 Slide 2 / 215 6th Grade Fraction & Decimal Computation 2015-10-20 www.njctl.org 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
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
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 = 2 8 1 2 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 = 16 1 2 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 / 215 2 1 3
1 Evaluate the following problem using the model below. Slide 8 / 215 3 1 = 4 3 1 4 1 Evaluate the following problem using the model below. Slide 8 () / 215 3 1 = 4 3 12 1 4 2 Evaluate the following problem using the model below. 5 1 = 2 Slide 9 / 215 5 1 2
2 Evaluate the following problem using the model below. 5 1 = 2 Slide 9 () / 215 5 10 1 2 Visual Model A fraction can be divided by a whole number using the following visual model. 3/5 4 1 2 3 4 Slide 10 / 215 Divide into 4 groups Visual Model A fraction can be divided by a whole number using the following visual model. 3/5 4 1 2 3 4 Slide 10 () / 215 Divide into 4 groups 3/5 4 = 3/20
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? 1 2 3 4 Each friend will receive 3/20 lb. of popcorn. Slide 12 / 215 Slide 12 () / 215
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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.
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 / 215 1 2 2 3 = 1 2 2 3 = 1 2 2 3 x 3 2 x 3 2 = 1 2 x 3 2 1 = 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 - http://www.helpwithfractions.com/dividing-fractions.html 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. 1 1 1 5 2 = 5 x 2 1 = 1 x 2 5 x 1 = 2 5
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 7 8 = 3 5 x 8 7 = 3 x 8 5 x 7 = 24 35 Slide 25 / 215 Checking Your Slide 26 / 215 To check your answer, use your knowledge of fact families. 3 5 7 = 8 24 35 3 5 = 7 24 8 x 35 3 5 is 7 8 of 24 35
Slide 27 / 215 7 ) 4 5 8 10 = 5 4 x 8 10 True False Slide 27 () / 215 7 ) 4 5 8 10 = 5 4 x 8 10 True False FALSE Slide 28 / 215 8 ) 3 4 2 7 = 2 7 8 True False
Slide 28 () / 215 8 ) 3 4 2 7 = 2 7 8 True False FALSE Slide 29 / 215 9 ) 4 5 8 10 = A 1 B C 39 40 40 42 Slide 29 () / 215 9 ) 4 5 8 10 = A 1 B C 39 40 40 42 A
10 ) Slide 30 / 215 10 ) Slide 30 () / 215 11 ) Slide 31 / 215
Slide 31 () / 215 Simplify Slide 32 / 215 Sometimes you can cross simplify prior to multiplying. without cross simplifying with cross simplifying 1 5 2 3 12 Can this problem be cross simplified? Slide 33 / 215 Yes No
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
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
15 Can this problem be cross simplified? Slide 36 () / 215 Yes No YES 16 ) Slide 37 / 215 16 ) Slide 37 () / 215
17 ) Slide 38 / 215 17 ) Slide 38 () / 215 18 ) Slide 39 / 215
18 ) Slide 39 () / 215 19 ) Slide 40 / 215 19 ) Slide 40 () / 215
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 () / 215 18 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 1/2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2 2/3 2 2/3 is equivalent to 16 sections on the number line. So 1 1/2 2 2/3 = 9/16
Visual Model Slide 43 / 215 What if the problem were written as? 2 2/3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 1/2 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 1 1 2 = 6 1 3 2 = 6 x 2 = 12 = 4 1 3 3 Example Slide 45 / 215 Evaluate: 1 2 3 3 1 2 = 5 3 7 2 = 5 3 x 2 7 = 10 21
Slide 46 / 215 20 ) 1 1 2 2 2 3 = Slide 46 () / 215 20 ) 1 1 2 2 2 3 = Slide 47 / 215 21 ) 2 1 2 5 =
Slide 47 () / 215 21 ) 2 1 2 5 = Slide 48 / 215 22 ) 4 2 5 5 1 2 = Slide 48 () / 215 22 ) 4 2 5 5 1 2 =
Slide 49 / 215 23 ) 3 1 2 2 3 8 = Slide 49 () / 215 23 ) 3 1 2 2 3 8 = 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? 2 3 1 6 2 3 x 6 1 = 12 3 = 4 1 4 pieces or 2 2 3 x 6 1 = 1 4 1 = 4 pieces
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? 1 2 3 1 2 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? 6 3 4 6 1 3 4 6 1 x 4 3 = 24 3 8 = = 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? 9 1 3 1 1 6 28 3 7 6 4 28 3 1 x 2 6 7 1 = 8 1 = 8 robots
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
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
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?
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
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
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
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
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
When we are dividing, we are breaking apart into equal groups Slide 67 / 215 EXAMPLE 1 Find 132 3 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 4 4 3 132-12 1 2-12 0 3 x 4 = 12 13-12 = 1 Compare 1 < 3 3 x 4 = 12 12-12 = 0 Compare 0 < 3 Step 3: Check your answer. Slide 68 / 215 44 x 3 132 Estimating Your Before any calculations, estimate your answer to make sure you are on the right track. Slide 69 / 215 357 15 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
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 2 15 357-30 5 15 x 2 = 30 35-30 = 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 23 15 357-30 57-45 12 15 x 3 = 45 57-45 =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. 23.8 15 357.0-30 57-45 120-120 0 15 x 8 = 120 120-120 = 0 Compare 0 < 15 Is our answer close to our estimate?
Check your answer. Slide 73 / 215 23.8 x 15 357 Estimate the following problems. Discuss your answers with your group. Slide 74 / 215 35 300 15 20 Now solve the following problems. Discuss your answers with your group. Slide 75 / 215 41 324 19.5 23.2
35 Estimate the quotient. Slide 76 / 215 779 19 35 Estimate the quotient. Slide 76 () / 215 779 19 40 36 Compute. Slide 77 / 215 779 19 =
36 Compute. Slide 77 () / 215 779 19 = 41 37 Estimate the quotient. Slide 78 / 215 1,551 55 37 Estimate the quotient. Slide 78 () / 215 1,551 55 Approximately 33
38 Compute. Slide 79 / 215 1,551 55 = 38 Compute. Slide 79 () / 215 1,551 55 = 28.2 39 Estimate the quotient. Slide 80 / 215 1,288 35
39 Estimate the quotient. Slide 80 () / 215 1,288 35 25 40 Compute. Slide 81 / 215 1,288 35 = 40 Compute. Slide 81 () / 215 1,288 35 = 36.8
41 The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row. Slide 82 / 215 41 The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row. Slide 82 () / 215 30 42 The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row? Slide 83 / 215
42 The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row? Slide 83 () / 215 26 43 Compute. Slide 84 / 215 4706 104 = 43 Compute. Slide 84 () / 215 4706 104 = 45.25
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 / 215 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 () / 215 49 45 Compute. Slide 86 / 215 1032 24 =
45 Compute. Slide 86 () / 215 1032 24 = 43 46 Compute. Slide 87 / 215 4922 92 = 46 Compute. Slide 87 () / 215 4922 92 = 53.5
47 Enter your answer in the box. Slide 88 / 215 34,992 81 = From PARCC EOY sample test non-calculator #18 47 Enter your answer in the box. Slide 88 () / 215 34,992 81 = 432 From PARCC EOY sample test non-calculator #18 Slide 89 / 215 Adding Decimals Return to Table of Contents
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... 0.25 0.25 0.25 0.25 1.00 + 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. 0.25 + 1.00
Estimating Your Before any calculations, estimate your answer to make sure you are on the right track. Slide 92 / 215 5.1 + 1.25 + 0.04 + 1.99 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 5.1 + 1.25 + 0.04 + 1.99 + 5.10 1.25 0.04 1.99 You can add a zero as a place holder to help line your numbers up. 8.38 TRY THESE. Estimate the following sums in your notebook. Check with the rest of your group. Slide 94 / 215 1) 8.23 + 4.125 + 0.1189 2) 3.178 + 12.28 + 9 8 + 4 + 0 = 12 3 + 12 + 9 = 24 3) 17.009 + 2.965 + 8.4 4) 9.999 + 3.1567 + 4.5656 17 + 3 + 8 = 28 10 + 3 + 5 = 18
TRY THESE. Complete in your notebook then check with the rest of your group. Slide 95 / 215 1) 8.23 + 4.125 + 0.1189 2) 3.178 + 12.28 + 9 8.23 3.178 4.125 12.28 + 0.1189 + 9. 12.4739 24.458 3) 17.009 + 2.965 + 8.4 4) 9.999 + 3.1567 + 4.5656 17.009 9.999 2.965 3.1567 + 8.4 + 4.5656 28.374 17.7213 TRY THESE. Complete in your notebook then check with the rest of your group. Slide 95 () / 215 1) 8.23 + 4.125 + 0.1189 2) 3.178 + 12.28 + 9 MP 1 8.23 3.178 4.125 Remind students to 12.28 compare their + 0.1189 estimates to their + exact 9. answers to see 12.4739 if their exact answers 24.458 make sense. Math Practice 3) 17.009 + 2.965 + 8.4 4) 9.999 + 3.1567 + 4.5656 17.009 9.999 2.965 3.1567 + 8.4 + 4.5656 28.374 17.7213 48 Add the following: Slide 96 / 215 0.6 + 0.55 = A 6.1 B 0.115 C 1.15 D 0.16
48 Add the following: Slide 96 () / 215 0.6 + 0.55 = A 6.1 B 0.115 C 1.15 D 0.16 C 49 Joanne and Peter are working together to solve the problem 0.6 + 0.55. 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 0.6 + 0.55. 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.
50 Find the sum. Slide 98 / 215 1.025 + 0.03 + 14.0001 = 50 Find the sum. Slide 98 () / 215 1.025 + 0.03 + 14.0001 = 15.0551 51 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. Estimate how much Franco spent on the video games. Slide 99 / 215
51 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. 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 $21.95. How much did he spend on video games? Slide 100 / 215 52 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. How much did he spend on video games? Slide 100 () / 215 $65.85
53 What is the sum of Slide 101 / 215 12.034 and 0.0104? A 12.1344 B 12.0444 C 12.138 D 1.20444 53 What is the sum of Slide 101 () / 215 12.034 and 0.0104? A 12.1344 B 12.0444 C 12.138 B D 1.20444 54 Estimate the sum. Slide 102 / 215 8.5 + 0.042 + 12.31 A 20 B 21 C 22 D 23
54 Estimate the sum. Slide 102 () / 215 8.5 + 0.042 + 12.31 A 20 B 21 C 22 D 23 B 55 Find the sum. Slide 103 / 215 8.5 + 0.042 + 12.31 = A 13.58 B 21.23 C 20.852 D 20.14 55 Find the sum. Slide 103 () / 215 8.5 + 0.042 + 12.31 = A 13.58 B 21.23 C 20.852 D 20.14 C
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 / 215 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 D thickness of the papers collected to be recycled? A.561 cm. B.452 cm. C.480 cm. D.473 cm. Slide 104 () / 215 57 Find the sum. Slide 105 / 215 5 + 100.145 + 57.8962 + 2.312 =
57 Find the sum. Slide 105 () / 215 5 + 100.145 + 57.8962 + 2.312 = 165.3532 58 What is the sum of 74.835 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 74.835 and 2.67? Slide 106 () / 215 Enter your answer in the box. 77.505 From PARCC EOY sample test non-calculator #19
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. 1.1-0.3 Subtract the numbers from right to left using the same rules as whole numbers. 0 1 1.1-0.3 0.8 Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.
Estimating Your Before any calculations, estimate your answer to make sure you are on the right track. Slide 110 / 215 21.7-8.21 What place value should we round to? Round to the nearest whole number. 21.7 rounds to 8.21 rounds to Our answer should approximately be... 14 Subtracting Decimals Slide 111 / 215 What do we do if there aren't enough decimal places when we subtract? 21.7-8.21 Don't forget...line Them Up! 21.7 8.21 What goes here? 11 61 21.70 8.21 13.49 TRY THESE. Estimate the following differences in your notebook. Then check with the rest of your group. Slide 112 / 215 1) 8.23-0.1189 2) 12.283-9.025 8-0 = 8 12-9 = 3 3) 17.009-8.4 4) 9.999-4.5656 17-8 = 9 10-5 = 5
TRY THESE. Complete in your notebook then check with the rest of your group. Slide 113 / 215 1) 8.23-0.1189 2) 12.283-9.025 8.23 12.283-0.1189-9.025 8.1111 3.258 3) 17.009-8.4 4) 9.999-4.5656 17.009 9.999-8.4-4.5656 8.609 5.4334 TRY THESE. Complete in your notebook then check with the rest of your group. Slide 113 () / 215 1) 8.23-0.1189 2) 12.283-9.025 8.23 MP 1 12.283-0.1189 Remind students - to compare 9.025 their 8.1111 estimates to their exact 3.258 answers to see if their exact answers make sense. 3) 17.009-8.4 4) 9.999-4.5656 Math Practice 17.009 [This object is 9.999 a pull tab] - 8.4-4.5656 8.609 5.4334 59 ) 5-0.238 = Slide 114 / 215
59 ) 5-0.238 = Slide 114 () / 215 4.762 60 ) 12.809-4 = Slide 115 / 215 60 ) 12.809-4 = Slide 115 () / 215 8.809
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
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 ) 1897.112-0.647 = Slide 118 / 215 63 ) 1897.112-0.647 = Slide 118 () / 215 1896.465
64 The Johnson twins raced each other in the 200-meter dash. Jordan finished in 23.48 seconds, and Max finished in 26.13 seconds. How much faster was Jordan than Max? Slide 119 / 215 64 The Johnson twins raced each other in the 200-meter dash. Jordan finished in 23.48 seconds, and Max finished in 26.13 seconds. How much faster was Jordan than Max? Slide 119 () / 215 2.65 seconds 65 Timothy is working on the problem 4.1-0.094. 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 Timothy is working on the problem 4.1-0.094. 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 () / 215 66 ) 4.1-0.094 = Slide 121 / 215 66 ) 4.1-0.094 = Slide 121 () / 215 4.006
67 ) 17-13.008 = Slide 122 / 215 67 ) 17-13.008 = Slide 122 () / 215 3.992 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 27.85-12.91 B 14.17-8.2 C 7.9-3.88 D 21.25-18.16
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 27.85-12.91 B 14.17-8.2 C 7.9-3.88 D 21.25-18.16 D 69 If you buy two movie tickets for $8.25 each, what will your change be from $20? Slide 124 / 215 69 If you buy two movie tickets for $8.25 each, what will your change be from $20? Slide 124 () / 215 $3.50
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.
Distributive Property Slide 128 / 215 Evaluate 200 x 41.5 8,300 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 41.5 200 x (41 + 0.5) (200 x 41) + (200 x 0.5) 8,200 + 100 = 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 41.5 200 x (41 + 0.5) Apply the distributive property Apply the order of operations (200 x 41) + (200 x 0.5) 8,200 + 100 = 8,300 Distributive Property Slide 129 / 215 Evaluate 400 x 18.33 400 x ( + ) (400 x ) + (400 x ) + = 7332 This method is known as partial products.
Distributive Property Slide 130 / 215 How can we use partial products to calculate the area of the rectangle shown below? 5858.6 ft ft 0.6 ft 200 x 58.6 200 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 5858.6 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
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(76 + 0.8)
72 Calculate the product using partial products. Slide 133 / 215 5(48) 72 Calculate the product using partial products. Slide 133 () / 215 5(48) 240 73 Calculate the product using partial products. Slide 134 / 215 13(5.2)
73 Calculate the product using partial products. Slide 134 () / 215 13(5.2) 67.6 74 Calculate the product using partial products. Slide 135 / 215 300(7.4) 74 Calculate the product using partial products. Slide 135 () / 215 300(7.4) 2,220
75 Calculate the product using partial products. Slide 136 / 215 200(6.5) 75 Calculate the product using partial products. Slide 136 () / 215 200(6.5) 1,300 76 Calculate the area of the rectangle using partial products. Slide 137 / 215 300 units 43.9 units
76 Calculate the area of the rectangle using partial products. Slide 137 () / 215 300 units 13,170 43.9 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? 63 1000 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
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 0.13 3) 0.08 x 0.231 Multiplication Slide 141 / 215 Do you notice a pattern for multiplying decimals? 3.5 x 1.72 3 5 x 10 1 72 100 35 10 x 172 100 6020 1000 Where does the decimal point go? Drag the decimal point. 6 0 2 0 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.
Multiplication Slide 143 / 215 3.21 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 / 215 23.2 x 4.04 What place value should we round to? Round to the nearest whole number. 23.2 rounds to 4.04 rounds to Our answer should approximately be... 92 Exact 23.2 x 4.04 928 0000 92800 93.728 } 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!
Estimate Your Estimate your answer for the following problem by rounding the numbers to the nearest whole number. Slide 146 / 215 9.5 x 0.05 9.5 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) 14.512 2) 8.31 x 4.21 x 1.008 15 x 4 = 60 8 x 1 = 8 3) 7.0045 4) 3.214 x 5.2 x 0.0034 7 x 5 = 35 smaller than 3.214 TRY THESE. Complete in your notebook then check with the rest of your group. Slide 148 / 215 1) 14.512 2) 8.31 x 4.21 x 1.008 14512 6648 290240 5804800 61.09552 0000 00000 831000 8.37648 3) 7.0045 4) 3.214 x 5.2 x 0.0034 140090 3502250 36.42340 12856 96420 0.0109276
TRY THESE. Complete in your notebook then check with the rest of your group. Slide 148 () / 215 1) 14.512 2) 8.31 x 4.21 MP 1 x 1.008 14512 6648 290240 Remind students 0000 to compare their 5804800 61.09552 estimates to their 00000 exact answers to see if their exact answers 831000 make sense. 8.37648 3) 7.0045 4) 3.214 x 5.2 x 0.0034 140090 3502250 36.42340 12856 96420 0.0109276 Math Practice 77 Estimate the product. Slide 149 / 215 0.42 x 0.032 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 () / 215 0.42 x 0.032 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
78 The product of 0.42 x 0.032 will have 4 digits to the right of the decimal point. True False Slide 150 / 215 78 The product of 0.42 x 0.032 will have 4 digits to the right of the decimal point. True False Slide 150 () / 215 False 79 Multiply 0.42 x 0.032 Slide 151 / 215
79 Multiply 0.42 x 0.032 Slide 151 () / 215 0.1344 80 Multiply 3.452 x 2.1 Slide 152 / 215 80 Multiply 3.452 x 2.1 Slide 152 () / 215 7.2492
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
82 You need to buy 6 notebooks that cost $0.87 each. How much will this cost? Slide 154 () / 215 $5.22 83 Multiply 53.24 x 0.089 Slide 155 / 215 83 Multiply 53.24 x 0.089 Slide 155 () / 215 4.73836
84 The regular price of a pair of jeans is $29.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $22.50. Slide 156 / 215 What would the total cost be of four pairs of jeans on sale? A $119.96 B $90.00 C $86.00 D $52.49 84 The regular price of a pair of jeans is $29.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $22.50. Slide 156 () / 215 What would the total cost be of four pairs B of jeans on sale? A $119.96 B $90.00 C $86.00 D $52.49 85 How many digits will be to the right of decimal point the product for the problem 4.0156 x 7.8? A 2 B 3 C 4 D 5 Slide 157 / 215
85 How many digits will be to the right of decimal point the product for the problem 4.0156 x 7.8? A 2 B 3 C 4 D 5 D Slide 157 () / 215 86 Multiply 4.0156 x 7.8 Slide 158 / 215 86 Multiply 4.0156 x 7.8 Slide 158 () / 215 31.32168
87 Multiply 0.012 x 0.21 Slide 159 / 215 87 Multiply 0.012 x 0.21 Slide 159 () / 215 0.00252 88 Enter your answer in the box. Slide 160 / 215 18.3 x 4.39 = From PARCC EOY sample test non-calculator #7
88 Enter your answer in the box. Slide 160 () / 215 18.3 x 4.39 = 80.337 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
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. 28 04 2 56.08 Try This! Slide 164 / 215 12.45 5 =
Try This! Slide 164 () / 215 12.45 5 = 2.49 10 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) 51.293 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) 51.293 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
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! 15.6 6.24 156 62.4 Multiply by 10, so that 15.6 becomes 156 6.24 must also be multiplied by 10.234 23.4 234 23400 Multiply by 1000, so that.234 becomes 234 23.4 must also be multiplied by 1000 Power of Ten Slide 168 / 215 Rewrite each problem after multiplying by a power of 10. 1) 250.2 4.15 415 25020 2).008 4.2 008 4200 3) 0.9 678.921 09 6789.21 4) 68.342 2.2 22 683.42
Estimating Your Before any calculations, estimate your answer to make sure you are on the right track. Slide 169 / 215 23.2 4.04 What place value should we round to? Round to the nearest whole number. 23.2 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 / 215 4.04 23.2 5.743 Estimate Slide 171 / 215 Estimate your answer for the following problem by rounding the numbers to the nearest whole number. 9.5 0.05 9.5 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!
Estimate Slide 171 () / 215 Estimate your answer for the following problem by rounding the numbers to the nearest whole number. Math Practice MP 6 9.5 0.05 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 9.5 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! 90 Divide Slide 172 / 215 0.78 0.02 = 90 Divide Slide 172 () / 215 0.78 0.02 = 39
91 Use estimation to figure out if the quotient will be 4.866 0.6 Slide 173 / 215 A less than 4.866 B around 4.866 C greater than 4.866 91 Use estimation to figure out if the quotient will be 4.866 0.6 Slide 173 () / 215 A less than 4.866 B around 4.866 C C greater than 4.866 92 Slide 174 / 215 0.6 4.866
92 Slide 174 () / 215 0.6 4.866 8.11 93 ) 10 divided by 0.25 = Slide 175 / 215 93 ) 10 divided by 0.25 = Slide 175 () / 215 40
94 ) 12.03 0.04 = Slide 176 / 215 94 ) 12.03 0.04 = Slide 176 () / 215 300.75 95 Slide 177 / 215 0.012 24.6
95 Slide 177 () / 215 0.012 24.6 2050 96 Estimate. 36 1.2 Slide 178 / 215 96 Estimate. 36 1.2 Slide 178 () / 215 36
97 Evaluate. 36 1.2 = Slide 179 / 215 97 Evaluate. 36 1.2 = Slide 179 () / 215 30 98 Estimate. 9.116 2.12 Slide 180 / 215
98 Estimate. 9.116 2.12 Slide 180 () / 215 4.5 99 Evaluate. 9.116 2.12 = Slide 181 / 215 99 Evaluate. 9.116 2.12 = Slide 181 () / 215 4.3
100 Enter your answer in the box. 33.8 32.5 = Slide 182 / 215 From PARCC EOY sample test #2 non-calculator 100 Enter your answer in the box. 33.8 32.5 = Slide 182 () / 215 1.04 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.
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 / 215 63 48 45 39 Click 36 to Reveal 32 27 51 45 60 54 6
Repeating Example Slide 186 / 215 6600 2342 2200 14200 Click 13200 to Reveal 10000 8800 12000 11000 10000 8800 12000 11000 101 ) 15.5 0.3 Slide 187 / 215 101 ) 15.5 0.3 Slide 187 () / 215
102 ) 0.8 0.003 = Slide 188 / 215 102 ) 0.8 0.003 = Slide 188 () / 215 103 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 / 215
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 () / 215 5.571 gallons 104 ) 25 1.1 = Slide 190 / 215 A 2.27 B 22.73 C 22.7 D 22.72 104 ) 25 1.1 = Slide 190 () / 215 A 2.27 B 22.73 C 22.7 D 22.72 D
105 Slide 191 / 215 105 Slide 191 () / 215 106 If 6 people are on an elevator and together they weigh 931.56 pounds, find the average weight of each person. Slide 192 / 215
106 If 6 people are on an elevator and together they weigh 931.56 pounds, find the average weight of each person. Slide 192 () / 215 155.26 pounds 107 ) 0.007 0.9 = Slide 193 / 215 107 ) 0.007 0.9 = Slide 193 () / 215
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 / 215 108 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 () / 215 0.647 lbs 109 Slide 195 / 215
109 Slide 195 () / 215 110 ) 91.84 4.8 = Slide 196 / 215 110 ) 91.84 4.8 = Slide 196 () / 215
111 Texas suffered through a heat wave in August 2011. The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, 101.9 and 102.5. What was the average temperature for those four days? Slide 197 / 215 111 Texas suffered through a heat wave in August 2011. The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, 101.9 and 102.5. What was the average temperature for those four days? Slide 197 () / 215 102.65 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
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 $5.00 113 ) 9 0.22 Slide 199 / 215 A 40.9 B 40.90 C 40.91 D 40.9 113 ) 9 0.22 Slide 199 () / 215 A 40.9 B 40.90 C 40.91 D 40.9 B
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: 24 + 12 = Add the ones then add the tens It's like a cooking recipe for mathematics. Back to Instruction
Average The value/amount of each item when the total is distributed across each item equally. Slide 202 / 215 3 + 4 + 2 = 9 = 9 3 = 3 Back to Instruction Complex Fraction Slide 203 / 215 A fraction whose numerator or denominator or both contain fractions. 3 1 5 2 3 1 5 = 3 1 5 = 2 3 1 5 2 3 1 5 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. 1 5 15 + 20 GCF of 5 and 15 is 5. 1 5 1 3 15 + 20 = 3 1 + 20 Back to Instruction
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 / 215 5 3 (3 + 2) 3x5=3(3+2) 2 3 4 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. 8 3 24 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 / 215 3 8 24 Divisor 24 8 = 3 Divisor 25 8 = 3 R1 Must divide evenly. Back to Instruction
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 = 10 10 2 = 100 10 3 = 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. 12 3 = 4 Quotient 12 Quotient 12 3 4 3 = Quotient 4 Back to Instruction
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..333... 3 1.0 00-9 10 9-10 - 9 1 1 3 =.3 7 33 =.21 (.212121...) Back to Instruction Terminating Decimal Slide 213 / 215 A decimal that ends and doesn't go on forever. 1/2 =.5 3/8 =.375.333... 3 1.0 00-9 10 9-10 - 9 1 Back to Instruction
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.