5th Grade. Measurement & Data.

Transcription

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2 5th Grade Measurement & Data

3 Table of Contents click on the topic to go to that section Standard Measurement Conversions Metric Measurement Conversions Unit Cubes Volume of a Solid with Unit Cubes Volume Problem Solving 3

4 Standard Measurement Conversions Return to Table of Contents 4

5 Conversion Chart Students will need access to a conversion chart for the next two sections. 5

6 Standard Measurement US Measurement (Standard or Customary System) Weight Volume/Capacity Length ounces pounds tons ounce cup pint quart gallon inches feet yards miles 6

7 Standard Measurement Standard Measurement System (US Customary) Converting From One Unit of Measurement to Another What happens if you are given a measurement in one unit, but need to use it in another? For example, you are baking cupcakes, and the recipe calls for 4 cups of oil. The bottle of oil says that it contains 3 pints. How do you know if you have enough oil? In order to find out, you would need to do something called converting. You need to convert the unit of cups to the unit of pints. 7

8 Cups and Pints There are 2 cups in every pint. + = 1 cup 1 cup 1 pint 8

9 Cups and Pints So how many cups are there in 3 pints? + = 1 cup 1 cup 1 pint + = 1 cup 1 cup 1 pint + = 1 cup 1 cup 1 pint 3 pints 2 cups x 3 pints = 6 cups in 3 pints 9

10 Converting Measurement When converting measurements, use your arms to help you. We can spread our arms out wide to show that something is bigger. We can fold our arms in a hug to show that something is smaller. To convert a smaller unit to a larger unit, we divide the amount. To convert a larger unit to a smaller unit, we multiply the amount. 10

11 Conversions Troy has 6 popsicles that are 5 in long each. If he places them all in a line, how many feet would they be? 5 in + 5 in + 5 in + 5 in + 5 in + 5 in = 30 in How many feet are 30 in? We are going from inches to feet, so we are converting a smaller unit to a larger unit. Therefore, we need to. 30 in X or = ft in (# of inches in a foot) 11

12 Conversions Another example: I bought a set of 4 glasses from the market. A glass weighs 8 ounces. How many pounds does the set weigh? Find the total ounces: oz x glasses = oz. We are going from ounces to pounds so we are converting a smaller unit to a larger unit. Therefore, we need to. 32 oz X or = (# of oz in a lb) lbs 12

13 Fractional Measurements How can we write measurements using fractions? Think about what half a foot is in inches. If a foot is 12 in, then 1/2 a foot So, half a foot is 6 in. How many inches is a foot and a half? A foot and a half is 12 x 1.5. So, a foot and a half is 18 in. How many feet are there in 30 inches? = 2.5 So, there are 2 1/2 feet in 30 inches. 13

14 Standard Conversions Match Up 14

15 1 12 yards = ft 15

16 2 95 ft = yds 16

17 3 18 cups = pints 17

18 4 6 gal = pts 18

19 5 1.5 tons = lbs 19

20 6 This morning, Tom ran 1.5 miles. How many feet did Tom run? 20

21 7 If Tom ran 1.5 miles, how many inches did he run? 21

22 8 Marie is buying yarn to make a blanket. The yarn comes in 4 feet rolls. She needs 8 yards of yarn. How many rolls should she buy? 22

23 9 Approximately how many 100 yd football fields are there in a mile? A 5,280 B 1760 C

24 10 At the zoo, we saw bears eating honey from two jars. Each jar contains one cup of honey. One bear ate 1/2 of the honey in the first jar. Another bear ate only 1/4 of the honey from his jar. How many fluid ounces of honey did the bears eat? 24

25 11 Tom has a water tank that holds 5 gallons of water. Part A Tom uses water from a full tank to full 6 boggles that each hold 16 ounces and a pitcher that holds 1/2 gallon. How many ounces of water are left in the water tank? From PARCC EOY sample test #5 25

26 12 Tom has a water tank that holds 5 gallons of water. Part B Tom drinks 4 pints of water a day. How many full tanks of water will he drink in 30 days? From PARCC EOY sample test #5 26

27 Metric Measurement Conversions Return to Table of Contents 27

28 Metric Measurement Mass/Weight Capacity/Volume Length grams liters meters 28

29 Comparing Units of Metric Measure 1. Work with a partner. Measure the length in cm of ten Base 10 logs placed end to end. 2. Record the length in a table. (see table on next page.) 3. Measure the length a second time in mm. Record your measure in the table. 4. Measure the length a third time using the meter ruler. Record your measure in the table. Teacher Notes 29

30 Comparing Units of Metric Measure Number of Base 10 Logs m cm mm 10 30

31 Comparing Units of Metric Measure Describe any patterns you see. Number of Base 10 Logs m cm mm 10 31

32 Comparing Units of Metric Measure Fill in the blanks to describe the relationships that you find among the three metric units. To convert m to cm by. To convert cm to m by. To convert cm to mm by. To convert mm to cm by. To convert m to mm by. To convert mm to m by. 32

33 To convert measurements within the metric system, we multiply or divide by multiples of 10. To step down, or convert to a smaller unit, you. To step up, or convert to a larger unit, you. 33

34 Comparing Units of Metric Measure A gram is a base unit. To convert a gram to a milligram, hop down steps. or by. (multiply/divide) 34

35 Comparing Units of Metric Measure Think about this: A paperclip weighs one gram. So, imagine what could weigh one milligram. 35

36 Metric Conversion Match Up 36

37 13.08 ml = L 37

38 14 1,235,000 mm = km 38

39 kg = mg 39

40 16 Each morning Paul rides 500 m on an exercise bike. How many kilometers does he ride in one week? 40

41 17 A kitten weighs 500 g. A puppy weighs 2 kg. Freddy says that the puppy weighs more. Is Freddy correct? Yes No 41

42 18 I make 2.5 kg of popcorn, and I eat 450 g of it while watching a movie. How much popcorn is left? 42

43 19 How many 200 ml paper cups can be filled from a 2 liter jug of lemonade? 43

44 20 Rose needs 5 meters of fabric. The length of a fabric roll is 1,000 mm, and it costs $30. What is the total cost of the fabric that Rose needs too buy? A $150 B $1.50 C $5 D $5,000 44

45 21 Rose also needs 6 meters of rope. The length of a roll of rope is 380 mm. How many rolls does Rose need to buy? 45

46 22 7 km 20 m = m 46

47 23 Complete each conversion by dragging and dropping the correct number into each box. 7 mm = cm 7 cm = m m = 7 mk From PARCC EOY sample test #28 47

48 Unit Cubes Return to Table of Contents 48

49 Unit Cubes Unit Cubes help us to measure volumes. There are: cubic centimeters cubic inches cubic feet Teacher Notes 49

50 24 What would be the best unit to measure the volume of a cereal box? A cubic feet B cubic meters C cubic centimeters D cubic miles 50

51 25 What would be the best unit to measure the volume of a classroom? A cubic miles B cubic centimeters C cubic inches D cubic meters 51

52 26 What would be the best unit to measure the volume of a desk drawer? A cubic yards B cubic inches C cubic meters D cubic millimeters 52

53 27 What would be the best unit to measure the volume of a soccer ball? A cubic millimeters B cubic centimeters C cubic meters D cubic kilometers 53

54 Volume of a Solid with Unit Cubes Return to Table of Contents 54

55 Volume of a Solid with Unit Cubes Blocks Problem Morgan is helping his younger sister put away her alphabet blocks in a box. She has already put away one layer of blocks. It takes 15 blocks to make one layer. If the box is filled with 4 layers of blocks, without any gaps, how many blocks will be in the box? Steps: Use unit cubes to model a layer that is 3 by 5 blocks. Make 4 layers. How many total blocks did you use to make the model? 55

56 Volume of a Solid with Unit Cubes The total number of blocks used is the volume of the box. This box is called a 3 Dimensional Figure (3 D). A 3 D figure has a length, width and a height. height width length 56

57 Volume of a Solid with Unit Cubes base The 3 D shape also has a base. 57

58 Volume of a Solid with Unit Cubes All of these 3 D shapes are right rectangular prisms. 58

59 Volume of a Solid with Unit Cubes List some 3 D shapes that are right rectangular prisms in the classroom: 59

60 28 Is this shape a right rectangular prism? Yes No 60

61 29 Is this shape a right rectangular prism? Yes No 61

62 30 Is this shape a right rectangular prism? Yes No 62

63 31 Which of the following would not be used to describe a right rectangular prism? A length B height C perimeter D width 63

64 Volume of a Solid with Unit Cubes Volume The amount of space occupied by or inside a 3 D Figure The number of cubic units needed to FILL a 3 D Figure (layering) Label Units 3 or cubic units 64

65 Volume of a Solid with Unit Cubes Use unit cubes to build a model of the prism shown. length (l) width (w) height (h) number of cubes Now use unit cubes to build 4 other rectangular prisms. Fill in the length, width, height and number of cubes in the table. 65

66 32 Model the rectangular prism described in the table. What is its volume? length (l) width (w) height (h) number of cubes 2 1 4? cubic units 66

67 33 Model the rectangular prism described in the table. What is its volume? length (l) width (w) height (h) number of cubes 6 2 3? cubic units 67

68 34 Model the rectangular prism described in the table. What is its volume? length (l) width (w) height (h) number of cubes 4 3 2? cubic units 68

69 35 Model the rectangular prism described in the table. What is its volume? length (l) width (w) height (h) number of cubes 6 3 2? cubic units 69

70 36 Model the rectangular prism described in the table. What is its volume? length (l) width (w) height (h) number of cubes 4 2 3? cubic units 70

71 Volume of a Solid with Unit Cubes Work with a partner, and build as many possible right rectangular prisms that you can with 24 cubes. Record the dimensions in the table below. length width height 71

72 37 Which set of dimensions has the same volume as the first row? A B C length (l) width (w) height (h) number of cubes 4 2 3?

73 38 Which set of dimensions has the same volume as the first row? length (l) width (w) height (h) number of cubes 6 4 2? A B C

74 39 Which set of dimensions has the same volume as the first row? A B C length (l) width (w) height (h) number of cubes 7 1 2?

75 Volume of a Solid with Unit Cubes So far we have found the volume of right rectangular prisms by counting unit cubes. We can also find the area by thinking of layering unit cubes. Think of the base as the bottom layer. 75

76 40 The number of unit cubes that it takes to cover the base is also the of the base. A perimeter B volume C area D cubic units 76

77 Volume of a Solid with Unit Cubes If you know the area of the base, l = 5 units w = 2 units area = lw = 5(2) = 10 and that it is 2 layers high, h = 2 units then... volume = area of the base times height = B x h = 10(2) = 20 cubic units 77

78 41 What is the area of the base of this rectangular prism? l = 8 in. h = 4 in. w = 3 in. square inches 78

79 42 What is the volume of this rectangular prism? h = 4 in. l = 8 in. w = 3 in. cubic inches 79

80 43 What is the area of the base of this rectangular prism? h = 50 ft. w = 20 ft. l = 30 ft. square feet 80

81 44 What is the volume of this rectangular prism? w = 20 ft. l = 30 ft. h = 50 ft. cubic feet 81

82 45 What is the area of the base of this rectangular prism (cube)? h = 5 cm. w = 5 cm. l = 5 cm. square centimeters 82

83 46 What is the volume of this rectangular prism (cube)? h = 5 cm. w = 5 cm. l = 5 cm. cubic centimeters 83

84 Volume of a Solid with Unit Cubes To find the volume of a right rectangular prism the length, width and height can all be multiplied together. h = 3 inches w = 4 inches l = 7 inches V = l x w x h V = (7 inches) x (4 inches) x (3 inches) V = 84 (inches) x (inches) x (inches) V = 83 in 3 84

85 Volume of a Solid with Unit Cubes Volume Formulas Formula 1 V= lwh; where l = length, w = width, h = height Multiply the length, width and height of the rectangular prism. Formula 2 V=Bh; where B = area of base, h = height Find the area of the rectangular prism's base and multiply it by the height. 85

86 Volume of a Solid with Unit Cubes Click for source. (3 x 2) represents the 1st layer 5 layers high Three ways to solve: (3 x 2) x 5 = 30 units 3 (3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) = 30 units = 30 units 3 86

87 47 Find the volume. cm 3 8 cm 2 cm 5 cm 87

88 48 Find the volume. cm 3 9 cm 5 cm 12 cm 88

89 49 Find the volume. ft 3 70 ft 80 ft 40 ft 89

90 50 Find the volume of a rectangular prism with the following dimensions: l = 8 in, w = 10 in, h = 4 in in 3 90

91 51 Find the volume of a rectangular prism with the following dimensions: l = 11 cm, w = 8 cm, h = 3 cm cm 3 91

92 52 Find the volume of a rectangular prism with the following dimensions: l = 5 ft, w = 6 ft, h = 8 ft cubic feet 92

93 53 Which is a possible length, width and height for a rectangular prism whose volume = 18 units 3 A 1 x 2 x 18 B 6 x 3 x 3 C 2 x 3 x 3 D 3 x 3 x 3 93

94 54 Which is a possible length, width and height for a rectangular prism whose volume = 40 units 3 A 8 x 2 x 3 B 5 x 8 x 2 C 6 x 1 x 5 D 2 x 5 x 4 94

95 55 Which is a possible length, width and height for a rectangular prism whose volume = 36 units 3 A 9 x 4 x 2 B 3 x 4 x 3 C 1 x 4 x 8 D 2 x 3 x 4 95

96 Volume Problem Solving Return to Table of Contents 96

97 Volume Problem Solving A 3 D object can be decomposed (broken) into rectangular prisms to find the volume of the whole object. click for source this figure can be broken into these two figures V = 3 cm 3 V = 2 cm 3 total volume = 5 cm 3 97

98 56 What is the volume of this object? + = cubic units 98

99 57 What is the volume of this object? cubic units 99

100 58 What is the volume of this object? cubic units 100

101 59 What is the volume of this object? cubic units 101

102 60 What is the volume of concrete needed to build the steps shown in this diagram? cubic feet click for source 102

103 61 What is the volume of concrete needed to build the steps shown in this diagram? 3 cm 8 cm 2 cm 9 cm 3 cm cubic cm 103

104 62 An architect needs to know how much cement is needed to fill a decorative column that is 2 feet wide by 2 feet deep. It will be 8 feet tall. How many cubic feet of cement will the architect need? 104

105 63 How much water is needed to fill a pool that is 50 meters long, 30 meters wide and 4 meters deep? 105

106 64 A path is 120 inches long and 24 inches wide. How much gravel is needed to put a three inch layer of gravel over the whole path? 106

107 65 A box shaped refrigerator measures 12 by 10 by 7 on the outside. All six sides of the refrigerator are 1 unit thick. What is the inside volume of the refrigerator in cubic units? HINT: You may want to draw a picture! 107

108 66 Planters that are 10 inches long, 8 inches deep and 6 inches high are being placed by the main entrance to school. How many cubic inches of soil is needed to fill six planters? 108

109 67 A window air conditioner is put in for a room that is 5 meters long, 4 meters wide and 3 meters high. What is the volume of the air in the room that needs to be cooled? 109

110 68 The right rectangular prism shown is made from cubes. Each cube is 1 cubic unit. What is the volume, in cubic units, of the right rectangular prism? From PARCC EOY sample test #10 110

111 69 A cereal box has a height of 32 centimeters. It has a base with an area of 160 square centimeters. What is the volume, in cubic centimeters, of the cereal box? From PARCC EOY sample test #20 111

112 70 There are two tanks at the aquarium. Tank A and Tank B. Each tank has two sections. Part A The volume of one section of Tank A is 24 cubic feet. The volume of the other section of Tank A is 96 cubic feet. What is the total volume, in cubic feet, of Tank A? A 4 B 72 C 120 D 2,304 From PARCC EOY sample test #31 112

113 71 There are two tanks at the aquarium. Tank A and Tank B. Each tank has two sections. Part B Tank B has the same volume as Tank A. The volume of one section of Tank B is 45 cubic feet. What is the volume, in cubic feet, of the other section of Tank B? From PARCC EOY sample test #31 113

114 72 What is the volume of the rectangular prism in cubic units? From PARCC PBA sample test #1 114

115 73 In this right rectangular prism, each small cube measures 1 unit on each side. What is the volume of the prism? Explain how you found the volume. You may show your work in your explanation. What would be the dimensions of a new right rectangular prism that has 20 fewer unit cubes than the original prism? Explain how you determined the dimensions of the new right rectangular prism. From PARCC PBA sample test #13 115