Slide 1 / 115 Slide 2 / 115 5th Grade Measurement & Data 2015-11-23 www.njctl.org Slide 3 / 115 Table of Contents Standard Measurement Conversions Metric Measurement Conversions Unit Cubes click on the topic to go to that section Slide 4 / 115 Standard Measurement Conversions Volume Problem Solving Return to Table of Contents Slide 5 / 115 Slide 6 / 115 Conversion Chart Students will need access to a conversion chart for the next two sections.
Slide 7 / 115 Standard Measurement Standard Measurement System (US Customary) Converting From One Unit of Measurement to Another Slide 8 / 115 Cups and Pints There are 2 cups in every pint. What happens if you are given a measurement in one unit, but need to use it in another? + = 1 cup 1 cup 1 pint 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. Slide 9 / 115 Cups and Pints So how many cups are there in 3 pints? + = 1 cup 1 cup 1 pint Slide 10 / 115 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. + = 1 cup 1 cup 1 pint + = 1 cup 1 cup 1 pint 3 pints 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. 2 cups x 3 pints = 6 cups in 3 pints Slide 11 / 115 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? Another example: Slide 12 / 115 Conversions I bought a set of 4 glasses from the market. A glass weighs 8 ounces. How many pounds does the set weigh? 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) 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
Slide 13 / 115 Fractional Measurements Slide 14 / 115 Standard Conversions Match-Up 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 12 2. 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? 30 12 = 2.5 So, there are 2 1/2 feet in 30 inches. Slide 15 / 115 Slide 16 / 115 1 12 yards = ft 2 95 ft = yds Slide 17 / 115 Slide 18 / 115 3 18 cups = pints 4 6 gal = pts
5 1.5 tons = lbs Slide 19 / 115 Slide 20 / 115 6 This morning, Tom ran 1.5 miles. How many feet did Tom run? Slide 21 / 115 7 If Tom ran 1.5 miles, how many inches did he run? Slide 22 / 115 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? Slide 23 / 115 9 Approximately how many 100-yd football fields are there in a mile? A 5,280 Slide 24 / 115 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? B 1760 C 17.6
Slide 25 / 115 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? Slide 26 / 115 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 Slide 27 / 115 From PARCC EOY sample test #5 Slide 28 / 115 Metric Measurement Conversions Return to Table of Contents Slide 29 / 115 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. Number of Base 10 Logs Slide 30 / 115 Comparing Units of Metric Measure 10 m cm mm
Slide 31 / 115 Comparing Units of Metric Measure Describe any patterns you see. Slide 32 / 115 Comparing Units of Metric Measure Fill in the blanks to describe the relationships that you find among the three metric units. Number of Base 10 Logs 10 m cm mm 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. Slide 33 / 115 Slide 34 / 115 To convert measurements within the metric system, we multiply or divide by multiples of 10. Comparing Units of Metric Measure A gram is a base unit. To convert a gram to a milligram, hop down steps. or by. To step down, or convert to a smaller unit, you. (multiply/divide) To step up, or convert to a larger unit, you. Slide 35 / 115 Comparing Units of Metric Measure Slide 36 / 115 Metric Conversion Match-Up Think about this: A paperclip weighs one gram. So, imagine what could weigh one milligram.
Slide 37 / 115 Slide 38 / 115 13.08 ml = L 14 1,235,000 mm = km Slide 39 / 115 Slide 40 / 115 15.053 kg = mg 16 Each morning Paul rides 500 m on an exercise bike. How many kilometers does he ride in one week? Slide 41 / 115 17 A kitten weighs 500 g. A puppy weighs 2 kg. Freddy says that the puppy weighs more. Is Freddy correct? Slide 42 / 115 18 I make 2.5 kg of popcorn, and I eat 450 g of it while watching a movie. How much popcorn is left? Yes No
Slide 43 / 115 19 How many 200 ml paper cups can be filled from a 2 liter jug of lemonade? Slide 44 / 115 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 Slide 45 / 115 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? 22 7 km 20 m = m Slide 46 / 115 Slide 47 / 115 Slide 48 / 115 23 Complete each conversion by dragging and dropping the correct number into each box. 7 mm = cm Unit Cubes 7 cm = m m = 7 mk Return to Table of Contents From PARCC EOY sample test #28
Slide 49 / 115 Unit Cubes Unit Cubes help us to measure volumes. There are: cubic centimeters cubic inches cubic feet Slide 50 / 115 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 Slide 51 / 115 Slide 52 / 115 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 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 Slide 53 / 115 Slide 54 / 115 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 Volume of a Solid with Unit Cubes Return to Table of Contents
Slide 55 / 115 Slide 56 / 115 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? 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. Steps: -Use unit cubes to model a layer that is 3 by 5 blocks. height width -Make 4 layers. length -How many total blocks did you use to make the model? Slide 57 / 115 Slide 58 / 115 All of these 3-D shapes are right rectangular prisms. base The 3-D shape also has a base. Slide 59 / 115 List some 3-D shapes that are right rectangular prisms in the classroom: Slide 60 / 115 28 Is this shape a right rectangular prism? Yes No
Slide 61 / 115 Slide 62 / 115 29 Is this shape a right rectangular prism? Yes No 30 Is this shape a right rectangular prism? Yes No Slide 63 / 115 31 Which of the following would not be used to describe a right rectangular prism? A length B height C perimeter D width Volume Slide 64 / 115 - 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 Slide 65 / 115 Use unit cubes to build a model of the prism shown. length (l) width (w) height (h) number of cubes 3 2 5 30 Slide 66 / 115 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? Answer cubic units Now use unit cubes to build 4 other rectangular prisms. Fill in the length, width, height and number of cubes in the table.
Slide 67 / 115 Slide 68 / 115 33 Model the rectangular prism described in the table. 34 Model the rectangular prism described in the table. What is its volume? What is its volume? length (l) width (w) height (h) number of cubes 6 2 3? Answer length (l) width (w) height (h) number of cubes 4 3 2? Answer cubic units cubic units Slide 69 / 115 Slide 70 / 115 35 Model the rectangular prism described in the table. 36 Model the rectangular prism described in the table. What is its volume? What is its volume? length (l) width (w) height (h) number of cubes 6 3 2? Answer length (l) width (w) height (h) number of cubes 4 2 3? Answer cubic units cubic units Slide 71 / 115 Slide 72 / 115 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 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? 4 1 3 2 4 3 3 3 3 Answer
Slide 73 / 115 Slide 74 / 115 38 Which set of dimensions has the same volume as the first row? 39 Which set of dimensions has the same volume as the first row? A B length (l) width (w) height (h) number of cubes 6 4 2? 2 9 1 2 5 6 Answer A B length (l) width (w) height (h) number of cubes 7 1 2? 8 1 1 2 7 1 Answer C 2 4 6 C 6 2 2 Slide 75 / 115 Slide 76 / 115 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. 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 If you know the area of the base, Slide 77 / 115 Slide 78 / 115 41 What is the area of the base of this rectangular prism? l = 5 units w = 2 units area = lw = 5(2) = 10 h = 4 in. and that it is 2 layers high, h = 2 units l = 8 in. w = 3 in. then... volume = area of the base times height = B x h = 10(2) = 20 cubic units square inches
Slide 79 / 115 Slide 80 / 115 42 What is the volume of this rectangular prism? 43 What is the area of the base of this rectangular prism? h = 4 in. h = 50 ft. l = 8 in. w = 3 in. w = 20 ft. l = 30 ft. cubic inches square feet Slide 81 / 115 Slide 82 / 115 44 What is the volume of this rectangular prism? 45 What is the area of the base of this rectangular prism (cube)? w = 20 ft. l = 30 ft. h = 50 ft. w = 5 cm. h = 5 cm. l = 5 cm. cubic feet square centimeters Slide 83 / 115 46 What is the volume of this rectangular prism (cube)? Slide 84 / 115 To find the volume of a right rectangular prism - the length, width and height can all be multiplied together. h = 5 cm. h = 3 inches w = 5 cm. l = 5 cm. cubic centimeters 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
Formula 1 Slide 85 / 115 Volume Formulas 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. Click for source. Slide 86 / 115 (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 3 6 + 6 + 6 + 6 + 6 = 30 units 3 Slide 87 / 115 Slide 88 / 115 47 Find the volume. cm 3 48 Find the volume. cm 3 9 cm 8 cm 5 cm 2 cm 5 cm 12 cm Slide 89 / 115 49 Find the volume. ft 3 Slide 90 / 115 50 Find the volume of a rectangular prism with the following dimensions: l = 8 in, w = 10 in, h = 4 in 80 ft 70 ft 40 ft in 3
Slide 91 / 115 51 Find the volume of a rectangular prism with the following dimensions: l = 11 cm, w = 8 cm, h = 3 cm Slide 92 / 115 52 Find the volume of a rectangular prism with the following dimensions: l = 5 ft, w = 6 ft, h = 8 ft cm 3 cubic feet Slide 93 / 115 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 Slide 94 / 115 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 Slide 95 / 115 Slide 96 / 115 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 Volume Problem Solving Return to Table of Contents
Slide 97 / 115 Volume Problem Solving A 3-D object can be decomposed (broken) into rectangular prisms to find the volume of the whole object. Slide 98 / 115 56 What is the volume of this 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 cubic units Slide 99 / 115 Slide 100 / 115 57 What is the volume of this object? 58 What is the volume of this object? cubic units cubic units Slide 101 / 115 Slide 102 / 115 59 What is the volume of this object? 60 What is the volume of concrete needed to build the steps shown in this diagram? cubic feet click for source cubic units
Slide 103 / 115 Slide 104 / 115 61 What is the volume of concrete needed to build the steps shown in this diagram? 3 cm 8 cm cubic cm 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? 2 cm 9 cm 3 cm Slide 105 / 115 Slide 106 / 115 63 How much water is needed to fill a pool that is 50 meters long, 30 meters wide and 4 meters deep? 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? Slide 107 / 115 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? Slide 108 / 115 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? HINT: You may want to draw a picture!
Slide 109 / 115 Slide 110 / 115 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? 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 Slide 111 / 115 Slide 112 / 115 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? 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 #20 Slide 113 / 115 From PARCC EOY sample test #31 Slide 114 / 115 71 There are two tanks at the aquarium. Tank A and Tank B. Each tank has two sections. 72 What is the volume of the rectangular prism in cubic units? 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 From PARCC PBA sample test #1
Slide 115 / 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