SLIDE 1 Slide 1 / 115 Slide 2 / 115
5th Grade
Measurement & Data
2015-11-23 www.njctl.org
Slide 3 / 115
click on the topic to go to that section
Table of Contents
· Unit Cubes · Volume of a Solid with Unit Cubes · Volume Problem Solving · Standard Measurement Conversions · Metric Measurement Conversions
Slide 4 / 115
Standard Measurement Conversions
Return to Table
Slide 5 / 115
Students will need access to a conversion chart for the next two sections.
Conversion Chart Slide 6 / 115
SLIDE 2 Slide 7 / 115
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? 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. 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?
Standard Measurement Slide 8 / 115
1 pint 1 cup 1 cup
+ =
There are 2 cups in every pint.
Cups and Pints Slide 9 / 115
3 pints
1 pint 1 cup 1 cup
+ =
1 pint 1 cup 1 cup
+ =
1 pint 1 cup 1 cup
+ = So how many cups are there in 3 pints? 2 cups x 3 pints = 6 cups in 3 pints
Cups and Pints Slide 10 / 115
When converting measurements, use your arms to help you. We can spread our arms
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.
Converting Measurement Slide 11 / 115
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
_____ (# of inches in a foot)
=
___ ft ___ in
Conversions Slide 12 / 115
I bought a set of 4 glasses from the market. A glass weighs 8
- unces. How many pounds does the set weigh?
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 Another example: Find the total ounces: ___ oz x __ glasses = ___ oz.
Conversions
SLIDE 3
Slide 13 / 115
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.
Fractional Measurements Slide 14 / 115 Standard Conversions Match-Up Slide 15 / 115
1 12 yards = ______ ft
Slide 16 / 115
2 95 ft = ______ yds
Slide 17 / 115
3 18 cups = _____ pints
Slide 18 / 115
4 6 gal = ______ pts
SLIDE 4
Slide 19 / 115
5 1.5 tons = ______ lbs
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 B 1760 C 17.6
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?
SLIDE 5 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?
From PARCC EOY sample test #5
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
Metric Measurement Conversions
Return to Table
Slide 28 / 115 Slide 29 / 115
- 1. Work with a partner. Measure the length in cm of ten Base 10
logs placed end to end.
Comparing Units of Metric Measure
- 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.
Slide 30 / 115
Number of Base 10 Logs m cm mm 10
Comparing Units of Metric Measure
SLIDE 6 Slide 31 / 115
Number of Base 10 Logs m cm mm 10 Describe any patterns you see.
Comparing Units of Metric Measure Slide 32 / 115
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 ______.
Comparing Units of Metric Measure Slide 33 / 115
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 ______.
Slide 34 / 115
A gram is a base unit. To convert a gram to a milligram, hop down ___ steps.
________ by ________.
(multiply/divide)
Comparing Units of Metric Measure Slide 35 / 115
Think about this: A paperclip weighs
So, imagine what could weigh one milligram.
Comparing Units of Metric Measure Slide 36 / 115
Metric Conversion Match-Up
SLIDE 7
Slide 37 / 115
13 .08 ml = _____ L
Slide 38 / 115
14 1,235,000 mm = _____ km
Slide 39 / 115
15 .053 kg = ____ mg
Slide 40 / 115
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? Yes No
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?
SLIDE 8 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?
Slide 46 / 115
22 7 km 20 m = _______ m
Slide 47 / 115
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
Slide 48 / 115
Unit Cubes
Return to Table
SLIDE 9 Slide 49 / 115
Unit Cubes help us to measure volumes. There are: cubic centimeters cubic inches cubic feet
Unit Cubes 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
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
Slide 52 / 115
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
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
Slide 54 / 115
Volume of a Solid with Unit Cubes
Return to Table
SLIDE 10 Slide 55 / 115
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?
Blocks Problem
Volume of a Solid with Unit Cubes Slide 56 / 115
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. length width height
Volume of a Solid with Unit Cubes Slide 57 / 115
The 3-D shape also has a base. base
Volume of a Solid with Unit Cubes Slide 58 / 115
All of these 3-D shapes are right rectangular prisms.
Volume of a Solid with Unit Cubes Slide 59 / 115
List some 3-D shapes that are right rectangular prisms in the classroom:
Volume of a Solid with Unit Cubes Slide 60 / 115
28 Is this shape a right rectangular prism? Yes No
SLIDE 11 Slide 61 / 115
29 Is this shape a right rectangular prism? Yes No
Slide 62 / 115
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
Slide 64 / 115
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
Volume of a Solid with Unit Cubes 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 Now use unit cubes to build 4 other rectangular prisms. Fill in the length, width, height and number of cubes in the table.
Volume of a Solid with Unit Cubes 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 ?
_____ cubic units
Answer
SLIDE 12
Slide 67 / 115
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
Answer
Slide 68 / 115
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
Answer
Slide 69 / 115
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
Answer
Slide 70 / 115
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
Answer
Slide 71 / 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
Volume of a Solid with Unit Cubes Slide 72 / 115
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 13
Slide 73 / 115
38 Which set of dimensions has the same volume as the first row? A B C
length (l) width (w) height (h) number of cubes 6 4 2 ? 2 9 1 2 5 6 2 4 6 Answer
Slide 74 / 115
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 ? 8 1 1 2 7 1 6 2 2 Answer
Slide 75 / 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.
Volume of a Solid with Unit Cubes Slide 76 / 115
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
Slide 77 / 115
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
Volume of a Solid with Unit Cubes Slide 78 / 115
41 What is the area of the base of this rectangular prism? l = 8 in. w = 3 in. h = 4 in. _________ square inches
SLIDE 14
Slide 79 / 115
42 What is the volume of this rectangular prism? l = 8 in. w = 3 in. h = 4 in. _________ cubic inches
Slide 80 / 115
43 What is the area of the base of this rectangular prism? l = 30 ft. w = 20 ft. h = 50 ft. _________ square feet
Slide 81 / 115
44 What is the volume of this rectangular prism? l = 30 ft. w = 20 ft. h = 50 ft. _________ cubic feet
Slide 82 / 115
45 What is the area of the base of this rectangular prism (cube)? l = 5 cm. w = 5 cm. h = 5 cm. _________ square centimeters
Slide 83 / 115
46 What is the volume of this rectangular prism (cube)? l = 5 cm. w = 5 cm. h = 5 cm. _________ cubic centimeters
Slide 84 / 115
To find the volume of a right rectangular prism - the length, width and height can all be multiplied together. l = 7 inches h = 3 inches w = 4 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 in3
Volume of a Solid with Unit Cubes
SLIDE 15 Slide 85 / 115
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.
Volume of a Solid with Unit Cubes Slide 86 / 115
Click for source.
(3 x 2) represents the 1st layer 5 layers high Three ways to solve: (3 x 2) x 5 = 30 units3 (3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) = 30 units3 6 + 6 + 6 + 6 + 6 = 30 units3
Volume of a Solid with Unit Cubes Slide 87 / 115
47 Find the volume. ________ cm3 5 cm 8 cm 2 cm
Slide 88 / 115
48 Find the volume. _________ cm 3 5 cm 9 cm 12 cm
Slide 89 / 115
49 Find the volume. __________ ft 3 40 ft 70 ft 80 ft
Slide 90 / 115
50 Find the volume of a rectangular prism with the following dimensions: l = 8 in, w = 10 in, h = 4 in __________ in 3
SLIDE 16 Slide 91 / 115
51 Find the volume of a rectangular prism with the following dimensions: l = 11 cm, w = 8 cm, h = 3 cm __________ cm 3
Slide 92 / 115
52 Find the volume of a rectangular prism with the following dimensions: l = 5 ft, w = 6 ft, h = 8 ft __________ 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
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
Slide 96 / 115
Volume Problem Solving
Return to Table
SLIDE 17 Slide 97 / 115
A 3-D object can be decomposed (broken) into rectangular prisms to find the volume of the whole object. can be broken into these two figures this figure V = 3 cm3 V = 2 cm3 total volume = 5 cm3
click for source
Volume Problem Solving Slide 98 / 115
56 What is the volume of this object? __________ cubic units
+
=
Slide 99 / 115
57 What is the volume of this object? __________ cubic units
Slide 100 / 115
58 What is the volume of this object? __________ cubic units
Slide 101 / 115
59 What is the volume of this object? __________ cubic units
Slide 102 / 115
60 What is the volume of concrete needed to build the steps shown in this diagram?
click for source
_________ cubic feet
SLIDE 18 Slide 103 / 115
61 What is the volume of concrete needed to build the steps shown in this diagram? _________ cubic cm 9 cm 3 cm 2 cm 8 cm 3 cm
Slide 104 / 115
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?
Slide 105 / 115
63 How much water is needed to fill a pool that is 50 meters long, 30 meters wide and 4 meters deep?
Slide 106 / 115
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
- n 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!
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?
SLIDE 19 Slide 109 / 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?
Slide 110 / 115
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
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
Slide 112 / 115
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?
From PARCC EOY sample test #31
A 4 B 72 C 120 D 2,304
Slide 113 / 115
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
Slide 114 / 115
72 What is the volume of the rectangular prism in cubic units?
From PARCC PBA sample test #1
SLIDE 20 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
