Slide 1 / 115 5th Grade Measurement & Data 2015-11-23 www.njctl.org Slide 2 / 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 3 / 115
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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
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1 pint1 cup 1 cup
+ =
There are 2 cups in every pint.
Cups and Pints
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3 pints
1 pint1 cup 1 cup
+ =
1 pint1 cup 1 cup
+ =
1 pint1 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
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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.
Converting Measurement
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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
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I bought a set of 4 glasses from the market. A glass weighs 8 ounces. 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
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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
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Standard Conversions Match-Up
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1 12 yards = ______ ft
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1 12 yards = ______ ft
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3 ft
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2 95 ft = ______ yds
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2 95 ft = ______ yds
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31 yds 2 ft
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3 18 cups = _____ pints
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3 18 cups = _____ pints
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9 pints
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4 6 gal = ______ pts
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4 6 gal = ______ pts
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48 pts
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5 1.5 tons = ______ lbs
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5 1.5 tons = ______ lbs
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3000 lbs
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6 This morning, Tom ran 1.5 miles. How many feet did Tom run?
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6 This morning, Tom ran 1.5 miles. How many feet did Tom run?
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7920 ft
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7 If Tom ran 1.5 miles, how many inches did he run?
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7 If Tom ran 1.5 miles, how many inches did he run?
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95,040 in
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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?
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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?
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6 rolls
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9 Approximately how many 100-yd football fields are there in a mile?
A 5,280
B 1760
C 17.6
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9 Approximately how many 100-yd football fields are there in a mile?
A 5,280
B 1760
C 17.6
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C
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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?
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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?
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6 oz
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11 Tom has a water tank that holds 5 gallons of water.
Part ATom 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
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11 Tom has a water tank that holds 5 gallons of water.
Part ATom 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?
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.
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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.
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Teac
her N
otes Materials for each group:
· Ten base 10 logs· Ruler with cm and mm
measures· meter ruler
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Number of
Base 10 Logs
m cm mm
10
Comparing Units of Metric Measure
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Number of
Base 10 Logs
m cm mm
10
Describe any patterns you see.
Comparing Units of Metric Measure
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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
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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 ______.
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A gram is a base unit.
To convert a gram to a
milligram, hop down ___ steps.
or
________ by ________.
(multiply/divide)
Comparing Units of Metric Measure
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Think about this:
A paperclip weighs
one gram.
So, imagine what could weigh one milligram.
Comparing Units of Metric Measure
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Metric Conversion Match-Up
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13 .08 ml = _____ L
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13 .08 ml = _____ L
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80 L
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14 1,235,000 mm = _____ km
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14 1,235,000 mm = _____ km
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1,235 km
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15 .053 kg = ____ mg
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15 .053 kg = ____ mg
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53,000 mg
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16 Each morning Paul rides 500 m on an exercise bike. How many kilometers does he ride in one week?
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16 Each morning Paul rides 500 m on an exercise bike. How many kilometers does he ride in one week?
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3.5 km
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17 A kitten weighs 500 g. A puppy weighs 2 kg. Freddy says that the puppy weighs more. Is Freddy correct?
Yes
No
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17 A kitten weighs 500 g. A puppy weighs 2 kg. Freddy says that the puppy weighs more. Is Freddy correct?
Yes
No
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Yes
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18 I make 2.5 kg of popcorn, and I eat 450 g of it while watching a movie. How much popcorn is left?
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18 I make 2.5 kg of popcorn, and I eat 450 g of it while watching a movie. How much popcorn is left?
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2.05 kg
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19 How many 200 ml paper cups can be filled from a 2 liter jug of lemonade?
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19 How many 200 ml paper cups can be filled from a 2 liter jug of lemonade?
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10
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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
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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
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Ans
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A
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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?
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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?
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16
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22 7 km 20 m = _______ m
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22 7 km 20 m = _______ m
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7020 m
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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
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23 Complete each conversion by dragging and dropping the correct number into each box.
There are: cubic centimeterscubic inchescubic feet
Unit Cubes
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Unit Cubes help us to measure volumes.
There are: cubic centimeterscubic inchescubic feet
Unit Cubes
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Teac
her N
otes
Have inch cubes and centimeter cubes available for students to
compare. Model what a cubic foot would look like.
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24 What would be the best unit to measure the volume of a cereal box?
A cubic feetB cubic metersC cubic centimetersD cubic miles
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24 What would be the best unit to measure the volume of a cereal box?
A cubic feetB cubic metersC cubic centimetersD cubic miles
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C
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25 What would be the best unit to measure the volume of a classroom?
A cubic milesB cubic centimetersC cubic inchesD cubic meters
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25 What would be the best unit to measure the volume of a classroom?
A cubic milesB cubic centimetersC cubic inchesD cubic meters
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D
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26 What would be the best unit to measure the volume of a desk drawer?
A cubic yardsB cubic inchesC cubic metersD cubic millimeters
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26 What would be the best unit to measure the volume of a desk drawer?
A cubic yardsB cubic inchesC cubic metersD cubic millimeters
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B
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27 What would be the best unit to measure the volume of a soccer ball?
A cubic millimetersB cubic centimetersC cubic metersD cubic kilometers
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27 What would be the best unit to measure the volume of a soccer ball?
A cubic millimetersB cubic centimetersC cubic metersD cubic kilometers
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B
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Volume of a Solid with Unit Cubes
Return to Table of Contents
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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?
61 What is the volume of concrete needed to build the steps shown in this diagram?
_________ cubic cm
9 cm3 cm2 cm
8 cm
3 cm
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61 What is the volume of concrete needed to build the steps shown in this diagram?
_________ cubic cm
9 cm3 cm2 cm
8 cm
3 cm
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81 cm3
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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?
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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?
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32 ft3
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63 How much water is needed to fill a pool that is 50 meters long, 30 meters wide and 4 meters deep?
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63 How much water is needed to fill a pool that is 50 meters long, 30 meters wide and 4 meters deep?
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6000
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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?
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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?
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8,640 in3
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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!
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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!
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840 u3
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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?
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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?
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480 in3
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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?
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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?
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60 m3
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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?
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
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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
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Ans
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Sample Student Response:
The volume of the prism is 60 cubic units because 4 x 5 x 3 = 60.
The dimensions of a new right rectangular prism that has 20 fewer unit cubes than the original prism could be 4 units wide by 5 units tall by 2 units deep. I determined these dimensions by recognizing that each layer of the original prism that is 4 units wide by 5 units tall by 1 unit deep has a volume of 20 cubic layers. So I took one of these layers away from the original prism.