5th grade - njctl
TRANSCRIPT
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5th Grade Measurement & Data
20151123
www.njctl.org
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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
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StandardMeasurement Conversions
Return to Table of Contents
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Students will need access to a conversion
chart for the next two sections.
Conversion Chart
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US Measurement
(Standard or Customary System)
ounces
pounds
tons
ounce
cup
pint
quart
gallon
inches
feet
yards
miles
Weight Volume/Capacity Length
Standard Measurement
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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 MatchUp
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1 12 yards = ______ ft
Answer
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2 95 ft = ______ yds
Answer
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3 18 cups = _____ pints
Answer
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4 6 gal = ______ pts
Answer
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5 1.5 tons = ______ lbs
Answer
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6 This morning, Tom ran 1.5 miles. How many feet did Tom run?
Answer
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7 If Tom ran 1.5 miles, how many inches did he run?
Answer
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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?
Answer
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9 Approximately how many 100yd football fields are there in a mile?
A 5,280
B 1760
C 17.6
Answer
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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?
Answer
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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
Answer
480 ounces
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12 Tom has a water tank that holds 5 gallons of water.
Part BTom 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
Answer
3
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Metric Measurement Conversions
Return to Table of Contents
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Metric Measurement
grams liters meters
Mass/Weight Capacity/Volume Length
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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.
Teacher N
otes
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Number of Base 10 Logs
m cm mm
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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 MatchUp
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13 .08 ml = _____ L
Answer
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14 1,235,000 mm = _____ km
Answer
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15 .053 kg = ____ mg
Answer
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16 Each morning Paul rides 500 m on an exercise bike. How many kilometers does he ride in one week?
Answer
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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
Answer
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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?
Answer
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19 How many 200 ml paper cups can be filled from a 2 liter jug of lemonade?
Answer
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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
Answer
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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?
Answer
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22 7 km 20 m = _______ m
Answer
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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
Answer
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Unit Cubes
Return to Table of Contents
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Unit Cubes help us to measure volumes.
There are: cubic centimeterscubic inchescubic feet
Unit Cubes
Teacher 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 A
nswer
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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
Answer
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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 A
nswer
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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 A
nswer
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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?
Blocks Problem
Volume of a Solid with Unit Cubes
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The total number of blocks used is the volume of the box.
This box is called a 3 Dimensional Figure (3D).
A 3D figure has a length, width and a height.
length
widthheight
Volume of a Solid with Unit Cubes
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The 3D shape also has a base.
base
Volume of a Solid with Unit Cubes
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All of these 3D shapes are right rectangular prisms.
Volume of a Solid with Unit Cubes
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List some 3D shapes that are right rectangular prisms in the classroom:
Volume of a Solid with Unit Cubes
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28 Is this shape a right rectangular prism?
Yes
No
Answer
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29 Is this shape a right rectangular prism?
Yes
No
Answer
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30 Is this shape a right rectangular prism?
Yes
No
Answer
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31 Which of the following would not be used to describe a right rectangular prism?
A lengthB heightC perimeterD width
Answer
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Volume
The amount of space occupied by or inside a 3D Figure The number of cubic units needed to FILL a 3D Figure (layering)
Label
Units3 or cubic units
Volume of a Solid with Unit Cubes
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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.
Volume of a Solid with Unit Cubes
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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
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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
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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
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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
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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
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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
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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 32 4 33 3 3
Answer
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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 12 5 62 4 6
Answer
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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 12 7 16 2 2
Answer
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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
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40 The number of unit cubes that it takes to cover the base is also the _______ of the base.
A perimeterB volumeC areaD cubic units
Answer
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If you know the area of the base,
l = 5 unitsw = 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
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41 What is the area of the base of this rectangular prism?
l = 8 in.w = 3 in.
h = 4 in.
_________ square inches
Answer
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42 What is the volume of this rectangular prism?
l = 8 in.w = 3 in.
h = 4 in.
_________ cubic inches
Answer
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43 What is the area of the base of this rectangular prism?
l = 30 ft.w = 20 ft.
h = 50 ft.
_________ square feet
Answer
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44 What is the volume of this rectangular prism?
l = 30 ft.w = 20 ft.
h = 50 ft.
_________ cubic feet
Answer
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45 What is the area of the base of this rectangular prism (cube)?
l = 5 cm.w = 5 cm.
h = 5 cm.
_________ square centimeters
Answer
25 square centimeters
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46 What is the volume of this rectangular prism (cube)?
l = 5 cm.w = 5 cm.
h = 5 cm.
_________ cubic centimeters
Answer
125 cubic centimeters
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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 hV = (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
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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
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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
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47 Find the volume. ________ cm3
5 cm
8 cm
2 cm
Answer
Volume:
x510 (Area of Base)x8 (Height)80 m3
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48 Find the volume. _________ cm 3
5 cm
9 cm
12 cm
Answer
89
49 Find the volume. __________ ft 3
40 ft
70 ft
80 ft
Answer
90
50 Find the volume of a rectangular prism with the following dimensions:l = 8 in, w = 10 in, h = 4 in
__________ in 3
Answer
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51 Find the volume of a rectangular prism with the following dimensions:l = 11 cm, w = 8 cm, h = 3 cm
__________ cm 3
Answer
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52 Find the volume of a rectangular prism with the following dimensions:l = 5 ft, w = 6 ft, h = 8 ft
__________ cubic feet Answer
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53 Which is a possible length, width and height for a rectangular prism whose volume = 18 units 3
A 1 x 2 x 18B 6 x 3 x 3C 2 x 3 x 3D 3 x 3 x 3
Answer
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54 Which is a possible length, width and height for a rectangular prism whose volume = 40 units 3
A 8 x 2 x 3B 5 x 8 x 2C 6 x 1 x 5D 2 x 5 x 4 A
nswer
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55 Which is a possible length, width and height for a rectangular prism whose volume = 36 units 3
A 9 x 4 x 2B 3 x 4 x 3C 1 x 4 x 8D 2 x 3 x 4 A
nswer
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Volume Problem Solving
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A 3D object can be decomposed (broken) into rectangular prisms to find the volume of the whole object.
can be broken intothese two figures
this figure
V = 3 cm3 V = 2 cm3
total volume = 5 cm3
click for source
Volume Problem Solving
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56 What is the volume of this object?
__________ cubic units
+ =
Answer
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57 What is the volume of this object?
__________ cubic units
Answer
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58 What is the volume of this object?
__________ cubic units
Answer
101
59 What is the volume of this object?
__________ cubic units
Answer
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60 What is the volume of concrete needed to build the steps shown in this diagram?
click for source
_________ cubic feet
Answer
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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 cm3 cm
Answer
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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?
Answer
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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?
Answer
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64 A path is 120 inches long and 24 inches wide. How much gravel is needed to put a threeinch layer of gravel over the whole path?
Answer
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65 A boxshaped 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!
Answer
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?
Answer
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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?
Answer
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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?
From PARCC EOY sample test #10
Answer
30 units3
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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
Answer
5120 cm3
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70 There are two tanks at the aquarium. Tank A and Tank B. Each tank has two sections.
Part AThe 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
Answer
C
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71 There are two tanks at the aquarium. Tank A and Tank B. Each tank has two sections.
Part BTank 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
Answer
75 cubic feet
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72 What is the volume of the rectangular prism in cubic units?
From PARCC PBA sample test #1
Answer
60 cubic units
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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
Answer