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5th Grade

Measurement & Data

2015-11-23

www.njctl.org

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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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page1svg

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

[This object is a pull tab]

Ans

wer

3 ft

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2 95 ft = ______ yds

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2 95 ft = ______ yds


Ans

wer

31 yds 2 ft


3 18 cups = _____ pints

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3 18 cups = _____ pints


Ans

wer

9 pints


4 6 gal = ______ pts

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4 6 gal = ______ pts


Ans

wer

48 pts


5 1.5 tons = ______ lbs

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5 1.5 tons = ______ lbs


Ans

wer

3000 lbs


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?


Ans

wer

7920 ft


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?


Ans

wer

95,040 in


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?


Ans

wer

6 rolls


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


Ans

wer

C


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?


Ans

wer

6 oz


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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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?



Ans

wer

480 ounces


http://practice.parcc.testnav.com/#



Part BTom drinks 4 pints of water a day.How many full tanks of water will he drink in 30 days?


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Part BTom drinks 4 pints of water a day.How many full tanks of water will he drink in 30 days?



Ans

wer

3


Metric Measurement Conversions


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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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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.


Teac

her N

otes Materials for each group:

· Ten base 10 logs· Ruler with cm and mm

measures· meter ruler


Number of

Base 10 Logs

m cm mm

10


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Number of

Base 10 Logs

m cm mm

10

Describe any patterns you see.


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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 ______.


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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)


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Think about this:

A paperclip weighs

one gram.

So, imagine what could weigh one milligram.


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Metric Conversion Match-Up

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13 .08 ml = _____ L

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13 .08 ml = _____ L


Ans

wer

80 L


14 1,235,000 mm = _____ km

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14 1,235,000 mm = _____ km


Ans

wer

1,235 km


15 .053 kg = ____ mg

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15 .053 kg = ____ mg


Ans

wer

53,000 mg


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?


Ans

wer

3.5 km


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


Ans

wer

Yes


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?


Ans

wer

2.05 kg


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?


Ans

wer

10


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

D $5,000[This object is a pull tab]

Ans

wer

A


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?


Ans

wer

16


22 7 km 20 m = _______ m

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22 7 km 20 m = _______ m


Ans

wer

7020 m


23 Complete each conversion by dragging and dropping the correct number into each box.

7 mm = cm

7 cm = m

m = 7 mk


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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



Ans

wer


Unit Cubes


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page1svg

Unit Cubes help us to measure volumes.

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


Teac

her N

otes

Have inch cubes and centimeter cubes available for students to

compare. Model what a cubic foot would look like.


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


Ans

wer

C


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


Ans

wer

D


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


Ans

wer

B


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


Ans

wer

B


Volume of a Solid with Unit Cubes


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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


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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

widthheight


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The 3-D shape also has a base.

base


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All of these 3-D shapes are right rectangular prisms.


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List some 3-D shapes that are right rectangular prisms in the classroom:


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28 Is this shape a right rectangular prism?

YesNo

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YesNo


Ans

wer

Yes



YesNo

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YesNo


Ans

wer

No



YesNo

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YesNo


Ans

wer

Yes


31 Which of the following would not be used to describe a right rectangular prism?

A lengthB heightC perimeterD width

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31 Which of the following would not be used to describe a right rectangular prism?

A lengthB heightC perimeterD width


Ans

wer

C


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

- Units3 or cubic units


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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.


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32 Model the rectangular prism described in the table.

What is its volume?


2 1 4 ?

_____ cubic units

Ans

wer

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What is its volume?


6 2 3 ?

_____ cubic units

Ans

wer

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What is its volume?


4 3 2 ?

_____ cubic units

Ans

wer

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What is its volume?


6 3 2 ?

_____ cubic units

Ans

wer

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What is its volume?


4 2 3 ?

_____ cubic units

Ans

wer

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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


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37 Which set of dimensions has the same volume as the first row?

ABC


4 2 3 ?

4 1 32 4 33 3 3

Ans

wer

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ABC


6 4 2 ?

2 9 12 5 62 4 6

Ans

wer

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ABC


7 1 2 ?

8 1 12 7 16 2 2

Ans

wer

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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.


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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

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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


Ans

wer

C


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


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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

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l = 8 in.w = 3 in.

h = 4 in.

_________ square inches


Ans

wer

24 square inches


42 What is the volume of this rectangular prism?

l = 8 in.w = 3 in.

h = 4 in.

_________ cubic inches

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l = 8 in.w = 3 in.

h = 4 in.

_________ cubic inches


Ans

wer

96 cubic inches



l = 30 ft.w = 20 ft.

h = 50 ft.

_________ square feet

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l = 30 ft.w = 20 ft.

h = 50 ft.

_________ square feet


Ans

wer

600 square feet



l = 30 ft.w = 20 ft.

h = 50 ft.

_________ cubic feet

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l = 30 ft.w = 20 ft.

h = 50 ft.



Ans

wer

30,000 cubic feet


45 What is the area of the base of this rectangular prism (cube)?

l = 5 cm.w = 5 cm.

h = 5 cm.

_________ square centimeters

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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


Ans

wer

25 square centimeters


46 What is the volume of this rectangular prism (cube)?

l = 5 cm.w = 5 cm.

h = 5 cm.

_________ cubic 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


Ans

wer

125 cubic centimeters


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


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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.


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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


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http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf


47 Find the volume. ________ cm3

5 cm

8 cm

2 cm

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47 Find the volume. ________ cm3

5 cm

8 cm

2 cm [This object is a pull tab]

Ans

wer

Volume:2

x510 (Area of Base)x8 (Height)80 m3

Volume:

V= B x h

V= l x w x h

V= 5 x 2 x 8

V= 10 x 8

V= 80 m3


48 Find the volume. _________ cm 3

5 cm

9 cm

12 cm

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48 Find the volume. _________ cm 3

5 cm

9 cm

12 cm [This object is a pull tab]

Ans

wer

540 cm3


49 Find the volume. __________ ft 3

40 ft

70 ft

80 ft

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49 Find the volume. __________ ft 3

40 ft

70 ft

80 ft[This object is a pull tab]

Ans

wer

224,000 ft3


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

__________ in 3

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

__________ in 3


Ans

wer

320 in3


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

__________ cm 3

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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

[This object is a pull tab]A

nsw

er

264 cm3


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

__________ cubic feet

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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


Ans

wer

240 cubic feet


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

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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


Ans

wer

C


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

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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


Ans

wer

D


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

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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


Ans

wer

B


Volume Problem Solving


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A 3-D 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

+ =

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page1svg




+ =


Ans

wer

11 cubic units




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__________ cubic units[This object is a pull tab]

Ans

wer

10 cubic units




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__________ cubic units[This object is a pull tab]

Ans

wer

28 cubic units




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Ans

wer

21 cubic units


60 What is the volume of concrete needed to build the steps shown in this diagram?

click for source


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click for source



Ans

wer

22.5 ft3







_________ cubic cm

9 cm3 cm2 cm

8 cm

3 cm

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_________ cubic cm

9 cm3 cm2 cm

8 cm

3 cm


Ans

wer

81 cm3


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?


Ans

wer

32 ft3


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?


Ans

wer

6000


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?


Ans

wer

8,640 in3


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!


Ans

wer

840 u3


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?


Ans

wer

480 in3


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?


Ans

wer

60 m3


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?


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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?



Ans

wer

30 units3


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?


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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?



Ans

wer

5120 cm3





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

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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


Ans

wer

C



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?


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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?



Ans

wer

75 cubic feet


72 What is the volume of the rectangular prism in cubic units?

From PARCC PBA sample test #1

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72 What is the volume of the rectangular prism in cubic units?



Ans

wer

60 cubic units





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.


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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.



Ans

wer

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.




5th grade - njctlcontent.njctl.org/courses/math/5th-grade-math/...2015/11/23 · 5th grade...

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