Measurement
SIXTH GRADE COMPACTED MATHEMATICS
CHAPTER 8
TOPICS COVERED:
 Customary Units (Mass, Capacity, Length)
 Metric Units (Mass, Capacity, Length)
 Time
STAAR GRADE 6 MATHEMATICS
REFERENCE MATERIALS
STAAR
®
State of Texas
Assessments of
Academic Readiness
Metric
Customary
1kilometer(km)=1,000meters(m)
1yard(yd)=3feet(ft)
1meter(m)=100centimeters(cm)
1foot(ft)=12inches(in.)
1centimeter(cm)=10millimeters(mm)
2
VOLUME AND CAPACITY
1
1mile(mi)=1,760yards(yd)
0
Inches
LENGTH
Customary
1gallon(gal)=4quarts(qt)
Metric
1liter(L)=1,000milliliters(mL)
3
1quart(qt)=2pints(pt)
1pint(pt)=2cups(c)
1cup(c)=8fluidounces(floz) Customary
4
WEIGHT AND MASS
Metric
1kilogram(kg)=1,000grams(g)
1pound(lb)=16ounces(oz)
1gram(g)=1,000milligrams(mg)
5
1ton(T)=2,000pounds(lb)
TIME
6
1year=12months
1year=52weeks
1week=7days
7
1day=24hours
1hour=60minutes
1minute=60seconds
8
20
STAAR GRADE 6 MATHEMATICS
REFERENCE MATERIALS
Square
P = 4s
Rectangle
P = 2l + 2w
17
18
19
PERIMETER
16
CIRCUMFERENCE
15
Circle
C = 2π r
or
C = πd
bh
2
or
A = 1 bh
2
14
AREA
12
Rectangle
A =
A = s2
or
A = lw
A = bh
10
Square
11
13
Triangle
Parallelogram
9
A = bh
8
Trapezoid
2
or
7
A = 1 (b1 + b2)h
2
A = πr 2
6
VOLUME
V = s3
4
5
Cube
Rectangular prism
3
2
1
(b + b )h
1
2
Circle
V = lwh
or
V = Bh
ADDITIONAL INFORMATION
Centimeters
0
A =
Pi
π ≈ 3
Activity 8-1: Measurement Comparisons
Name:
Name
Abbreviation
inch
in
foot
ft
Approximate Comparison
length of half a thumb
length of a paper clip
length of an adult male foot
yard
yd
length from nose to outstretched fingertip
mile
mi
length of 14 football fields
ounce
oz
weight of a birthday card
pound
lb
weight of three apples
quart
qt
amount in a medium container of milk
gallon
gal
amount in a small bucket
kilometer
km
meter
m
centimeter
cm
millimeter
mm
kilogram
kg
gram
g
milligram
mg
liter
L
milliliter
mL
9 football fields
a little more than half a mile
half the height of a door
a meter stick
a little bit more than 3 feet
the width of a door
length of a raisin
the width of your pinky
the width of an M&M
the width of a paper clip
width of a period at the end of a sentence
the width of a dime
the point of a pencil
mass of a cantaloupe
the mass of a few apples
the mass of a hammer
mass of a raisin
the weight of a paperclip
the weight of a Cheerio
the weight of a marshmallow
the weight of a grain of sand
the weight of a grain of rice
half of a large bottle of soda
half an eyedropper
a raindrop
Activity 8-2: Measurement Conversions
Name:
There are several different ways to convert between units of measurement. One very good way
is to use proportions.
Example
14 gallons = x qt.
Use the fact that 1 gal = 4 qt.
Example #2
14 qt. = x gal.
1 gallon x gallons

4 quart 14 quarts
1  14 4 x

4
4
3.5 gal  x
1 gallon 14 gallons

4 quart
x quarts
1  q  4  14
q  56 quarts
A conversion factor is a ratio of two equivalent measurements. Since the two measurements in a
conversion factor are equivalent, a conversion factor is equal to 1.
Example While weight lifting, John adds 11.35 kilograms to his bar. About how many pounds
does he add to his bar?
1 pound  0.454 kilograms
To complete the conversion multiply the kilograms by the conversion factor.
11.35 kg 
1 lb
 25 pounds
0.454 kg
Putting multiple conversion factors together is called dimensional analysis. This method will
better prepare you for advanced math and science classes in the future.
Example
14 gallons = x qt.
14 gallons 4 quarts

 56 quarts
1
1 gallon
Let’s say you want to convert 55 miles per hour to feet per second.
Example #2
55 miles 5280 feet 1 hour 1 min. 80.7 ft.




1 hour
1 mile
60 min. 60 sec. 1 sec.
The units cancel each other out leaving just feet per second left. This tells you that your answer
is in the correct units.
Activity 8-3: Metric Measurement
Name:
Choose an appropriate metric unit of mass for each.
1.
a grain of rice
2.
a bag of groceries
3.
a feather
4.
a cat
5.
a leaf
6.
an eraser
Choose an appropriate metric unit of capacity for each.
7.
a gasoline tank
8.
a coffee mug
9.
6 raindrops
10.
a pitcher of juice
11.
a swimming pool
12.
a can of paint
State whether each of the following is best measured in terms of mass or capacity.
13.
a bag of potatoes
14. water in a birdbath
15.
an apple
16.
a puppy
17.
a cup of hot cider
18.
the inside of the
refrigerator
19.
juice in a baby’s
bottle
20.
water in a fish tank
Write true or false.
The mass of a horse is about
21.
500 kg.
A mug holds 250 mL of hot
23.
chocolate.
25.
A teaspoon holds about 5 L.
Choose the most reasonable measurement.
About how tall would your friend be?
27.
A. 1.5 mm
B. 1,500 cm
About how wide would your desk be?
28.
A. 50 mm
B. 50 m
A tree is about how tall?
29.
A. 20 km
B. 20 m
An envelope is about how long?
30.
A. 24 cm
B. 2.4 cm
22.
Jason drank 5.8 L of juice
at breakfast.
24.
A penny is about 3 kg.
26.
A textbook is about 1 kg.
C. 1.5 km
D. 1,500 mm
C. 5 m
D. 50 cm
C. 20 cm
D. 2 km
C. 24 mm
D. 2.4 m
A beaker contains 62 milliliters of solution. When full it holds 1.5 liters. Which
expression shows how much you can still add?
31.
a. 0.0015-62 mL
b. 1500-62 mL
c. 1.5-.62 L
d. 1.5-62000L
Activity 8-4: Metric Measurement
Name:
Solve all problems with proportions and show all steps.
1. How many kilometers long was the Titanic?
2.
How many millimeters did the Titanic travel from Southampton to
Cherbourg? Write your answer in scientific notation.
3.
How many kilometers high is very large iceberg?
4.
What is the maximum height of a bergy bit in millimeters?
5.
What is the sum of the lengths of slits 2 through 5 on the Titanic in
centimeters?
6.
3.72 L =
9.
0.018 kg =
12. 0.56 kg =
mL
7.
9.75 m =
cm
g 10. 149 cm =
m
8.
6.8 g =
11. 524 cm =
kg
m
g 13. 3 mm =
cm
14. 14 L =
15. 6.7 g =
mg 16. 9.3 L =
mL
17. 0.89 m =
cm
18. 0.085 g =
mg 19. 4,600 mm =
m
20. 3.904 L =
mL
21. 205 g =
kg 22. 609 mg =
g
23. 0.0019 m =
mm
24. 38 mL =
L 25. 720 m =
26. 150 cm =
mm
km
What unit of measure would you use to measure each item?
the height of an office building
27.
A. km
B. cm
C. m
the width of a page of text
28.
A. km
B. cm
C. m
the length of an ant
29.
A. km
B. cm
C. m
the depth of a lake
30.
A. km
B. cm
C. m
31.
32.
33.
34.
D. mm
D. mm
D. mm
D. mm
Suzy wants to build a doghouse for Buster. She wants the doghouse to be 4 meters by 3
meters. When she arrives at the lumber store, the clerk tells her the lumber is measured
in centimeters. What are the dimensions for Buster’s doghouse in centimeters?
Sammy needs to replace all the strings on his kite collection. George’s Hobby Shop sells
kite string for $15.00/meter. Hobby Depot sells kite string for $13.50/50 centimeters.
Sammy needs 8 meters of kite string. How much would Sammy pay for the string at
George’s Hobby Shop? How much would Sammy pay for the string at Hobby Depot?
Sarah is trying to determine which container to use for her leftovers. She has 2 liters of
soup leftover. One of her containers can hold 1000 milliliters of a liquid and the other
container can hold 0.1 kiloliters. Which container should she use?
Brian is trying to choose the best deal. He can buy 1 liter of soda for $1.39 or he can buy
1500 milliliters of soda for $1.99. Which soda should he buy?
mL
Activity 8-5: Metric Measurement
Name:
Use a ruler to measure the following lines to the nearest centimeter and the nearest
millimeter.
1
2
3
4
5
6
7
8
9
10
11
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Which weighs more: an ounce of water or an ounce of lead?
Surprise! The water weighs more because it is measured by volume, while lead is measured by
weight. If you set a cup with a fluid ounce of water on a balance scale across from an ounce of
lead in an identical cup, the scale will tip toward the water.
Activity 8-6: Measurement Scavenger Hunt
Name:
Find three objects or activities that you estimate are close to each measurement below. Write the
names of the objects or activities next to the appropriate measure.
1.
weighs 2 pounds
2.
is 16 inches in diameter
3.
holds 2 pints when full
4.
takes 25 seconds to complete
5.
is 8 feet long
6.
requires 2 cups to fill
7.
can be recited in 12 minutes
8.
is 6 centimeters wide
9.
weighs 7 ounces
10.
is half a yard long
11.
takes 5 minutes to walk to
12.
is one meter long
13.
holds 10 gallons when full
14.
can drive to in half an hour
15.
weighs 5 grams
16.
holds 5 liters when full
17.
weighs 10 kilograms
18.
takes 5 seconds to do
Activity 8-7: Metric Treasure Hunt
Name:
To become more familiar with metric units of measurement, the class is going to take a walk
around the school. During your walk around the school find three items to fit into each category.
Choose items that best fit into the category given. For example, one could measure the distance
from DIS to EIS in millimeters, but kilometers would be a more appropriate choice.
For one of your three items in each category make an estimate of its metric measurement.
Metric Length
Item 1
Item 2
Item 3
Meters
Centimeters
Millimeters
Metric Volume/Capacity
Item 1
Item 2
Item 3
Liters
Milliliters
Metric Weight/Mass
Item 1
Kilograms
Grams
Milligrams
Item 2
Item 3
Activity 8-8: Metric Measurement
Name:
Helpful reminders:
A shovel is about a meter long. The head of a thumbtack is about a centimeter wide. The point
of a thumbtack is about a millimeter wide. The landing strip at an airport is about a kilometer
long.
The mass of a hammer is about a kilogram. The mass of a nail is about a gram. The mass of a
piece of sawdust is about a milligram.
A can of motor oil contains 1 liter. The spill of a drop of oil is about 1 milliliter.
Write the unit that you would use to measure each of the following.
1.
mass of a bicycle
2. mass of a pencil
3.
glass of juice
4.
grain of sand
5.
mass of a penny
6.
water in a swimming pool
7.
8.
mass of a bowling ball
11.
mass of a feather
hot chocolate in a large
thermos
mass of a watermelon
13.
water in an aquarium
14. mass of a car key
15.
mass of a vitamin pill
16. can of soup
17.
mass of an egg
18. mass of a cat
19.
water in a team’s cooler
20. mass of a sewing needle
21.
mass of a mosquito
22. liquid in a test tube
23.
mass of student’s desk
24. mass of a sandwich
25.
bottle of expensive perfume
27.
water in a washing machine
29.
mass of an apple
26. mass of a sugar cube
mass of a bag full of
28.
groceries
30. mass of a leaf
9.
Circle the appropriate measure.
31. mass of a screwdriver
32. mass of a tennis racket
33. mass of a baby
34. mass of a dictionary
35. mass of a grain of sand
36. paint can
37. drinking glass
38. bathtub
39. soup spoon
40. length of a roadrace
10. loaf of bread
12. cup of hot cider
46 mg
46 g
5g
50 g
75 g
7.5 kg
0.2 kg
2 kg
1 mg
1g
4L
4mL
250 L
250mL
400 mL 400 L
1.5 mL 15 mL
6m
6 km
46 kg
500 g
0.75 kg
20 kg
1 kg
Activity 8-9: Metric Measurement
Name:
Helpful reminders:
A shovel is about a meter long. The head of a thumbtack is about a centimeter wide. The point
of a thumbtack is about a millimeter wide. The landing strip at an airport is about a kilometer
long.
The mass of a hammer is about a kilogram. The mass of a nail is about a gram. The mass of a
piece of sawdust is about a milligram.
A can of motor oil contains 1 liter. The spill of a drop of oil is about 1 milliliter.
Circle the appropriate measure.
1. A pen is about 14 ____ long.
km
m
cm
mm
2.
A pencil point is a bout 1 ____ wide.
km
m
cm
mm
3.
A coffee mug is about 90 _____ tall.
km
m
cm
mm
4.
An ear of corn is about _____ long.
km
m
cm
mm
5.
Two cities could be 12 _____ apart.
km
m
cm
mm
6.
Motion picture film is 35 _____ wide.
km
m
cm
mm
7.
A discuss is thrown 56 _____.
km
m
cm
mm
8.
A person can jump 1.5 _____ high.
km
m
cm
mm
9.
A pilot flew 5,000 _____ yesterday.
km
m
cm
mm
10. A newborn baby is about 50 _____ long.
km
m
cm
mm
Activity 8-10: Measurement/Gallon Guy
1 pint
Name:
1 quart
1 quart
1 pint
1 gallon
1 pint
1 pint
1 quart
1
pint
1.
13 yd. =
4.
7.
1
pint
1 quart
1
pint
in.
2.
12 qt. =
5 c. =
fl. oz.
5.
7 c. =
pt.
10. 3 gal. =
1
pint
gal.
3.
10 c. =
pt.
16 fl. oz. =
c.
6.
12 pt. =
qt.
8.
24 pt. =
c.
9.
53 qt. =
gal.
qt.
11.
20 qt. =
gal.
12. 3.5 c. =
fl. oz.
13. 5 mi. =
ft.
14.
12 qt. =
pt.
15.
1
c. =
2
fl. oz.
16. 11 c. =
pt.
17.
6 pt. =
c.
18. 0.5 qt. =
pt.
3
The sign before a bridge says maximum weight 5 tons. Joe’s truck weighs 7,350 pounds. Can
the bridge support his weight?
Kroger is selling 16 ounces of cream cheese for $2.79. Costco is selling 4 pounds of cream
20.
cheese for $7.99. Which store has the best price on cream cheese?
Recipe: 1 quart apple juice, 2.75 cups of lemon-lime soda, 64 ounces pineapple juice, 2 quarts
21. cold water, 0.25 cups lemon juice
What is the smallest container that will hold all of this punch? 4, 5, 6, or 7 quart
22. How long will it take the students at DIS to drink 1,000,000 pints of milk?
19.
Activity 8-11: Customary Measurement
Name:
Use a ruler to measure the following lines to the nearest quarter of an inch.
1
2
3
4
5
6
7
8
9
10
11
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Activity 8-12: Measure With Pleasure
Name:
Follow the directions, measure carefully, and you will get the picture!
1
in.
2
high. Place Point A at the top left, B at the top right, C at the bottom right, and D at the
bottom left.
1
Place your ruler on AB . Measure 3 in. across from point A. Make a dot at this point
8
and label it Point E.
1
Place your ruler on BC . Measure down 1 in. from point B. Make a dot at this point
4
and label it point F.
7
On BC , measure down 5 in. from B. Label this Point G.
8
1
Point H is on BC , 7 in. from B.
2
3
Point I is on BC , 8 in. from B.
8
Point J is on AD , 7 in. from A. Connect points H and J.
1
Point K in on AD , 8 in. from A. Connect points I and K.
2
1
Point L is on JH , 3 in. from J. Draw EL .
8
7
Point M is on EL ,
in. from E. Draw GM .
8
3
Point N is on AD , 5 in. from A. Draw MN .
4
Line up your ruler on Points E and F. Mark a point 1 in. from E and label it point O.
Connect points E and O.
5
Point P is on EL , in. from E. Draw OP .
8
1
Point Q is on EL , 6 in. from E. Draw GQ .
4
5
Point R is on EL , 6 in. from E. Draw NR .
8
3
Point S is on NR , 2 in. from N. Draw MS .
4
1
Point T is on KI , 1 in. from K. Draw JT .
8
Point U is on KI , 6 in. from K. Draw HU .
Draw rectangle ABCD on another sheet of paper. The rectangle is 7 in. wide and 9
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Activity 8-13: Converting Between Systems
Name:
Length
1 in = 2.54 cm
Mass
1 oz = 28.35 g
Capacity
1 pt = 0.47 L
1 cm = 0.39 in
1 g = 0.035 oz
1 L = 2.11 pt
1 ft = 30.48 cm
1 lb = 0.45 kg
1 qt = 0.95 L
1 m = 3.28 ft
1 kg = 2.2 lb
1 L = 1.06 qt
1 mi = 1.61 km
1 gal = 3.79 L
1 km = 0.62 mi
1 L = 0.26 gal
1 m = 39.37 in
1 in = 0.0254 m
1 m = 1.09 yd
Note: Most of these conversions are approximate and not exact.
Use proportions to convert between measurement systems.
The length of the sheet of paper is 11 inches. What is the length in
1.
centimeters?
2. 6 quarts equals how many liters?
3.
255.6 grams equals how many ounces?
4.
14 feet equals how many meters?
5.
7 liters equals how many quarts?
6.
45 feet is how many meters?
7.
18 feet is how many meters?
A flower bed is 2 meters wide and 3 meters long. What is the area of
8.
the flower bed in square feet?
9. Kate ran 5 miles. How far did she run in kilometers?
Alex filled a 5-gallon jug with water. How many liters of water are in
10.
the container?
11. A ruler is 12 inches long. What is the length of the ruler in centimeters?
12. A kitten weighs 4 pounds. What is the approximate mass of the kitten?
13. 20 yards  __________ meters
14. 400 meters  __________ yards
15. 5 quarts  __________ liters
16. 137.25 meters  __________ feet
17. 10 liters  __________ gallons
18. 10,000 kilometers  __________ miles
19. 12 ounces  __________ grams
20. 60 inches  ___________ centimeters
Activity 8-14: Unfamiliar Units of Measure
1
2
3
4
5
6
7
8
27
28
29
nose
magnum
lux
volume of firewood
capacity of liquid
volume of dry items
weight of precious stones
amount of gold
electric work capability
length of cloth or paper
capacity, wet or dry
heat energy or fuel valuefood
length – land
length – land
length – horse height
area – land
volume – lumber
amount of paper
frequency –light wave
volume – ship
speed – ships and planes
length – space
capacity – liquid
capacity – liquid
weight – precious metals
speed – ships and planes
amount of paper
amount of items
capacity – computer
memory
length – horse racing
capacity – liquid
illumination
30
horsepower
work capability – engine
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
cord
hogshead
peck
carat
karat
watt
bolt
barrel
calorie
rod
furlong
hand
acre
board foot
ream
hertz
gross tonnage
Mach 1
light year
jigger
gill
Troy pound
knot
quire
gross
bit
Name:
8 ft. by 4 ft. by 4 ft. stack
63 gallons
537.61 cu. in.
one-fifth of a gram
24k = 100%
based on current, resistance
varies
31.5 gallons
energy to raise temperature
16.5 ft.
200 yd.
about 4 in
43,560 sq. ft.
1 in. by 12 in. by 12 in.
about 500 sheets
waves per second
100 cu. ft.
speed of sound
about 6 trillion miles
2 mouthfuls
one-fourth pint
12 oz.
1.852 mph
25 sheets
12 dozen
8 bits
small distance
2 quarts
light 1m from candle source
energy for one horse to life 33,000 lbs. 1
ft. in 1 min.
Activity 8-15: Converting Between Systems
____
____Name:____________________
Complete. Round to the nearest hundredth if necessary.
1. 5 in. ≈ _________ cm
9. 54 cm ≈ _____________ in.
2. 15 cm ≈ __________ in.
10. 17 mi ≈ _____________ km
3. 2 L ≈ __________ qt
11. 32gal ≈ ______________ L
4. 650 lb ≈ ___________ kg
12. 350 Ib ≈ _____________ kg
5. 4 qt ≈ __________ L
13. 19 kg ≈ ___________ lb.
6. 10 mL ≈ ___________ c
14. 3 T ≈ _____________ kg
7. 63.5 T ≈ ___________ kg
15. 6 in. ≈ ____________ cm
8. 50 mL ≈ _____________ fl oz
16. 12 in. ≈ ___________ m
17. COMPUTERS - A notebook computer has a mass of 2.25 kilograms. About how many pounds does the
notebook weigh?
18. TREES - A Cabbage Palmetto has a height of 80 feet. What is the estimated height of the tree in
meters?
19. BUIIDINGS - The Willis Tower has a height 1,451 feet. What is the estimated height of the building in
meters?
20. WATER - Which is greater, a bottle containing 64 fluid ounces of water or a bottle containing 2 liters of
water?
21. FOOD - Which box is greater, a 1.5-pound box of raisins or a 650-gram box of raisins?
22. BAKING - A bakery uses 900 grams of peaches in a cobbler. About how many pounds of peaches does
the bakery use in a cobbler?
Determine which quantity is greater.
23. 3 gal, 10 L
24. 1.4 oz, 0.4 kg
25. 4 mi, 6.2 km