1. M5.B.1 Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems and processes of measurement.
M5.B.1.2 Solve problems using simple conversions and/or add and subtract measurements.

2. M5.B.1.2 Eligible Content
M5.B Convert using linear measurements, capacity, and weight (mass) within the same system to the unit immediately above or below the given unit (using only the units below – use a conversion chart or a “hint” with problems e.g., hint: 16oz = 1lb).
• Metric using mm, cm, m and km; mL and L; g and kg
• Customary using cup, pint, quart, gallon; in, ft, yd; oz, lb
M5.B Add or subtract linear measurements, (feet and inches) or units of time (hours and minutes), without having to regroup with subtraction (answer should be in simplest form).

3. M5.B Convert using linear measurements, capacity, and weight (mass) within the same system to the unit immediately above or below the given unit (using only the units below – use a conversion chart or a “hint” with problems e.g., hint: 16oz = 1lb). • Metric using mm, cm, m and km; mL and L; g and kg • Customary using cup, pint, quart, gallon; in, ft, yd; oz, lb

4. PSSA Sample Item

5. Converting Customary Measurement Length, Capacity, and Weight

6. Customary Length 12 inches (in) = 1 foot (ft)
Copy this in your booklet page 12
12 inches (in) = 1 foot (ft)
36 inches = 3 feet or 1 yard (yd)
5,280 feet = 1 mile (mi)
To change from a larger unit of measure to a smaller unit, MULTIPLY.
To change from a smaller unit of measure to a larger unit, DIVIDE.

7. This represents about 1 mile.
Customary Length
A mile is about half the length of Talladega Super Speedway.
Talladega is 2.9 miles long.
This represents about 1 mile.
Talladega Super Speedway

8. Customary Length
A yard is about the length of a walking stick.

9. Customary Length
A foot is about the length of a floor tile.

10. Customary Length
An inch is about the length of a drink bottle top.

11. Customary Capacity 4 quarts = 1 gallon (gal) 2 pints = 1 quart (qt)
Copy this in your booklet page 12
4 quarts = 1 gallon (gal)
2 pints = 1 quart (qt)
2 cups = 1 pint (pt)
8 fluid ounces (fl oz) = 1 cup (c)
To change from a larger unit of measure to a smaller unit, MULTIPLY.
To change from a smaller unit of measure to a larger unit, DIVIDE.

12. Meet Mr. Gallon
1 gallon

13. Meet Mr. Gallon
4 quarts

14. Meet Mr. Gallon
8 pints

15. Meet Mr. Gallon
16 cups

16. Customary Weight 16 ounces (oz) = 1 pound (lb)
Copy this in your booklet page 12
16 ounces (oz) = 1 pound (lb)
2,000 pounds = 1 ton (T)
To change from a larger unit of measure to a smaller unit, MULTIPLY.
To change from a smaller unit of measure to a larger unit, DIVIDE.

17. Customary Weight
A small car weighs about a ton.

18. Customary Weight
A bag of coffee weighs about 1 pound.

19. Customary Weight
An ounce weighs the same as 8 nickels.

26. Practice

27. 1.  8 qt  =  ________ c
2.  11 qt  =  ________ fl oz
3.  108 in  =  ________ yd
4.  384 in  =  ________ ft
5.  20 lb  =  ________ oz
6.  128 pt  =  ________ gal
7.  15 yd  =  ________ ft
8.  21 gal  =  ________ qt
9.  31 lb  =  ________ oz
10.  336 oz  =  ________ lb

28. 11. 6 inches = ______foot
feet = _____yards_____feet
feet = ________inches
14.  24 qt = _______ gal
15. 8 pt = _______ qt
16.  192 oz = _______ lb
17.  4 pt = _______ qt
18.  33 ft = _______ yd
19. 1 yd = _______ in
20. 3 lb = _______ oz
21. 4 gal = _______ qt

29. Converting Metric Measurements
Metric System

30. metres grams litres Converting Units kilometres centimetres kilograms
Joanne Smithies Our Lady & St. Gerards RCP

31. We use different metric units to measure :-
Distance
Capacity
Weight
We can use our knowledge of multiplying and dividing by 10, 100 or 1000 to change or convert measurements in one unit to measurements in another unit.

32. Containers and objects come in various shapes and sizes
Containers and objects come in various shapes and sizes. How can you tell if: one container holds as much liquid as another? one object weighs the same as another? Or if they have equal measurements? It is easy if you convert the measurements.

33. Liters measure volume of a liquid substance

34. Grams measure weight

35. Meters measure distance or length

36. Metric System
The metric system is based on a base unit that corresponds to a certain kind of measurement
Length = meter
Volume = liter
Weight (Mass) = gram
Prefixes plus base units make up the metric system
Example:
Centi + meter = Centimeter
Kilo + liter = Kiloliter

37. Metric System The three prefixes that we will use the most are: kilo
centi
milli
kilo
hecto
deca
Base Units
meter
gram
liter
deci
centi
milli

38. Metric System
So if you needed to measure length you would choose meter as your base unit
Length of a tree branch
1.5 meters
Length of a room
5 meters
Length of a ball of twine stretched out
25 meters

39. Metric System
But what if you need to measure a longer distance, like from your house to school?
Let’s say you live approximately 10 miles from school
10 miles = meters
16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage:
16093 meters = kilometers (or 16.1 if rounded to 1 decimal place)

40. Metric System
These prefixes are based on powers of 10. What does this mean?
From each prefix every “step” is either:
10 times larger or
10 times smaller
For example
Centimeters are 10 times larger than millimeters
1 centimeter = 10 millimeters
kilo
hecto
deca
Base Units
meter
gram
liter
deci
centi
milli

41. Metric System
Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length
1 centimeter = 10 millimeters
Example not to scale 40 41
1 mm 40 41
1 cm

42. Metric System For each “step” to right, you are multiplying by 10
For example, let’s go from a base unit to centi
1 liter = 10 deciliters = 100 centiliters
2 grams = 20 decigrams = 200 centigrams
( 1 x 10 = 10) = (10 x 10 = 100)
(2 x 10 = 20) = (20 x 10 = 200)
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

43. Metric System
An easy way to move within the metric system is by moving the decimal point one place for each “step” desired
Example: change meters to centimeters
1 meter = 10 decimeters = 100 centimeters or
1.00 meter = 10.0 decimeters = 100. centimeters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

44. Metric System
Now let’s try our previous example from meters to kilometers:
16093 meters = decameters = hectometers = kilometers
So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left (the same direction as in the diagram below)
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

45. Metric System
If you move to the left in the diagram, move the decimal to the left
If you move to the right in the diagram, move the decimal to the right
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

46. Metric System
Now let’s start from centimeters and convert to kilometers
centimeters = 4 kilometers
centimeters = kilometers
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

47. Metric System Now let’s start from meters and convert to kilometers
4000 meters = 4 kilometers
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Now let’s start from centimeters and convert to meters
4000 centimeters = 40 meters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

48. Metric System Now let’s start from meters and convert to centimeters
5 meters = 500 centimeters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Now let’s start from kilometers and convert to meters
.3 kilometers = 300 meters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

49. Metric System
Now let’s start from kilometers and convert to millimeters
4 kilometers = millimeters or
4 kilometers = 40 hectometers = 400 decameters
= 4000 meters = decimeters
= centimeters = millimeters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli

50. We are going to use our knowledge about multiplying and dividing by 100 to convert centimetres to metres and to convert metres to centimetres.

51. Prefixes for Unit Measurements
Kilo-
hecto-
deca-
Unit
deci-
centi-
milli-

52. When you walk up the steps, you move the decimal to the left one position for each step you take. Add a zero to hold each step.

53. When you walk down the steps, you move the decimal to the right one position for each step you take. Add a zero to hold each step.

54. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

55. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

56. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

57. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

58. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

59. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

60. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

61. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

62. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

63. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

64. 4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T
There are 100 centimetres in 1 metre
When we change from cm to m we divide by:-
100
Remember!
When we divide by 100 the units move two places to the right.
This is how we change 427cm into metres:- H T U th
hth 4 2 7
÷100

65. Therefore:-
427cm = 4.27m cm m H T U t h th 3 2 6 H T U t h th 3 2 6
÷100 H T U t h th 4 7 6 H T U t h th 4 7 6
÷100 H T U t h th 1 6 5 3 H T U t h th 1 6 5 3
÷100

66. Convert from centimetres to metres
354cm
15.4cm
779cm
52.4cm
939cm
395cm
25.8cm
3.54m
0.154m
7.79m
0.524m
9.39m
3.95m
0.258m
÷100

67. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

68. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

69. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

70. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

71. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

72. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

73. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

74. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

75. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

76. 3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = H T U t h th 3 5 1

77. To change from metres to centimetres we MULTIPLY BY 100.
REMEMBER
When we multiply by 100 we move each digit two places to the left:-
3.51m = 351cm H T U t h th 3 5 1

78. Try changing these measurements in metres into centimetres
540cm
620cm
1270cm
300cm
760cm
54cm
30cm
5.4m
6.2m
12.7m 3m
7.6m
0.54m
0.3m
x100

79. Let’s Practice! Convert 4 deciliters to kiloliters.
Step 1: On the stairs, write the number 4 on the correct level.
Step 2: Decide where the new unit is that you want to have as your end measurement. Is it to the left or to the right?
Step 3: Count the number of stairs you moved, either up or down.
Step 4: Write the 4 and place the zeroes to the left of the 4 to hold the spot.
Step 5: The decimal comes before your last zero.
.0004
Kilo- 4
deci-
Answer: 4 deciliters = kiloliters

80. Let’s Practice! Convert 3 grams to centigrams.
Step 1: On the stairs, write the number 3 on the correct level.
Step 2: Decide where the new unit is that you want to have as your end measurement. Is it to the left or to the right?
Step 3: Count the number of stairs you moved, either up or down.
Step 4: Write the 3 and place the zeroes to the right to hold the spot.
Step 5: The decimal comes after your last zero. 3
gram
300.
Centi-
Answer: 3 grams = 300. centigrams

81. My garden has a length of 34 decimeters and a width of 2 meters
My garden has a length of 34 decimeters and a width of 2 meters. Which measurement is larger? On a separate piece of paper, show your work and explain your answer.
Choose which number to convert. Draw the stairs.
Step 1: On the stairs, write that number.
Step 2: Decide where the new unit is that you want to have as your end measurement. Is it to the left or to the right?
Step 3: Count the number of stairs you moved, either up or down.
Step 4: Write that number on the new step. (Ask yourself if you moved left or right)
Step 5: Place the zeroes on the correct side of the number(s). Then place the decimal point in the correct position.
Answer: Conversion of 34 decimeters to meters.
34 decimeters = 3.4 meters
Answer: Conversion of 2 meters to decimeters.
2 meters = 20. decimeters

82. Practice

83. Prefixes for Unit Measurements
Kilo-
hecto-
deca-
Unit
deci-
centi-
milli-

84. On Your Own
On a separate sheet of paper, convert the following measurements.
23 kilograms = ___ centigrams grams= ____ milligrams
62 meters = ____ decimeters centimeters = ____ meters
milliliters = ____ kiloliters deciliters = ____ milliliters

85. On Your Own
On a separate sheet of paper, convert the following measurements.
23 kilograms = 2300 centigrams grams= 23,000 milligrams
62 meters = 620 decimeters centimeters = .62 meters
milliliters = kiloliters deciliters = milliliters

86. More Practice 2,570 L = ____ DL 2. 25 mm = ___ m 3. 54.5 mg = ____ g
4. 15 mm = ____Km
cL = ____ L
Kg=____g
mL = ____L
8.125,000 cm = _____Km
270 cm = _______mm

87. More Practice 2,570 L = 257 DL 2. 25 mm = .025 m 3. 54.5 mg = .0545 g
4. 15 mm = Km
cL = 3.4 L
Kg=250,000 g
mL = 8.75 L
8.125,000 cm = 1.25 Km
270 cm = 2,700 mm

88. M5.B Add or subtract linear measurements, (feet and inches) or units of time (hours and minutes), without having to regroup with subtraction (answer should be in simplest form).

89. PSSA Sample Item

90. PSSA Sample Item

91. PSSA Sample Item

92. PSSA Sample Item

93. Adding and Subtracting Time Advice: Add or Subtract the hours and minutes separately. But you may need to do some adjusting if the minutes end up 60 or more, or less than zero!

95. Adding Times Follow these steps: Add the hours Add the minutes
If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours
Easy example: What is 2:45 + 1:10 ?
Add the Hours: 2+1 = 3 Add the Minutes: = 55 The minutes are ok, so the answer is 3:55
Hard example: What is 2:45 + 1:20 ?
Add the Hours: 2+1 = 3 Add the Minutes: = 65 The minutes are 60 or more, so subtract 60 from minutes (65-60 = 5 Minutes) and add 1 to Hours (3+1 = 4 Hours) ... so the answer is 4:05

96. Subtracting Times Follow these steps: Subtract the hours
Subtract the minutes
If the minutes are negative, add 60 to the minutes and subtract 1 from hours.
(Note: the easiest way to add 60 to the negative minutes is to start with 60 and subtract the minutes)
Easy example: What is 4:10 - 1:05 ?
Subtract the Hours: 4-1 = 3 Subtract the Minutes: 10-5 = 5 The minutes are fine, so the answer is 3:05
Hard example: What is 4:10 - 1:35 ?
Subtract the Hours: 4-1 = 3 Subtract the Minutes: = -25 The minutes are less than 0, so add 60 to Minutes ( = = 35 Minutes) and subtract 1 from Hours (3-1 = 2 Hours) ... answer is 2:35

104. Measurement Conversion: Scavenger Hunt
You will need to add, subtract, multiply, and divide measurements on the worksite. With your partner, find the following measurements around your classroom
and work through the problems. Use scratch paper to record your “work.” See the example below for how to convert inches to feet.
Example: Measure the length of two tables in the room. Add the two measurements together.What is the total?
(L. table #1) = 6 feet, 4 inches
(L. table #2) = 3 feet, 9 inches
9 feet, 13 inches
Simplify: 10 feet, 1 inch

105. 1. Find the height of two doors in the room
1. Find the height of two doors in the room. Add the two heights together.
2. What is the length of a table plus the height of a chair?
3.Measure four sides around a window. Add the total of all four sides.
4.Measure the total height of a bookshelf. Measure the height of the tallest book on the shelf. Subtract the height of the book from the height of the bookshelf.
5. Find the height of a door in the room.Measure your or your partner’s height. Subtract your (or your partner’s) height from the height of the door.