Measurement

1
Measurement

• What do we measure?

2
Distance

• How many units to travel a path?
• Length
• Width
• Depth
• Perimeter
• Circumference
• Height
• Standard units foot and meter

3
Distance

• Some Derived Units
• Inches
• Miles
• Centimeters
• Kilometers
• Yards

• Some Tools
• Ruler
• Yard stick
• Meter stick
• Measuring tape

4
Area

• How many units to cover a region?
• Standard units square feet and square meters

5
Area

• Some Derived Units
• Square inches
• Square miles
• Square centimeters
• Square yards
• Acre

• Tools
• Grids
• Find area indirectly with linear tools

6
Volume/Capacity

• How many units to fill a space?
• Standard units cubic feet, cubic meters, cup
  and liter

7
Volume/Capacity

• Some Derived Units
• Gallons
• Teaspoons
• Cubic centimeters
• Quarts
• Pints
• Bushels
• Pecks
• Milliliters
• Kiloliters

• Some tools
• Measuring cups
• Measuring spoons
• Gallon containers
• Graduated cylinders
• Beakers

8
Mass

• How many units to balance an object?
• Standard unit gram

9
Mass

• Some Derived Units
• Kilogram
• Milligrams

• Tools
• Balance

10
Weight

• How many units is gravity pulling down on an
  object?
• Standard unit pound

11
Weight

• Some Derived Units
• Ounces
• Tons

• Tools
• Scales

12
Angles

• How many units did you turn?
• Standard units degree and radian

13
Angles

• Units
• Degrees
• Radians

• Tools
• Protractor
• Compass

14
Estimate Angle Measure
900
600
1200
600
15
Time

• How many units has the earth turned?
• Standard unit day

16
Time

• Some Derived Units
• Hours
• Years
• Minutes
• Century
• Decade
• Seconds
• Weeks
• Months

• Some Tools
• Clocks
• Calendar
• Sun dial

17
Money

• How many units of buying power do you have?
• Standard units dollar, peso, euro, etc.

18
Money

• Some Derived Units
• Penny
• Dime
• Nickel
• Quarter

• Tools
• ?

19
Temperature

• How many units are the molecules moving?
• Standard units degrees Fahrenheit, Celsius, and
  Kelvin

20
Temperature

• No Derived Units

• Tools
• Thermometer

21
Sequence of Learning for Measurement

• First Understand what is being measured (or
  counted) and measure with nonstandard units.
• Grade K and 1 (except time and money)

22
Sequence of Learning for Measurement

• Second Recognize the relationship between the
  size of the unit and the count and the need for
  the standard unit.
• Grade 2

23
Sequence of learning for measurement

• Third Develop intuition about standard units
  and use standard units to make measurements
• Grade 2

24
Sequence of learning for measurement

• Fourth Realize the need for derived units,
  select an appropriate unit and measure with
  derived units
• Grade 3 and 4

25
Sequence of learning for measurement

• Fifth Make conversions between units.
• Grades 3 and 4

26
Sequence of learning for measurement

• Sixth Understand the continuous nature of
  measurements and use fractional units.
• Grades 4, 5 and 6

27
Sequence of learning for measurement

• Seventh Find measures indirectly.
• Grade 4-8

28
Sequence of learning for measurement

• Eighth Use related rates

29
Examples of Related Rate

• Miles per hour (velocity)
• Miles per gallon
• Pounds per square inch
• Dollars per gallon
• Dollars per linear foot
• Dollars per square foot