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Measurement
What do we measure?
DistanceHow many units to travel a path?• Length• Width• Depth • Perimeter• Circumference• Height
Standard units: foot and meter
DistanceSome Derived Units
• Inches
• Miles
• Centimeters
• Kilometers
• Yards
Some Tools
• Ruler
• Yard stick
• Meter stick
• Measuring tape
AreaHow many units to cover a region?
Standard units: square feet and square meters
Area
Some Derived Units
• Square inches
• Square miles
• Square centimeters
• Square yards
• Acre
Tools
• Grids
• Find area indirectly with linear tools
Volume/CapacityHow many units to fill
a space?
Standard units: cubic feet, cubic meters, cup and liter
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
MassHow many units
to balance an object?
Standard unit: gram
Mass
Some Derived Units
• Kilogram
• Milligrams
Tools
• Balance
WeightHow many units is
gravity pulling down on an object?
Standard unit: pound
Weight
Some Derived Units
• Ounces
• Tons
Tools
• Scales
AnglesHow many units did you turn?
Standard units: degree and radian
Angles
Units
• Degrees
• Radians
Tools
• Protractor
• Compass
Estimate Angle Measure
900
600
1200
600
TimeHow many units
has the earth turned?
Standard unit: day
Time
Some Derived Units• Hours• Years• Minutes• Century• Decade• Seconds• Weeks• Months
Some Tools• Clocks• Calendar• Sun dial
MoneyHow many units of
buying power do you have?
Standard units: dollar, peso, euro, etc.
Money
Some Derived Units
• Penny
• Dime
• Nickel
• Quarter
Tools
?
TemperatureHow many units
are the molecules moving?
Standard units: degrees Fahrenheit, Celsius, and Kelvin
Temperature
No Derived Units Tools• Thermometer
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)
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
Sequence of learning for measurement
Third: Develop intuition about standard units and use standard units to make measurements
Grade 2
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
Sequence of learning for measurement
Fifth: Make conversions between units.
Grades 3 and 4
Sequence of learning for measurement
Sixth: Understand the continuous nature of measurements and use fractional units.
Grades 4, 5 and 6
Sequence of learning for measurement
Seventh: Find measures indirectly.
Grade 4-8
Sequence of learning for measurement
Eighth: Use related rates
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