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Measurement. What do we measure?. Distance. How many units to travel a path? Length Width Depth Perimeter Circumference Height Standard units: foot and meter. Some Derived Units Inches Miles Centimeters Kilometers Yards. Some Tools Ruler Yard stick
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Measurement What do we measure?
Distance How many units to travel a path? • Length • Width • Depth • Perimeter • Circumference • Height Standard units: foot and meter
Some Derived Units Inches Miles Centimeters Kilometers Yards Some Tools Ruler Yard stick Meter stick Measuring tape Distance
Area How many units to cover a region? Standard units: square feet and square meters
Some Derived Units Square inches Square miles Square centimeters Square yards Acre Tools Grids Find area indirectly with linear tools Area
Volume/Capacity How many units to fill a space? Standard units: cubic feet, cubic meters, cup and liter
Some Derived Units Gallons Teaspoons Cubic centimeters Quarts Pints Bushels Pecks Milliliters Kiloliters Some tools Measuring cups Measuring spoons Gallon containers Graduated cylinders Beakers Volume/Capacity
Mass How many units to balance an object? Standard unit: gram
Some Derived Units Kilogram Milligrams Tools Balance Mass
Weight How many units is gravity pulling down on an object? Standard unit: pound
Some Derived Units Ounces Tons Tools Scales Weight
Angles How many units did you turn? Standard units: degree and radian
Units Degrees Radians Tools Protractor Compass Angles
Estimate Angle Measure 900 600 1200 600
Time How many units has the earth turned? Standard unit: day
Some Derived Units Hours Years Minutes Century Decade Seconds Weeks Months Some Tools Clocks Calendar Sun dial Time
Money How many units of buying power do you have? Standard units: dollar, peso, euro, etc.
Some Derived Units Penny Dime Nickel Quarter Tools ? Money
Temperature How many units are the molecules moving? Standard units: degrees Fahrenheit, Celsius, and Kelvin
No Derived Units Tools Thermometer Temperature
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