Measurement What do we measure?

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

Distance Some Tools Inches Ruler Miles Yard stick Centimeters Some Derived Units Inches Miles Centimeters Kilometers Yards Some Tools Ruler Yard stick Meter stick Measuring tape

Area How 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/Capacity How many units to fill a space? Standard units: cubic feet, cubic meters, cup and liter

Volume/Capacity Some Derived Units Some tools Measuring cups Gallons Teaspoons Cubic centimeters Quarts Pints Bushels Pecks Milliliters Kiloliters Some tools Measuring cups Measuring spoons Gallon containers Graduated cylinders Beakers

Mass How many units to balance an object? Standard unit: gram

Mass Some Derived Units Kilogram Milligrams Tools Balance

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

Weight Some Derived Units Ounces Tons Tools Scales

Angles How many units did you turn? Standard units: degree and radian

Angles Units Degrees Radians Tools Protractor Compass

Estimate Angle Measure 900 600 1200 600

Time How 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

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

Money Some Derived Units Penny Dime Nickel Quarter Tools ?

Temperature How 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