Measurement What do we measure Distance How many

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 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 Tools • Square inches • Grids • Square miles • Find area indirectly with linear tools • Square centimeters • Square yards • Acre

Volume/Capacity How 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

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