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