Quantity

A quantity is an attribute of an object or phenomenon that can be specified using a number and a unit, such as 2.7 centimeters, 42 questions or 28 miles per gallon. The length of a football field and the speed of light are both quantities. If we choose units of miles per second, then the speed of light has a value of approximately 186,000 miles per second. But the speed of light need not be expressed in miles per second; it may be approximated by 3 x 108 meters per second or in any other unit of speed. Bare numerical values such as 186,000 do not describe quantities unless they are paired with units.

Speed (distance divided by time), rectangular area (length multiplied by length), density (mass divided by volume), and population density (number of people divided by land area) are examples of derived quantities, obtained by multiplying or dividing quantities.

It can make sense to add two quantities, such as when a child 51 inches tall grows 3 inches to become 54 inches tall. To be added or subtracted, quantities must be of the same type (length, area, speed, etc.); to add or subtract their values, the quantities must be expressed in the same units. Converting quantities to have the same units is like converting fractions to have a common denominator before adding or subtracting. But, even when quantities have the same units it does not always make sense to add them. For example, if a wooded park with 300 trees per acre is next to a field with 30 trees per acre, they do not have 330 trees per acre. Doing algebra with units in a calculation reveals the units of the answer, and can help reveal a mistake if, for example, the answer comes out to be a distance when it should be a speed.

//Connections to Number, Expressions, Equations, Functions, Modeling and Statistics//. Operations described under Number and Expressions govern the operations one performs on quantities, including the units involved. Quantity is an integral part of any application of mathematics, and has connections to solving problems using data, equations, functions and modeling.

Students understand that: Students can and do:
 * Core Concepts**
 * 1) The value of a quantity is not specified unless the units are named or understood from the context.
 * 2) Quantities can be added and subtracted only when they are of the same type (length, area, speed, etc.).
 * 3) Quantities can be multiplied or divided to create new types of quantities, called derived quantities.
 * Core Skills**
 * 1) Know when and how to convert units in computations.
 * 2) Use and interpret quantities and units correctly in algebraic formulas.
 * 3) Use and interpret quantities and units correctly in graphs and data displays.
 * 4) Use units as a way to understand problems and to guide the solution of multi-step problems.