3.2: Units of Measurement

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Amy Lagusker
College of the Canyons

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How Common Core Changed Word Problems

Before the mathematicians wrote Common Core, they sat down with Physicists and asked what they would want from Math Teachers: The number one response was UNITS! Students who take physics are notorious for leaving off the units from their answers. Therefore, Common Core made learning units a standard, for grades one through five:

Common Core standards for Units

Grade 1: Measure lengths indirectly and by iterating length units.
Grade 2: Measure and estimate lengths in standard units.
Grade 3: Measure and estimate liquid volumes and masses of objects using standard units of grams \((\mathrm{g}),\) kilograms \((\mathrm{kg}),\) and liters \((\mathrm{L})\). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
Grade 4: Know relative sizes of measurement units within one system of units including \(\mathrm{km}, \mathrm{m}, \mathrm{cm} ; \mathrm{kg}, \mathrm{g} ; \mathrm{Ib}, \mathrm{oz} . ; \mathrm{I}, \mathrm{ml} ; \mathrm{hr}, \mathrm{min},\) sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that \(1 \mathrm{ft}\). is 12 times as long as 1 in. Express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs \((1,12),(2,24),(3,36), \ldots\)
Grade 5: Convert among different-sized standard measurement units within a given measurement system (e.g., convert \(5 \mathrm{cm}\) to \(0.05 \mathrm{m}\) ), and use these conversions in solving multi-step, real world problems.

Mathematical Practices for Teachers 6: Attend to Precision \((\) Did 1 Label My Answer?)

Example \(\PageIndex{1}\)

Table 2.2.1: Physical quantity and Units
Type	Units
Height (how tall?)	Feet, meters, miles, yards, etc
Weight (how much?)	Pounds, kilograms, ounces, liters, quarts, etc
Speed (how fast?)	Miles per hour (mph) and kilometers per hour (kph) and feet per second (f/s or fps)
Temperature (how hot?)	Celsius \(C^{\circ }\) and Fahrenheit \(F^{\circ }\)

Example \(\PageIndex{2}\)

Table 2.2.2: Quantity versus Quality
Quantifiable (Measureable units)	Qualitative (Descriptive Units)
Feet	Feelings
Gallons	Colors
Miles per Hour	Opinions
Weight	Taste
Money	Sound
Asking about something about a large group of people	Asking about something just about yourself

Practice Problems

Use Google to help you answer these questions:

How tall is the Eiffel Tower?
What is the average weight of a newborn baby?
What is the wealth of America?