Consider the following questions:

1. What is a Quantity? • How long do humans live? Consider the following questions: • How fast is the wind blowing? • How big is this room? • How far is it around the earth? • Which is more crowded, New York City or Mexico City? MTE 494 Arizona State University

2. The answer to each of these questions involves thinking about some quantity: Aquantity is anything—an object, event, or quality thereof—than can be measured or counted. • Avalue of a quantity is its measure or the number of items that are counted. A value of a quantity involves a number and a unit of measure. MTE 494 Arizona State University

3. Example of quantities: 1. A person’s age 2. Speed of wind 3. Area of a room 4. Distance around the equator 5. Population density Actually, most of these are just common names of quantities—they don’t explicate what attribute is being quantified. Ex. “speed” is the common name given to a particular attribute that can be quantified. How might we unpack this term to explicitly describe the attribute being quantified? MTE 494 Arizona State University

4. Example of quantities: • Explicitly describe the attribute being referred to in each of these: • - a person’s age • speed of wind • area of a room • - distance around the equator • - population density MTE 494 Arizona State University

5. 1. Characterize the quantity addressed in each of the following questions:a) How tall is the Eiffel tower?b) How fast does water pour out of a faucetc) Which is wealthier, Honduras or Mozambique?d) How much damage did the earthquake cause? 2. Identify an appropriate unit of measure that can be used to determine a value for the quantities involved in each of the above questions. Is the wealth of a country measured in the same as the wealth of an individual? Explain. MTE 494 Arizona State University

6. Are all attributes of objects, events, or persons quantities? Give examples of attributes that are difficult or impossible to measure (and are therefore arguably not quantities) MTE 494 Arizona State University

7. An important distinction: A quantity is not the same thing as a number or a value of the quantity One can think of a quantity without knowing its value. For example: the amount of snowfall on a given day is a quantity, regardless of whether someone actually measured this amount. One can think/speak about the amount of snowfall without knowing a value of this amount. MTE 494 Arizona State University

8. A quantity is not the same thing as a number or a value of the quantity The distinction between a quantity and values of it raises another important difference: the amount of a given quantity (the measurable attribute) is constant, but values of it may change depending on the measuring unit with which we choose to express how much of it there is. This is why quantities can have different values for their measure, and why we can form equations relating those values. Ex. The height of the Eiffel tower—its linear extension from its bottom to its tip—is a fixed amount that does not change. However, this amount can be expressed as 324 meters, as 1063 feet, as 12x1063 inches, etc. Give another such example. MTE 494 Arizona State University

9. But what does it mean to measure a quantity?? On one level it just means determining how much of the attribute there is! Think: What is the process we engage in when we measure something in an effort to determine how much of it there is? Give of an example of measuring something and step back to reflect on what that actually entails. MTE 494 Arizona State University

10. For instance: What do you mean when we say “the distance from point A to point B is 12 miles”? What process do we engage in that ends up having us associate the tag “12 miles” to this distance? MTE 494 Arizona State University