Introduction To Quantities, Variables, Expressions & Formulas

1. Introduction To Quantities, Variables, Expressions & Formulas Module 1 Investigation #1 Students will be able to identify quantities and variables.

2. Quantities & Variables What is a Quantity? A quantity is some measurable attribute to an object. What is a variable? A variable is a letter that stands for all the possible measurements a quantity can have. In this investigation we will learn how to identify the things being measured in a situation (quantities). In this investigation we will also learn to use variables to represent possible measurements a quantity can have.

3. In your summer job at the home improvement store you have the responsibility of ordering materials when they run low. You need to keep track of how much wire is remaining on wire spools in the store. Identify the quantities in this situation. Raise your hand and tell the class – What are some of the quantities in this situation? Turn and talk with your neighbor – What are some of the quantities in this situation?

4. In your summer job at the home improvement store you have the responsibility of ordering materials when they run low. You need to keep track of how much wire is remaining on wire spools in the store. A new spool of electrical wire has 60 feet of wire. What quantities vary (change) in this situation? Total amount of wire remaining on the spool Total amount of wire cut from the spool Surface area of the wire remaining on the spool • How does the amount of wire remaining on the spool vary (change) as some length of wire is cut from the spool? • The length of wire remaining on the spool decreases by the same length of wire that is cut from the spool.

5. Given the following total amounts of electrical wire that have been cut from the spool, determine the total amount of electrical wire remaining on the spool. Turn and work with your neighbor to determine the amounts of wire left on the spool. Be Prepare To Explain The Process You Used To Find Your Answer.

6. Given the following total amounts of electrical wire that have been cut from the spool, determine the total amount of electrical wire remaining on the spool. 48 feet 43 feet 20.5 feet 16.2 feet

7. In your summer job at the home improvement store you have the responsibility of ordering materials when they run low. You need to keep track of how much wire is remaining on wire spools in the store. Explain the process you used to compute the amount of wire remaining on the spool. The amount remaining on the spool can be determined by subtracting the total amount cut from the spool from the original length of 60 feet. 60 - 12 = 48 feet 60 - 17 = 43 feet 60 – 39.5 = 20.5 feet 60 – 43.8 = 16.2 feet

8. In algebra, we often want to write a general formula to describe the process of determining the value of one quantity (amount of wire remaining on the spool) for varying values of the other quantity (the total amount of wire cut from the spool). Mathematicians needed a way to talk about and represent these changing values when writing formulas. So they created the idea of variable. A variable is a letter or symbol that represents the varying values that a particular quantity can have.

9. In this course, we introduce variables in a context where students find them useful—for representing the values that a varying quantity may assume. Later in the course we introduce situations where it is useful to think of a variable as an unknown value. This way of thinking about a variable is useful when solving an equation. We can define two variables to represent values of the two quantities that are changing in our problem. We do this by writing: x = the total amount of wire (in feet) cut from the spool y = the total amount of wire (in feet) remaining on the spool

10. x = the total amount of wire (in feet) cut from the spool y = the total amount of wire (in feet) remaining on the spool Use these variables to write a formula to determine the amount of wire remaining in terms of (or when given) the total amount of wire cut from the spool. Use your formula from (e) to determine the total amount of wire remaining on the spool when 18.5 feet have been cut from the spool. Does your answer make sense? Explain. y = 60 - x Come up with a formula using the variables x & y with your partner. y = 60 – 18.5 ; y = 41.5 feet Yes the answer makes sense. If I cut 18.5 feet from a 60 foot spool of wire, I should have 41.5 feet left. With your partner determine how much wire is remaining and if your answer makes sense.

11. As the amount of wire cut from the spool varies from: • 0 to 5 feet, how does the amount of wire left on the spool change? The amount of wire left on the spool will decrease from 60 feet to 55 feet. • 5 to 10 feet, how does the amount of wire left on the spool change? The amount of wire left on the spool will decrease from 55 feet to 50 feet. • 0 to 60 feet, how does the amount of wire left on the spool change? The amount of wire left on the spool will decrease from 60 feet to 0 feet. Change the formula you wrote in part (e) to compute the number of feet of wire y left on a 90-foot spool of wire, given that x feet of wire are cut from the spool. y = 90 - x

12. In algebra we use a variable to represent the varying values of a quantity. A variable is defined by letting some letter (like x, y or n) be equal to the values that the quantity can assume. It is important to be specific in describing the quantity’s values when defining a variable. For example, instead of just writing d = distance, you should write d = the distance of the car from the starting line measured in yards.

13. Define variables to represent two quantities that could be related in each of the following situations. (There is not only one correct answer.) • A runner moving down the track from the starting line in a 100-meter race. • A person blowing up a balloon to increase the volume of air in the balloon. • The number of pounds of candy that a customer purchases at a store determines how much the customer must pay. d = the distance in meters of the runner from the starting line t = the elapsed time in seconds since the beginning of the 100 meter race OR t = the number of seconds since the beginning of the100 meter race V = the volume of air in the balloon S = the surface area of the balloon n = the number of pounds of candy that the purchaser wanted c = the cost of the total purchase in dollars

14. HOMEWORKDUE: Monday at START of class Homework Packet Questions #1 and #2 **Remember… to receive credit – you must complete the entire homework assignment. No skipping problems!!! Please show work and explanation of answers on a separate piece of paper.