Module 1 Investigation 2

1. Module 1Investigation 2 Day 2

2. 6. a. Compare the wording of the statement “Define the cost C of candy in dollars in terms of the number of pounds x of candy purchased” with the statement “Define the number of pounds x of candy purchased in terms of the cost C of a candy purchased”. b. How do you know which variable to isolate on one side of the formula? How do you know which variable to think about as the input variable and which variable to think about as the output variable? In terms of is the key word to look for. Example: “y in terms of x” implies that we want to write a formula in the form y is equal to some expression with an x. The x would be the input variable and y would be the output. c. What does the statement, “define s in terms of t” mean? “define s in terms of t” generally means s = some expression involving t. t is thought of as the input variable and s in thought as the output variable.

3. You have decided to purchase an area rug for your bedroom, but are unable to find a tape measure to measure the width and length of the area where you want to place the rug so are unable to use the standard units of yards, feet and inches. Your mother found a broken broomstick and suggested that you use its length as your measurement device and unit of measurement. The unit of broomstick length will be abbreviated bl. You mark off about 6 lengths of the broomstick for the desired width of your rug. Write an expression to represent the width of the rug in units of a broomstick length. 6 bl You mark off about 9.5 lengths of the broomstick for the desired length of your rug. Write an expression to represent the length of the rug in broomstick lengths bl as the unit of measurement. 9.5 bl

4. You have decided to purchase an area rug for your bedroom, but are unable to find a tape measure to measure the width and length of the area where you want to place the rug so are unable to use the standard units of yards, feet and inches. Your mother found a broken broomstick and suggested that you use its length as your measurement device and unit of measurement. The unit of broomstick length will be abbreviated bl. While in the store you spot a rug that you really like and want to determine if the rug will fit in your room. Explain how you will use your broomstick to determine the approximate length of the rug. Given the different lengths of the rug below, mark off the length of the actual rugs in broomstick lengths bl. (Note that the broom stick length bl is the unit used to measure the width and the length of the rugs and is not a variable.) Rug 1: 4 broomstick lengths Rug 2: 6 broomstick lengths Rug 3: 7 broomstick lengths

5. You have decided to purchase an area rug for your bedroom, but are unable to find a tape measure to measure the width and length of the area where you want to place the rug so are unable to use the standard units of yards, feet and inches. Your mother found a broken broomstick and suggested that you use its length as your measurement device and unit of measurement. The unit of broomstick length will be abbreviated bl. Let L represent the lengths of various rugs at a different store and suppose the broomstick length is represented by bl. Write and expression to describe the rug length L measured in lengths of the broomstick bl. L bl This expression will give how many times as long the rug is than the broomstick. It also represents the length of the rug measured in broomstick lengths bl.

6. Using this reasoning you can think of 8/3 as saying 8 is 8/3 times large as 3. • Using this reasoning what can you say about the relative size of the numerator and denominator in the fraction 15/3? • 15 is 15/3 (or 5) times as large as 3. • Using this reasoning what can you say about the relative size of the numerator and denominator in the fraction 12/5? • 12 is 12/5 times as large as 5. • Describe the operation you would perform to determine the relative size of x inches to 12 inches. • x/12. This expression will give you how many times as large x inches is than 12 inches. It also expresses x units measured in units of 12 inches.

7. Using this reasoning you can think of 8/3 as saying 8 is 8/3 times large as 3. • 32 inches is equal to 32/12 feet. If we rewrite the fraction 32/12 as 2 2/3, what does 2 2/3 say about the relative size of 32 inches and 1 foot? • 32 inches is 2 2/3 times as large as 1 foot or 12 inches. It also says that 32 inches can also be expressed as 2 2/3 feet.

8. Answer the following • How many different ways can you describe the meaning of 17/3? • 17 is 17/3 times as large as 3. • 17 is 5 2/3 times as large as 3. • What does 12/5 convey about the relative size of 12 and 5? • 12 is 12/5 times as large as 5. • 12 is 2 2/5 times as large as 5. • 12 is 2.4 times as large as 5. • The length of a table is 19 inches. Express the length of the table in feet. What does your answer convey about the relative size of 19 inches and 1 foot? • 19/12 feet • 19 is 19/12 times as large as one foot. (or 12 inches) • 19 is about 1.58 times as large as one foot. (or 12 inches)

9. Answer the following • Determine what operation is needed to answer the following; then find the answer. • How many times as tall a 12-foot ceiling is than a 5-foot boy. • The operation needed to answer this question is division. • A 12-foot ceiling is 12/5 times as tall as a 5-foot boy. • How much taller a 12-foot ceiling is than a 5-foot boy. • The operation needed to answer this question is subtraction. • A 12-foot ceiling is 7 feet taller than a 5-foot boy.

10. Answer the following • Determine what operation is needed to answer the following; then find the answer. • 5 times as large as 20. • The operation needed is multiplication. (5 x 20) • 100 is 5 times as large as 20. • 5 more than 20 • The operation needed is addition. (20 + 5) • 25 is 5 more than 20.