Superlesson
Project 2-3
Algebra
Chapter 2
Patterns, Change, and Expressions
Use the grammar of algebra to look at some formulas related to light trucks.
Part A, Order of Operations
1. Find out how much extra ground clearance will be provided under a light truck's axles of up change the size of your tires. Look at the site for Light truck formulas.
a. Suppose the diameter of your new tire is 33" and the diameter of your old tire is 28". Calculate the approximate change in ground clearance and center of gravity.
b. Suppose you saw your friend calculate the answer to a like this: 33 - ( 28 / 2 ). Explain what is wrong with this calculation and why.
c. When you change the tire size, it affects the speedometer. Calculate how far off the speedometer will be if you replace your original tires, which have a 28" diameter, with new tires, which have a 33" diameter, when the indicated speed is 65 mph.
Part B, The Distributive Property
2. Look again at the section entitled "How much extra ground clearance under the axles will be provided?"
a. Explain why 32.5"/2 - 27"/2 gives the same result as (32.5" - 27")/2.
b. Use the distributive property to explicitly rewrite the problem in a to show why the two expressions are equal.
3. Sometimes, if you need new tires, you also need new wheels.
a. If tires are $60 each and wheels are $120 each, write two different expressions that show the total cost of getting 4 tires and 4 wheels.
b. Calculate the answers to the expressions you wrote in a.
c. Are both your answers from b the same? Explain.
d. Which expression was easier to calculate? Explain.
Part C, Simplifying Expressions
4. Look at the expression for the approximate change in ground clearance and center of gravity: (New Tire Diameter - Original Tire Diameter) /2
a. What are the terms in the expression?
b. Is there a constant in the expression? If so, what is it?
5. Suppose you are going to change the oil in your car. To do this you need 8 quarts of oil and 1 oil filter.
a. If n is the cost of a quart of oil and f is the cost of an oil filter, write an expression that shows the total amount you will spend buying oil and a filter.
b. What is the coefficient of n?
c. What does this represent?
d. What is the coefficient of f?
e. What does this represent?
Part D, Making Connections
6. Look at the section entitled "How far off
will the speedometer be?" As the new tire diameter increases, what
happens to the actual speed? Make a chart showing at least 3 calculations
to justify your conjecture.
7. Let w = indicated speed, x = new tire diameter, y
= original tire diameter, and z = original axle ratio.
a. Write an expression in terms of w, x, y, and z for how far off the speedometer will be.
b. Write an expression for the required axle ratio using the information found in the section entitled "What can I do to regain the performance?"
c. Can you simplify your expressions in a and b? Explain.