Section	Section Title	Contents/Main Ideas and Activities	Link to Applet
2.1	Kinds of Numbers	Number sets, fractions <-> decimals
2.2	Behavior of Numbers and Variables	Commutative property, reciprocals, additive and multiplicative identities
2.3	Adding and Subtracting Signed Numbers and Variables	Adding/subtracting signed numbers on the number line	Number line Chip game
2.4	Multiplying And Dividing Signed Numbers And Variables	Multiplying and dividing signed numbers	Number line series
2.5	Operations with Fractions and Variables	Rules for multiplying fractions(numbers and variables)--canceling
2.6	Squares, Square Roots, and Absolute Value	Defining squares geometrically, Simplifying radicals,	Square root
2.7	Order of Operations	Examples with mult-div before add-subtract
3.1	Monomials	Defining monomials, exponents, coefficient terminology
3.2	Basic Rules for Exponents	Rules for adding, multiplying, etc. monomials with exponents
3.3	Additional Rules for Exponents	Canceling with negative exponents (the “elevator” metaphor)	Elevator??
3.4	From Words to Algebraic Expressions	Translations	Key word matching
3.5	Evaluating Expressions	Writing expressions and then plugging in values for the variables.	Simple and Compound Interest
3.6	Polynomials	Finding degrees, adding like terms, defining monomial,
4.1	The Distributive Property	Factoring expressions, distributing
4.2	Multiplying Binomials	FOIL Method
4.3	Squaring a Binomial	(a+b)^2; (a-b)^2	See example 3
4.4	Adding and Subtracting Polynomials	“Getting rid of parentheses”
5.1	Formulas for Perimeter, Area, and Volume	Area and perimeter of square, rectangle, finding area in terms of square units · Perimeter of a rectangle · Definition of pi · Area of a triangle · Area of a parallelogram · Area of a trapezoid · Volume	Average speed (race car)
5.2	Other Useful Formulas	Simple interest Compound interest	Attraction formula Compound interest formula Temperature conversion
5.3	Ratios, Rates, and Proportions	Ratios of triangle sides, comparing rates of gas usage, etc.	Scale factor for similar triangles Shadow problem
5.4	The Pythagorean Theorem	Proving, finding missing sides, finding missing angles	Pythagorean Area Proof
5.5	The Cartesian Coordinate Plane and the Distance Formula	Plotting points, finding distances between points	Critter race – plotting points
6.1	Solving Linear Equations by Addition and Subtraction	Algebraic manipulation	Show balance?
6.2	Solving Linear Equations by Multiplication and Division	Algebraic manipulation (canceling)
6.3	Solving General Linear Equations	Algebraic manipulation (combing 6.1 & 6.2)
6.4	Applications Involving Linear Equations	Using real-world formulas to solve word problems in one variable
6.5	Solving Linear Inequalities	Graphing solutions on a number line (open and closed circles)
7.1	Graphing Linear Equations in Two Variables	Finding points to satisfy an equation; graphing points to show they lie on a line. Also introduces intercepts	Graphing via intercepts, finding slope of line
7.2	Linear Equations: Slope and the Slope-Intercept Form	Finding slope intercept form (mostly manipulation)
7.3	Linear Equations: Point-Slope Form	Point-slope forms, perpendicular lines (no graphs included in section at all)
7.4	Relations and Functions	Domain, range, vertical line test,
7.5	Graphing Linear Inequalities in Two Variables	Graphing solutions by shading
8.1	Solving Systems of Linear Equations by Graphing	Plot two lines, see where they meet
8.2	Solving Systems of Linear Equations by Substitution	Use algebraic manipulation to solve systems via substitution
8.3	Solving Systems of Linear Equations by Elimination	Use algebraic manipulation to solve systems via elimination (also includes summary of three methods)
8.4	Applications of Linear Systems	Applying techniques to word problems	Bus and car
8.5	Systems of Linear Inequalities	Shading two regions
9.1	Introduction to Factoring Polynomials	Algebraic manipulation
9.2	Special Quadratic Factorizations	Recognizing formulas to factor
9.3	Factoring Quadratics with Integer Coefficients	Guess and check method
9.4	Special Cubic Factorizations	Summary of formulas for factoring quadratics and cubics
9.5	Solving Equations by Factoring	Setting factors=0. Algebraic manipulation only.
10.6	Direct and Inverse Variation	Algebraic exploration of concepts.	Exploring variation with Cars context Direct variation reversing quantities inverse variation
11.1	Multiplying and Dividing Radical Expressions	Simplifying radicals (algebra only)
11.2	Adding and Subtracting Radical Expressions	Simplifying radicals (algebra only)
11.3	Radical Equations	Setting radical factors=0. Algebraic manipulation only.
11.4	Complex Numbers	Manipulating and plotting	Adding/subtracting numbers in the complex plane
11.5	Rational Exponents	Manipulating expressions with factional exponents

Example 1:

Renting a truck costs $19.95 per day and $0.45 for each mile driven. Write an expression for the cost to rent a truck for one day and drive miles. Then use the expression to determine the cost to rent a truck for one day and drive 200 miles.

We are assuming that m miles are driven, at $0.45 per mile, so the cost for these miles is:

0.45m.

Add the $19.95 daily fee to the cost for the miles to find the total cost.

To rent for one day and drive 200 miles, it will cost:

Example 2:

Problem: José lives 150 miles east of Las Vegas. He drives west toward the city at 60 mph. Write an expression for Jose’s distance from the city after hours. Then, use the expression to find his distance after 2.25 hours.

Hint: The distance is originally 150 miles, and is decreasing as the car drives west at the rate of 60 mph.

Step 1: So, .

Hint: Substitute the given time for , and simplify.

Solution:

After 2.25 hours, the car is 15 miles from the city.

Example 3:

Problem: Expand:

Hint: In the rule ,

what is and what is ?

Step 1: .

Hint: Apply the rule .

Step 2:

Hint: Simplify.

Solution:

Example 4:

You can find the area of a plane geometric figure by counting the number of unit squares it contains.

· For example:

	inches
inches

We see 15 unit squares. The area is , which is read “15 square inches.”

Example 5:

Example 6:

Problem:

A pizzeria offers two small pizzas with 10-inch diameters for the same price as one large pizza with a 16-inch diameter. Which deal gives you the most pizza?

Hint 1: The area of a circle is .
Hint 2: Use this formula twice, with r=5 and with r=8.

Step 1:

Let A₁ be the area of one 10-inch pizza. Let A₂ be the area of one 16-inch pizza.

Hint: Use 3.14 for

Step 2:

Hint: Multiply the smaller area times 2, since you get two of these pizzas. Compare that area with the area of the larger pizza.

Solution: The smaller pizzas have a total area of . The larger pizza has a total area of .

The 16-inch pizza gives you almost more than the two 10-inch pizzas combined.

Example 7

Problem:

If you drove for 3 hours and traveled 216 kilometers, what was your average speed?

Hint: Substitute the given information into the equation .

Step 1:

Hint: Solve by dividing both sides by 3 hrs.

Solution:

Your speed averaged 72 kilometers per hour.

Example 8:

A plane takes off at 9:00 am, traveling north at 230 miles per hour. A jet takes off at 11:00 am, traveling north at 520 miles per hour. At what time will the jet overtake the plane? (Round your answer to the nearest minute.)

Example 9: