Thinking Mathematically

A review and summary of Algebra 1

Topics from your final project assignment sheet have been pasted into this very ordinary

slide show. You may begin with this file or you may find it easier to create your own design and style completely from scratch.

In the next slides you will review:

Solving 1st power equations in one variable

A. Don't forget special cases where variables cancel to get {all reals} or

B. Equations containing fractional coefficients

C. Equations with variables in the denominator – remember to throw out answers that cause division by zero

In the next slides you will review:

Review all the Properties and then take a Quiz on identifying

the Property Names

Addition Property (of Equality)

Multiplication Property (of Equality)

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Reflexive Property (of Equality)

Symmetric Property (of Equality)

Transitive Property (of Equality)

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Associative Property of Addition

Associative Property of Multiplication

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Commutative Property of Addition

Commutative Property of Multiplication

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Distributive Property (of Multiplication over Addition

Example: If blah blah, then blah blah.

Prop of Opposites or Inverse Property of Addition

Prop of Reciprocals or Inverse Prop. of Multiplication

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Identity Property of Addition

Identity Property of Multiplication

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Multiplicative Property of Zero

Closure Property of Addition

Closure Property of Multiplication

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Product of Powers Property

Power of a Product Property

Power of a Power Property

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Quotient of Powers Property

Power of a Quotient Property

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Zero Power Property

Negative Power Property

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Zero Product Property

Example: If blah blah, then blah blah.

Product of Roots Property

Quotient of Roots Property

Root of a Power Property

Power of a Root Property

Example: If blah blah, then blah blah.

Example: If blah blah, then blah blah.

Now you will take a quiz!Look at the sample problem and give the name of the property illustrated.

1. a + b = b + a

Click when you’re ready to see the answer.

Answer: Commutative Property (of Addition)

Now you will take a quiz!Look at the sample problem and give the name of the property illustrated.

2. Blah blah (you can duplicate this slide)

Click when you’re ready to see the answer.

Answer: Blah Blah set to Fade-in

In the next slides you will review:

Solving 1st power inequalities in one variable. (Don't forget the special cases of {all reals} and )A. With only one inequality signB. ConjunctionC. Disjunction

Type the answer here. Set to fade-in on click

Type a sample problem here. Blah blah blah. You can duplicate this slide.

Type any needed explanation or tips here. Set to fade-in 3 seconds after the answer appears above.

Click when ready to see the answer.

In the next slides you will review:

Linear equations in two variablesLots to cover here: slopes of all

types of lines; equations of all types of lines, standard/general form, point-slope form, how to graph, how to find intercepts, how and when to use the point-slope formula, etc. Remember you can make lovely graphs in Geometer's Sketchpad and copy and paste them into PPT.

In the next slides you will review:

Linear SystemsA. Substitution MethodB. Addition/Subtraction

Method (Elimination ) C. Check for understanding

of the terms dependent, inconsistent and consistent

In the next slides you will review:

Factoring – since we just completed the Inspiration Project on this topic, just summarize all the factoring methods quickly. Note that you will be using your factoring methods in areas 7 & 8 below so no need to include extra practice problems here.

In the next slides you will review:

Rational expressions – try to use all your factoring methods somewhere in these practice problems

A. Simplify by factor and cancel

B. Addition and subtraction of rational expressions

C. Multiplication and division of rational expressions

In the next slides you will review:

FunctionsA. What does f(x) mean? Are all

relations function?B. Find the domain and range of a

function.C. Given two ordered pairs of data,

find a linear function that contains those points.

D. Quadratic functions – explain everything we know about how to graph a parabola

In the next slides you will review:

Simplifying expressions with exponents – try to use all the power properties and don't forget zero and negative powers.

In the next slides you will review:

Simplifying expressions with radicals – try to use all the root powers and don't forget rationalizing denominators

In the next slides you will review:

Minimum of four word problems of various types. You can mix these in among the topics above or put them all together in one section. (Think what types you expect to see on your final exam.)

In the next slides you will review:

Line of Best Fit or Regression LineA. When do you use this?B. How does your calculator

help?C. Give a set of sample data in

question format to see if your students can find the regression equation.

Did Ms. Hardtke forget any other major topics covered in Semester 2? If so, add additional slides of your choice.