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The following two to three day lesson will establish the conceptual understanding required for student to tackle complicated exponential expressions.
Exponents are tricky because students must balance a procedural fluency with a conceptual

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Inequalities can be taught as an isolated skill, but there is a lot of rich mathematics and connections that can be made.
The approach of this lesson is to create such connections and to help students to learn how to read and discover procedures

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By the time kids get to high school they either already have the order of operations mastered or no amount of remediation can help.
This two day lesson takes a different approach by setting up clever problems for the students where they change

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This PowerPoint is set up to introduce students to some key concepts about reducing algebraic fractions (rational expressions). They try a few simple problems and together you explore how they know what's right and wrong, and more importantly, why.

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This lesson is on addition/subtraction of Algebraic Expressions. The lesson addresses the conceptual short-falls that cause so much trouble with fractions, but not in a way that students will recognize as remediation.
The slides are animated and

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This test covers basics of numbers, factoring, some properties of real numbers, and reducing and then adding and subtracting rational expressions.
This is a test designed for a regular (non-honors) algebra 1 class, or a math 081 class.

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This is an activity that really helps students discover held misunderstandings about integer arithmetic and the order of operations together, but in a way that does not just leave them with a wrong answer. The activity itself promotes them chasing

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This lesson tackles a famous fast food internet problem in a way that develops the concepts students need to make sense of Algebra. It is done in a way that no formal Algebra is used, but instead is heavily reliant on language and logical

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This is a two day lesson that focuses on a balance of conceptual understanding to promote procedural fluency. The powerpoint is animated and has two short review videos at the end of each day.
By the end students should know what square roots

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This lesson teaches students how to read the equations in a way that promotes their understanding of mathematics as a written language. The methods taught promote understanding of the nature of Algebra and how it is related to the order of

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This lesson is designed for students that struggle with signed number arithmetic. The idea behind the lesson is that misconceptions need to be exposed in order for learning to occur.
This is not an in-depth, "Why this works," lesson, because at

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This is not simply a How-To lesson, but a Why lesson. Through this lesson we revert back to what square roots mean. (That information is taught in part 1, which can be found here:

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This lesson takes two days even though it is about just one single problem. To approach this problem students need to know what sectors, arc lengths, how to calculate volume and some basic understanding of surface area.
As such, this is a great

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This is a fantastic problem that draws from multiple concepts and abilities, yet is entirely approachable.
If your students are learning scale factor and conversion between units, this is a fantastic problem.
There are notes at the bottom of

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This is a one day lesson where students learn how to rationalize the denominator. The lesson could be stretched into two days because there are a lot of practice problems embedded.
Feel free to make use of what you like, change what you don't.

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Rational exponents is a topic that is traditionally "how-to" lesson. However, the notation has meaning. I'll explain in greater detail below.
This is a two day lesson that should have students able to convert between radical notation and rational

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This is a short one day lesson that exposes students to the difference between compound and simple interest. This is not a huge focus in the US for high school, but for those teaching Cambridge IGCSE, this is something that is tested.
For more

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This quiz has 5 conceptual questions about Algebra and inverse operations and 9 procedural problems. The answer key is included.
For more math-type stuff and such please visit my site: http://thebeardedmathman.com

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TEACHING EXPERIENCE

I've taught all levels of math typically taught in American High Schools as well as Community Colleges. The majority of my teaching now is with Cambridge IGCSE. The national average of participating students that pass is usually around 18%, but I've had only two students NOT pass in the 4 years I've been doing it. Beyond that, last year, for example, there were two students outside of my classroom in the entire nation that earned a top mark on the Cambridge IGCSE Mathematics test. I had four. I have developed methods of dialogue and conversation that the language back in mathematics, naturally, all while properly identify the roles of "teacher" and student. I am currently developing a website to help teachers and students achieve greater success in mathematics. It is very upsetting that kids graduate from high school only to have to take remedial math courses in college. It is my mission to limit this occurrence as much as possible. http://thebeardedmathman.com

MY TEACHING STYLE

I am truly a student center teacher. I guide and direct some of the avenues of exploration, but that is only to prevent us from chasing down rabbit holes that lead nowhere. I am more of a facilitator than a teacher and I empower my students to take charge of their learning.

HONORS/AWARDS/SHINING TEACHER MOMENT

Teacher of the Year at Rio Rico HS, 2014 10 total A-star recipients on the Cambridge IGCSE mathematics test

MY OWN EDUCATIONAL HISTORY

I've been teaching since 2006 at Rio Rico High School and Cochise Community College

ADDITIONAL BIOGRAPHICAL INFORMATION

I grow a mean beard!

GRADES

6^{th}, 7^{th}, 8^{th}, 9^{th}, 10^{th}, 11^{th}, 12^{th}, Higher Education, Adult Education, Homeschool

SUBJECTS

Math, Algebra, Arithmetic, Basic Operations, Fractions, Geometry, Graphing, Measurement, Numbers, PreCalculus, Word Problems, Algebra 2, Basic Math