Tag: Algebra

Negative Differences

Math problems often include negative differences. Familiarity with ways of manipulating them will help to both avoid common errors and recognize equivalent expressions.

Geometric Sequences and Geometric Series

How to recognize, create, and describe a geometric sequence (also called a geometric progression) using closed and recursive definitions. Formulas for calculating the Nth term, the sum of the first N terms, and the sum of an infinite number of terms are derived. Also describes approaches to solving problems based on Geometric Sequences and Series.

Arithmetic Sequences and Arithmetic Series

How to recognize, create, and describe an arithmetic sequence (also called an arithmetic progression) using closed and recursive definitions. Formulas for calculating the Nth term, and the sum of the first N terms are derived. Also describes approaches to solving problems based on arithmetic sequences and series.

Linear Systems: Why Does Linear Combination Work (Graphically)?

A system of linear equations consists of multiple linear equations. You can think of this as multiple lines graphed on one coordinate plane. Three situations can arise when looking at such a graph. Either:1) No point(s) are shared by all lines shown2) There is one point that all lines cross through3) The lines lie on top…… Continue reading Linear Systems: Why Does Linear Combination Work (Graphically)?

Where’s the mistake?

I have started a separate blog devoted to helping students learn to find mistakes in worked problems (their own, or someone else’s). If this is of interest, check it out: http://mathmistakes.wordpress.com/ 7/17/11 Update: There can be great value in work that contains mistakes. Learning to catch your own mistakes is a critical life skill, as is…… Continue reading Where’s the mistake?

Algebra Intro 1: Numbers and Variables

This post begins a series intended to help introduce or re-introduce some of the core concepts of Algebra. It is often very helpful to re-visit these concepts with students who may have memorized their way through previous math courses without slowing down to contemplate some of the concepts behind Algebra. Numbers Numbers are used in…… Continue reading Algebra Intro 1: Numbers and Variables

Algebra Intro 2: Addition

Mathematical thinking probably started with addition. Someone may have combined two piles of bricks, and wondered how many were in the single large pile. Addition is the mathematical term that describes “joining quantities together”. Properties of Addition Looking at the patterns that can occur when quantities are joined together, you might have noticed that it does…… Continue reading Algebra Intro 2: Addition

Algebra Intro 4: Negative Numbers, Zero, Absolute Values, and Opposites

Negative Numbers Negative numbers are something new and interesting to think about. What do they mean? They arose from changing the order in which we subtracted two numbers. While we usually think of a “difference” by starting our thought process with the larger number, when we fail to do that and try to “take away”…… Continue reading Algebra Intro 4: Negative Numbers, Zero, Absolute Values, and Opposites