Category: Concepts

Logarithms

Explanation of logarithms: what are they, when are they useful, in what ways can logarithmic expressions be rewritten (laws of logarithms), and descriptions of the most common situations in which they are likely to be encountered or needed.

Quadratic Equations: How to Solve Them Algebraically

How to solve a quadratic equation by factoring or completing the square, with exploration of why these approaches work. Exploration of why solution techniques that worked for linear equations do not usually work for quadratic equations.

Multiplying Polynomials and FFFT!

Multiplying polynomials is easy once you have learned this approach. It works for any polynomials, including monomials, binomials, and trinomials. Exploration of how this is nothing more than a long-winded instance of the distributive property at work.

Angle Measures

Exploration of ways of measure the size of an angle: fraction of a circle, degrees, or radians. How to convert between differing measures of the same angle. Includes some reasons why 360 degrees is a convenient measure of a full circle.

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

Algebra Intro 6: Multiplication

We have all known our multiplication tables for years, and have successfully answered questions like “what is 6 times 7?”, but do we really understand what multiplication represents? Repeated Addition One interpretation of multiplication, which only works when multiplying by an integer, is “repeated addition”. From this perspective, “6 times 7” is a compact way to…… Continue reading Algebra Intro 6: Multiplication

Algebra Intro 7: Properties of Multiplication

Properties Of Multiplication Do the patterns that applied to addition also apply to multiplication… do the following all produce the same result? $latex 3 \cdot 5 \cdot 7 \\*~\\*3 \cdot (5 \cdot 7) \\*~\\*(3 \cdot 5) \cdot 7&s=2&bg=ffffff&fg=000000$ After carefully following the order of operations, we see that they all result in a value of 105.…… Continue reading Algebra Intro 7: Properties of Multiplication