Algebra is a combination of: A notation system for representing quantitative relationships, andA set of rules for manipulating notation without changing the underlying quantitative relationship that it represents. Why is algebra needed? Because: The notation provides a concise and commonly accepted way of accurately communicating quantitative relationships, andChanging the appearance of the notation describing a relationship,…… Continue reading What Is Algebra?
Category: Concepts
Why Quadratics?
Exploration of why quadratic equations are worth learning about: how they are related to linear equations and other polynomials, some of the skills students will learn by studying quadratics, and examples of where quadratic equations are useful outside of math class.
Keep Your Eye On The Variable
The following equations all have a similarity: $latex y = |x – 8| + 5\\*~\\*y = 4(x – 6) – 7\\*~\\*(x – 3)(13x + 11) = 0\\*~\\*y = (x + 1)^2 – 9&s=2&bg=ffffff&fg=000000$ The similarity is that they all have expressions like (x- 6) or (13x + 11), which are often either translations or factors.…… Continue reading Keep Your Eye On The Variable
Life Skills Learned In Math Class
Descriptions of life skills (skills useful in daily and business life) learned in elementary through high school mathematics courses.
Analyzing Linear Equations: a summary
Explanation of key linear equation concepts: slope, intercepts, and equation forms. Discussion of how slope-intercept form, point-slope form, and standard form are related to one another. Includes general descriptions of the various starting points a student is likely to encounter in problems, and how to proceed from there.
Equivalence Deserves More Attention
Most students taking courses in Algebra or higher seem quite comfortable with the idea of “equivalent fractions”: improper or unsimplified fractions all of which evaluate to the same decimal value. An example would be $latex \dfrac{2}{3}=\dfrac{4}{6}=\dfrac{12}{18}=\dfrac{60}{90}=0.\overline{666}&s=2&bg=ffffff&fg=000000$ To create such fractions, multiply whatever fraction you wish to start with by 1 (the multiplicative identity) in the…… Continue reading Equivalence Deserves More Attention
On the origin of algebra problems
As you are solving a math problem, have you ever wondered how textbook authors come up with algebra problems that have simple answers? Just as you use inverse functions to solve an algebra problem, problem authors reverse the solution process to create a problem: they start with the answer. From there they use the same…… Continue reading On the origin of algebra problems
Word Problems… !#$%@;*!!
Word problems can be… frustrating. Most of their reputation arises from their use of words to describe a quantitative problem. And if the problem’s author did not choose their words very carefully, you’ve got Trouble (with a capital T). So why are so many word problems assigned? Because they are more similar to the quantitative…… Continue reading Word Problems… !#$%@;*!!
Problems fall into four categories
Description of a useful way of categorizing math problems: easy, medium, ugly, and hard. When studying for quizzes or tests, make sure to seek out “ugly” problems if you have not solved many yet.
Operations are taught in pairs
Many High School students I have worked with have not spent much time pondering the sequence in which math topics were taught to them. So, it can be interesting to step into the “waaay-back” machine and investigate this question a bit: What was the very first arithmetic operation you were taught (probably in first grade)? What…… Continue reading Operations are taught in pairs
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