What are “like terms” in algebra, why can they be combined, and how should they be combined? Both an intuitive and an algebraic approach are described, with examples.
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Simplifying Fractions
Fractions whose numerator and denominator share a common factor can be simplified. See why this is the case, with multiple examples to demonstrate the process.
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.
Negative Fractions
Explanation of why a negative sign can be placed, or moved to, in front of a fraction, in front of its numerator, or in front of its denominator, without changing the value of the fraction.
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.
Piecewise Functions and Relations
Introduction to definitions that are a combination of various functions or relations, each over a specific domain. Such definitions are called piecewise functions or relations. Shows how a piecewise definition can define a “smiley face” .
Polynomials and VEX Drive Motor Control
Your knowledge of quadratic (or higher degree) polynomial equations can be useful in solving issues that arise when writing the code to translate joystick movements into VEX drive motor outputs.
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)?
Successfully Asking Questions In Class
Do you ask questions in class at least once per week? For many students, the answer is probably “no”. Reasons for such an answer may include one or more of: – I don’t want to let my peers or the teacher know I don’t understand something – I am uncertain about what to ask… I…… Continue reading Successfully Asking Questions In Class
What A Parent Wants From A School
As a parent, I look for two categories of attributes when choosing a school for my child: – Ones which benefit my child directly – Ones which benefit my child indirectly, by helping others (teachers, parents) do their jobs more effectivelySchools that satisfy more of the attributes in both categories are likely to have happier…… Continue reading What A Parent Wants From A School
Domain, Range, and Codomain of a Function
Explanation of the terms “Domain”, “Range”, and “Co-Domain” of a function. These concepts provide a critical foundation for analyzing and graphing any function.
Roots and Rational Exponents: a summary
Exploration of roots as the inverse of exponents. Includes description of how the laws of roots mirror the laws of exponents, since expressions involving roots can be rewritten as expressions with rational exponents.
Short Assessment Grading: Add or Average?
Long assessments can waste precious class time unless there is much material to be assessed, but shorter assessments (with few questions) can cause small errors to have too big an impact on a student’s grade. For example, consider the following assessment lengths where each question is worth 4 points, and the student has a total…… Continue reading Short Assessment Grading: Add or Average?
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.
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