I enjoy math and have been good at it most of my life. Over the years, I have tutored many people in all levels of math from upper elementary school to calculus. Most of the materials on this page had their origins in those tutoring sessions.
These are organized roughly into the different areas that middle and high school students, as well as college students, are likely to encounter. There is always a bit of overlap, as each field of mathematics builds upon the previous. If you can’t find what you are looking for, please look around. If you would like to suggest a resource for me to add, please contact me.
Please note that these handouts do not constitute a curriculum of any sort, nor are they meant to. They are simply summaries that I and the students I’ve tutored have found useful. If you are a teacher or college instructor, and would like to use these in your classroom, please read my permissions page. Thank you.
Click on each title below to view the resources available. Items with a red check mark () are new in the last 90 days. Items with a blue chevron () have been updated in the last ninety days.
A thorough grounding in basic operations (addition, substraction, multiplication, and division) lays the foundation for later success in mathematics. Math is often more difficult for students in middle and high school than it need be, simply because they lack basic arithmetic skills.
- Addition Facts table (small) can be cut out and pasted inside a folder or book cover.
- Addition Facts table (large) can be punched and kept in a notebook.
- Addition Flash Cards
- Multiplication Facts table (small) can be cut out and pasted inside a folder or book cover.
- Multiplication Facts table (large) can be punched and kept in a notebook.
- Multiplication Flash Cards
Algebra is the gateway to higher mathematics. There isn't a single field of mathematics where algebra isn't used. Unfortunately, many people think of algebra as difficult. There are aspects that are challenging, but at its root, you are using a group of known numbers to find one or more unknown values.
- Properties of Real Numbers — long version (2 pages — Added 7 Oct 2014)
- Properties of Real Numbers — short version (1 page — Updated 12 Oct 2014)
- Algebra Basic Formulas distance formula, midpoint formula, Pythagorean theorem, slope formula, and quadratic equations (1 page — Added 12 Oct 2014)
- Arithmetic Operations in Algebra — How to factor out common factors, multiplying and dividing by rational expressions, adding and subtracting rational expressions, dividing rational expressions (2 pages — added 14 March 2015)
- Properties of Exponents — (1 page — Added 14 March 2015)
- Factoring Formulas — (1 page — Added 13 March 2015)
- Set Theory — An Introduction — (3 pages — Added 13 Oct 2014)
There are two opposing schools of thought when it comes to geometry. One holds that geometry is a great place to teach the use of logic. Hence, the study of theorem and postulates and an emphasis on proofs. (This is the geometry that I had in high school and I loved it.) The other holds that geometry is merely a tool (albeit a highly useful one) in science and engineering.
This is a case where you can have it both ways. Geometry is a highly useful tool, and the best part is that you can master the basics in less than a day. But when you study it for its own sake, it is both beautiful and fun.
More to come.
Unfortunately, trigonomety is often still taught as if all its practitioners are going to be navigators or surveyors. The true value of trigonometry is in understanding periodic functions and their use in science. A thorough understanding of the unit circles underlies your success with the subject.
- Trig in a Nutshell — (4 pages — Added 7 November 2014)
Calculus models real life much more accurately than algebra. It is not difficult, but a solid foundation in algebra and trigonometry is required. Once you understand the basic concepts (such as limits and derivatives), much of calculus is simply applying algebra.
More to come.
Need some graph paper? Download a file and print it out. (These look great printed in color. Not so great printed on a laser printer.)
Each of the following a zip file, each containing that type of graph paper in six different colors: cyan, yellow, magenta, green, dark grey, and light grey.
Miscellaneous graph paper
- 4-up graph paper
3x3 inch square, 8 lines per inch, with axes.