Homeschool Math Blog

Maybe many of you already know about this, but I feel I am behind times sometimes. :) Desmos is a fantastic free online graphic calculator. It is super easy to use, also. It starts drawing the graph while you're still typing! Users can save graphs... see for example this one: a function, its derivative, and tangent drawn to a point . You can change the function as you wish. I changed it a little bit, and this is what I got: Here's another example: Riemann sums that someone created. Again, you can change the function and other parameters. The graphs can also be printed, emailed, and embedded on web pages.There's lots you can do: parameters (with sliders), inequalities, piecewise functions... In fact, many users have used it as a drawing platform by creating a bunch of piecewise functions, and so they come up with pictures like this one:

Today I wanted to highlight two companies that both offer lots of free high school level math materials in the form of videos. These are real, commercial companies, yet they have chosen to offer the videos online for free. Both have something else they sell, hoping to make some money obviously from that part of the business. The video content can really be of help for all students, teachers, or parents who need additional help with high school math (algebra, geometry, calculus). And since I'm highlighting these two, if you have a topic you have trouble with (such as polynomials or factoring or inequalities) you can even check out videos for that topic in both places. 1) BrightStorm Math . They currently have over 2,000 videos available for free - a free registration is required though. Algebra through calculus. What they are selling is test preparation courses. 2) MathTV.com MathTV.com has over 6,000 free math videos, including some in Spanish. Prealgebra through calculus. What the...

This review has been moved here .

I have recently had the pleasure to add Make It Real Learning workbooks to my site. These books contain real-life math activities with real-life data, companies, and situations. They are written by Frank Wilson. Arithmetic I Fractions, Percents, and Decimals I Linear Functions I Calculus I Periodic and Piecewise Functions I Some examples of the topics included in these activities are: cell phone plans, autism, population growth, cooking, borrowing money, credit cards, life spans, population growth, and music downloads. But there are many more, more than I can list here. As students work through the problems, they can use the math skills and concepts they have learned in their math curriculum (such as the concept of average or graphing), and apply those to a situation from real life. Each activity-lesson in the book contains several questions about the situation, starting with basics and going into more in-depth evaluations, and should be adequate for one-two complete class periods. W...

Just a fun little song (parody of "I will survive") for all of us who've taken calculus.

This story is fascinating; they found a long-lost works of Archimedes under the text of a prayer book, and used modern technology to "see" under the prayer text. After the text was recovered, it was discovered that Archimedes actually found some of the principles of calculus , and used them to figure out volumes and areas. He dealt with "actual" and "potential" infinity, which is exactly what calculus is about. And he lived thousands of years before Newton! A long-lost text by the ancient Greek mathematician shows that he had begun to discover the principles of calculus.

I got a question, " I am supposed to teach my calculus class one lesson. That lesson has to be on something that can be applied to whatever I am hoping to major in. I am planning on studying pre-med to become a doctor. Could you tell me how doctors apply math learned in calculus 1?" I suspect doctors don't actually use any calculus in their daily work with people. BUT, it is used in medical research and analysis. For example, calculus concepts are applied in studying how medicines act in the body. I found an article called Half-life and Steady State that talks about how the patient might be taking a medication and all the same time the body is clearing the previous doses... Eventually there comes a "steady state" where the amount of "the amount of drug going in is the same as the amount of drug getting taken out." QUOTE Many drug effects occur primarily when the blood level of the drug is either going up or going down. When the drug reaches steady s...

You can learn calculus concepts starting from the formula distance = velocity * time . Yes, that's true. That's what the book Calculus Without Tears is all about. It starts from the simple situation of a runner running with constant speed (velocity), and goes very step-by-step into actual calculus concepts, such as derivative, area under curve (integration), and differential equations. The idea of the book is to make basic calculus concepts accessible to younger students, without need of much algebra. Like I said earlier, calculus is the mathematics of change. It is usually studied as the last course in high school, or early in college studies. So should one study it earlier? I am sure people have varying opinions on that. Certainly the aim of this book is NOT to further crowd the "mile wide" mathematics curriculum. But it provides something extra for gifted kids, or for students very interested in calculus and math (and physics). It also provides an alternative way...

I recently read a calculus book (actually two) that brought me to reflect what IS calculus. First of all, let me state what calculus is not: Calculus is NOT the epitome of math, the highest mathematics there is, or anything such like. So what is calculus? It is basically the mathematics of change. Calculus allows us to study a thing that's changing (represented by some function), and the RATE of that change. I'll give you an example. Suppose you have a graph like the one below. Maybe this function (the red one) is depicting how temperature (or voltage or some other thing) changes over time. The black straight line is a tangent to the function - in other words it "touches" the function in one point. The steepness of the tangent tells us how steep the function itself is going at that point. Imagine that the tangent (the black straight line) was drawn into a point a little further on the red graph. The red function is increasing but it's coming to a 'hill'. W...