Showing posts from August, 2007

Percent of change

When some quantity changes, such as a price or the amount of students, we can measure either the absolute change ("The price increased by $5" or "There were 93 less students this year"), or the percent change.

In percent change, we express WHAT PART of the original quantity the change was.

For example, if a gadget costs $44 and the price is increased by $5, we measure the percent change by first considering WHAT PART $5 is of $44. Of course the answer is easy: it is 5/44 or five forty-fourths parts.

To make it percent change, however, we need to express that part using hundredths and not 44th parts. this happens to be easy, too. As seen in my previous post, you COULD make a proportion to find out how many hundredths 5/44 is:

5/44 = x/100

To solve this, you simply go 5/44 x 100, which is easy enough to remember in itself. In fact, this is the rule often given: you compare the PART to the WHOLE using division (5/44), and multiply that by 100.

There were 568 students one…

A free download of a digital Algebra 1 book

Kinetic Books Algebra 1 looks really interesting! It is not really just a book, but software, or a digital interactive textbook.

It contains text, interactive problems and activities, and a scoring system all on the computer. Students can get step-by-step assistance in the form of audio hints and one-click access to relevant examples.

See a demo here. But the best is that the company Kinetic Books is even offering a free download of the product till September 30!

That really sounds fantastic, so if you have algebra 1 student(s), don't fail to take advantage of this tremendous offer.

Equation wizard

Back last spring I promised I'd write something about this tool, so here goes.

Equation Wizard is a software, a tool, that solves first, second, third, and fourth degree equations, simplifies expressions, and calculates values of complex expressions.

I had my assistant use it when checking and making answers to my Algebra 1 worksheets.

Based on our experience, the tool works really well and was useful, for example with rational expressions, or checking answers to equations.

The two features I was missing were:
1) The ability to solve (even simple) systems of equations. There's quite a bit of work when solving a bunch of these by hand!
2) The ability to give exact roots (in our case to second-degree equations). It only gave them as decimals.

See screenshots and more here:
Equation Wizard
You can even get this software for free, with something called "TrialPay".

TrialPay allows you to purchase products by trying something else. Sign up with any one of our preselected partners a…

Measure the circumference of the earth - contest

I got word of an interesting contest where school children will form teams and attempt to measure the circumference of the Earth using the same method as Eratosthenes used back in ancient times.

Any students from USA, Mexico, and Peru can form these teams, whether homeschooled, after-schooled, public schooled or whatever.

Whether you will participate or not, go see the animation that explains the method Eratosthenes used (in the left sidebar).

This sounds like an exciting opportunity to connect geometry, measuring, and math history in a project!

And here's some more information:

Please help us get the word out on this new, exciting student centered event!

Measure Your World!

Join us this fall as we pilot a new student-centered project where teams from the United States, Chile, and Mexico partner to replicate the technique introduced by Eratosthenes to determine the circumference of the Earth. Around 240 BC, Eratosthenes used trigonometry and knowledge of the angle of elevation of the Su…

Changes in the blog appearance

I upgraded the blog template to the new one that Blogger provides, and then added the searchable "labels" in the side bar.

So now you can click on any of those "labels" (down on the right side), and find my past posts on that topic. I've written nearly 300 posts since I started the blog (in late 2005). Of course not all of those posts are of mathematical topics, but there is still quite a bit of material that is still as good as ever.

Hope this new feature improves the functionality of this blog. Enjoy reading!

Some percent basics

The word "percent" means "per hundred", as if dividing by hundred — a hundredth part of something.

We treat some quantity (say 65 or $489 or 1.392 or anything) as "one whole". This "one whole" is then divided to hundred equal parts in our minds, and each such part is one percent of the whole.

If the "one whole" is 650 people, then 1% of it would be 6.5 people (if you have a practical application, you'd need to round such an answer to whole peoples of course).

If the "one whole" is $42, then 1% of it is $0.42. Also, 2% of it would be $0.84.

So to find 1% of something, divide by 100.
To find 24% or 8% or any other percentage, you can technically first find the 1%, then take that times 24 or 8 or whatever is your percentage.

For example:
To find 7% of $41.50, first go $41.50/100 to find 1% or 1/100 of $41.50, then multiply that by 7. But this is the same as (7/100) x $41.50, and 7/100 is 0.07 as a decimal. In most calculat…

Master's degree in mathematics teaching and learning

First of all, I've updated my post about the percent problem — just scroll down to it.

Then, I thought maybe I have some math teachers in my readership that might be interested in a new Master's degree program offered by the university of Drexel, in collaboration with the Math Forum!

Knowing how much expertise the folks at Math Forum have this might be a unique opportunity for those math teachers who want to extend their education.

Online Master's in Mathematics Learning and Teaching - "Preparing teachers to incorporate creative, problem-based, student-centered instruction in their classroom."

The rest of you... can just continue reading my blog : )
I will post some more about the concept of percent soon.

Latex to images - online tool

Here's a handy math tool for those who know Latex (university folks and such). You type in a n mathematica expression using Latex language, and it makes an image. It even gives you a readily copyable code you can paste to a webpage.

Here's an example of one such image; it's hotlinked from their server.

So many percent more

Updated with an answer... see below

I'm continuing to catch up after vacation, and spotted a good discussion about problems with percent, at MathNotations. (via Let's Play Math blog).

Here's a problem to solve, first of all:

There are 20% more girls than boys in the senior class.
What percent of the seniors are girls?

The answer is NOT that 40% are boys and 60% are girls...

You see, let's say there were 40 boys and 60 girls, 100 students total. If there are 40 boys, then 20% more than that would be 40 + 4 + 4 = 48 girls and not 60!

Try solve it. I'll let you think a little before answering it myself. Don't just rush over to the Mathnotations blog either! Use your thinking caps! I've already given you a big hint!

You can easily solve this problem by taking any example number for the number of boys. Like I did above, if you have 40 boys, you'd need 48 girls and there'd be 88 students total. What percent of the seniors are girls then? It'd be 48/88 …

Geometry fun with GeoMag

While on vacation, a friend of mine gave my older daughter a set of Geomag. You might already know about it, but it was new for us.

This has proved to be a fantastic learning toy! She's thoroughly enjoying building various shapes.

For example, she made a cube with sides 2 bars long and was proudly explaining to me how to do it: "First do a square, then put legs up from each corner, and then another square."

I made a tetrahedron that also had 2 bars on each side, according to the model. She thought it was neat and built that one several times herself last night.

I can see how the toy can help build geometric insight and beautifully demonstrate the common three-dimensional figures.

We've already ordered another set to accompany the small 42-piece set she got. You can find Geomag kits of various sizes and colors at Amazon.