Showing posts from November, 2006

Mathematicians with tongue-in-cheek

Have you ever heard of the mathematician Niholas Bourbaki?

"Near the middle of the 20th century, Nicolas Bourbaki published several mathematics texts in areas such as Set Theory, Algebra, Topology, Functions of a Real Variable, etc. These texts had a profound impact on the mathematical landscape of the day and their affect is felt to this day."

So what's so important about Bourbaki?

Well, he never existed! It was just a tongue-in-cheek joke!

It's quite an interesting and funny story indeed... go read it at Natural Blogarithms.

Square root problem

prove that

5√20 × √45 × √5 = 150√5
This is a quite easy problem. You use two basic "ideas" or properties relating to square roots:

* that √b × b is b - or that you can "pull out" a number times itself from under the root (this is just the definition of a square root of course).

* that √a √b = √ab - or you can combine the radicands under the same root when they are multiplied.

So √20 * √45 is equal to √20*45 = √4 × 5 × 5 × 9
= √2 × 2 × 5 × 5 × 3 × 3 = 2 × 5 × 3 = 30.

So that's the crux of that problem.

Math Mammoth Grade 5 Worksheets ready

I hope you're not tired of hearing this.... but this is what I've been busy with lately.

Just as of today, I got Math Mammoth Grade 5 worksheets ready and available for purchasing.

Like the others, there are two separate books, A and B, plus answer keys.

Price for the whole package is $10. And that includes 123 quality math worksheets all total.

Click the link to see sample worksheets.

And, I've also set up a volume discount for any of my math books:

For order totals at least $34 - a 20% discount.
For order totals at least $50 - a 25% discount.
For order totals at least $70 - a 30% discount.
Use coupon code 8A2301338 when ordering to get these discounts.

4th grade worksheets

I spent this last Saturday working on an idea that I probably should have done a long ago... making better use of my various worksheet generators.

I created a single page that has pre-made worksheets for 4th grade math. It's just long list of links, each of which generates a certain kind of worksheet. Should be handy for my visitors.

So these are still randomly generated, each time it's a new one. Just hit 'refresh from the browser and a new one is there.

And while building that page, I also fixed a few litte things in the generators, and added a few more options... For example, Fractions worksheet generator now has the option to make missing addend/factor/dividend sheets.

So hopefully with these changes they will better serve my visitors.

And yeah, I can hear some asking, "When are you going to do a similar page for 3rd or 5th grade?"

Well, I hope get such done before the year is over. We will see! I DO hope to get those done as well!

Multiplication trick

If you enjoy math 'tricks', here's one presented nicely in a slide show:

How to multiply numbers with 11-19 in less than 5 seconds

It explains how to multiply by 11, 12, etc.

And... here's a challenge (you can ask this of students, too):
After watching the slideshow, explain how it actually has very similar things going on as the standard algorithm.

In other words, how do the standard multiplication algorithm (in columns) and this one compare?

Math Mammoth Grade 4 ready

Just tonight... I got my Math Mammoth grade 4-A and 4-B workbooks ready and available online. One of them is $5.50 and the other is $5...

I've truly put a lot of effort on those so I hope the worksheets serve well those who buy them.

They're mostly designed for teachers, but I've had homeschoolers buy the other grades so I guess they're for whoever needs a 4th grade math workbook or worksheets.

You can download sample sheets here.

All sorts of websites

I'm just going to drill through a few links people have sent me, or that I've taken notice of, lately. Hopefully you'll find something of interest!

1) is a teacher located in Singapore and his site has video tutorials (in English) and a forum getting started.

2) Weekly Math Problems from NASA - download free weekly math problems in the setting of space weather... quite interesting! You'll find topics such as radiation dosages at Mars, exposure calculations, background radiation on Earth... would be perfect for science-minded high school students.

3) This one you'll get to laugh at... Newton's laws revisited.

Some examples:
BATH THEOREM: When the body is immersed in water, the telephone rings.

LAW OF THE RESULT: When you try to prove to someone that a machine won’t work, it will!

LAW OF BIOMECHANICS: The severity of the itch is inversely proportional to the reach.

And so on... click on the link to read more.

4) Mathematical Moments - a series of one-page P…

Worksheet generators

Someone pointed out to me how my addition worksheet generator had a bug: they couldn't make missing addend worksheets where the student is completing the next whole hundred.

Well I was able to fix it somewhat so now it works for that situation, as long as you don't choose step 2 for the value 2.

These generators... many people have mentioned how they like them. When I first made them, I didn't realize that putting so many options on them would make them not always work... not for every possible combination of options.

I figure that's why on most websites, math worksheet generators don't have many options!

But I made mine originally with as many options as I could possibly think of, because I figured teachers would like them that way! You know, you can choose the number of problems, how many rows, columns, font size, range of numbers including a 'step', missing addend or factor, switching value 1 and 2, etc.

So then it follows, that if you choose some step for v…

Mental math tricks

Some children might be delighted to learn math 'tricks' - curious ways to do calculations such as multiplying 2-digit numbers.

The 'tricks' do not contain any magic but are based on solid mathematical principles.

For example, to subtract any number from 1000 or 10,000 or any power of ten... just subtract from 999 or 9999 etc. and add 1.

Subtracting 10,000 - 2,596 with the usual method in columns, you will get into lots of borrowing over zeros... and end up having a row of nines to subtract from - except in the ones column where you have 10.

So 10,000 - 2,596 is quickly done by looking at each digit's difference to 9 - except in the case of one's digit, when you will subtract from 10. The result: 7,404.

Another 'trick' is called vertically and crosswise and applies to multiplication.

It can easily be proven to work using simple algebra. But it is a nice little mental math method that can impress kids.

Read more about that trick here. You can also practice onl…

Math Mammoth 3rd grade worksheets

... are ready as of today!

There are lots of sheets for multiplication concept and multiplication tables, division concept, geometry, measuring, for example.

Check out the sample sheets:

Math Mammoth Grade 3 Worksheets

Teaching integers

Recently I answered a question about teaching integers on an email list, and decided to post all that on my site as well.

Also, I spent a few hours making downloadable fact sheets about all integer operations - these are free.

The sheets try to include quite a bit about "why" the rules for adding, subtracting, multiplying, dividing integers work.

Teaching integers

Also I will answer here a question left on my site... there was no email address left so I couldn't answer via email.

how do you do this problems: elizabeth bought 3 1/3 pounds of tomatoes for $2.50. how much did she pay per pound?

Prices per pound are always given in [dollars per pound] or [dollars / pounds ].

This gives you the idea: you need to take the dollar amount and DIVIDE it by the pounds.

$2.50 ÷ 3 1/3 lb = $2.50 ÷ 10/3 lb = $2.50 × 3/10 = $7.50/10 = $0.75 per lb.

Math learning and unhappiness

Recently Brown Center published a Report on American Education with a special sector about the happiness factor in learning.

The report is based on 2003 Trends in International Mathematics and Science Study (TIMMS) data.

The TIMSS study found that countries in which kids report enjoying mathematics and feeling confident in it do worse in math than kids who report they don't like math and are not feeling confident in it.

American students are much more confident about their math abilities than Singapore students, yet they do far worse: Even the least confident students in Singapore outscore the most confident students in America!

Check the charts (slides) from the report... a PDF file. It's quick and easy to glance over for more details and charts.

The report author Tom Loveless was questioning the idea of teaching math so that students like it... that we don't need to always make math enjoyable.

I can almost hear my homeschooling readers' anger raising...!

But wait a minute.