The IntMath Newsletter - Jan 2008

By Murray Bourne, 15 Jan 2008

In this Newsletter:
1. Math Tips
2. Math Software
3. The IntMath YouTube video
4. Attention Deficit
5. Poll Results
6. Spam
7. Latest from the math blog


Do you struggle with algebra? Most math students do - you are not alone.

One reason why a lot of people struggle with algebra is that they are not confident with number. If you use your calculator all the time, you tend to miss out on a lot of number skills. Algebra is basically just using letters in place of numbers. If you know how numbers work, algebra becomes much easier.

So this month's tips are about number properties that you might find useful.

You know that if a number is even, then that number can be divided evenly by 2, right? And if the last digit in a number is 0, then the number can be divided by 10.

Here's some more number divisibility tricks.

Division by 3, 6 and 9

You can check if a number can be divided evenly by 3 as follows.

Add the digits of the number. Can the sum be divided by 3? If so, the original number can also be divided by 3.

Example: The number 52,137 can be divided by 3 because

5 + 2 + 1 + 3 + 7 = 18

and we know 18 can be divided evenly by 3 (18/3 = 6).

However, the number 443 cannot be divided by 3 because

4 + 4 + 3 = 11

and 11 cannot be divided by 3 evenly.

Dividing by 6: If the sum of the digits of a number can be divided by 3 and the number is even, then it can be evenly divided by 6.

Example: The number 3,252 can be divided by 6 because

3 + 2 + 5 + 2 = 12.

Now 12 can be divided by 3 evenly and 3,252 is an even number.

Dividing by 9: Can the sum of the digits be divided by 9? Then the number itself can be divided by 9.

Example: The number 28,323 can be divided by 9 because

2 + 8 + 3 + 2 + 3 = 18

and 18 can be divided evenly by 9.

Dividing by 5: Does the number end in 0 or 5? If so, it can be divided evenly by 5.

Example: The numbers 420 and 476,375 can be divided by 5.

So now you have easy tests for whether a number can be evenly divided by 2, 3, 5, 6, 9 and 10.

Who cares? These number tricks can be very useful when you are factoring, especially when fractions are involved. The students who can recognise these number properties find such factoring much easier.

Watch for more number properties in future newsletters.


In November I conducted a poll on Interactive Mathematics and I asked 1000 users if they (or their teacher) uses math software.

I was quite amazed to read that 54% of users never use math software! Around 29% said that both they and their teacher use math software. The number saying they use it but their teacher does not was 9%. It was also 9% indicating that their teacher uses it but they do not.

Does it matter?

I think it matters a lot. Math software has radically changed the way we go about doing mathematics. It changes what we do, it changes what we need to learn in school and it changes what we can achieve - dramatically. Now that there are several good free computer algebra systems out there, there is little excuse for leaving this vital tool out of math lessons.

You may be interested to read these related articles in squareCircleZ:

Please comment on those articles in the blog and let me know how you feel about the use of math software in school.


I made a short video introducing trigonometric graphs.

Let me know (by commenting in the blog) if you like it!


The whole world is suffering from Attention Deficit Disorder! There are too many choices and too many demands on our time and attention.

One of the big problems is that we are addicted to communication.

Think about it - when most students are 'studying' they have their email open, they are using chat, they are meeting friends on Facebook, their mobile phone will ring, they will have several SMSs coming in and they are probably using the regular phone as well.

And the outcome? Often it's terrible time management and poor focus.

Does this make us happy? No, we are stressed all the time because we don't achieve as much as we know we can - and should.

Setting priorities is the most important thing we ever do. Brian Tracy in the book Eat That Frog says...

Successful, happy, prosperous people use their time far, far better than the average person.

Actually, setting priorities is a no-brainer. You just need to have the will-power to do it and make it work.

The Solution: First, write down all the things you want to (or must) achieve this week. Then decide which 6 are the most important.

Now, here comes the will-power part. Turn off all the communication devices - phone, email, MSN, Facebook, etc, and attack Task 1. Don't stop until it's done. Do the same each day (one vital task per day) so that you really achieve what you need to achieve. Enjoy the communication again after you have achieved your task. You'll have a 'warm inner glow' knowing that it is done.

Take a rest on the 7th day. ^_^

The 19th century steel magnate and multi-millionaire Andrew Carnegie used the above method. He said it contributed more to his success than anything else he did. He went on to say...

The ability to concentrate single-mindedly on your most important task, to do it well and to finish it completely, is the key to great success, achievement, respect, status and happiness in life.

For those of you who seem to have no time and have attention deficit disorder, the beginning of a new year is a good time to do something about it!

5. POLL RESULTS - Feelings about Math

The IntMath poll during December-January asked users about their feelings towards mathematics.

I am happy to report that 41% say that they "enjoy math". The proportion of those reporting that math is "OK but I find it hard" was 31%. Those who "hate math" was 22%.

Now I wonder if such a response would be common across all students, not just the ones who visit Interactive Mathematics?

The current poll asks about whether you prefer to study math alone, or with friends. You can vote on any page in Interactive Mathematics.


It has come to my attention that some intelligence-challenged person is spamming using my "" email address. I will never spam you or anyone. I hate spam.

Do you visit games sites? Or download sites? Take a spam quiz to see if you can spot the difference between 'clean' and 'spammer' websites. You may be surprised about the results.


1) In opinion polls, what does "margin of error" mean?
The Harris Poll finds that most people do not understand the concept "margin of error" in opinion polls.

2) McAffee's Site Advisor Spam Quiz
Take this spam quiz to see if you can spot the difference between 'clean' and 'spammy' websites.

3) Friday math movie - Angle Dance
Angle Dance is from Square One television, a PBS production that aimed to increase interest in mathematics.

4) Yet another computer-based math system?
Here's a computer-based mathematics learning system that gets students to obtain a good visual concept of mathematics before using number, symbols or language.

5) 21st century computer algebra literacies
A reader asked me to recommend a good Web 2.0 algebra tool.

Enjoy reading.

Be the first to comment below.

Leave a comment

Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can't mix both types of math entry in your comment.

Search IntMath, blog and Forum