# The IntMath Newsletter - Feb 2008

By Murray Bourne, 17 Feb 2008

1. Changes to the IntMath Newsletter
2. Real life math example - CO2 levels in the atmosphere
3. This month’s math tips - Divisibility
4. Poll Results
5. More from the math blog

## 1. Changes to the IntMath Newsletter

The newsletters have been getting longer and longer over the last few months (I have so many things I want to share with you ^_^). There was feedback last month that it was getting a bit too long and readers didn't have enough time to read everything.

I have listened and I will make the newsletters shorter and send them once every fortnight, instead of once a month. I hope that's OK with everybody.

You can expect the newsletters to come out around the 1st and 15th of each month.

## 2. Real life math example - CO2 levels in the atmosphere

One of the most important posts I've written in the math blog recently is about modeling the carbon dioxide increase over the last 50 years.

A model is an equation that describes the relationship between 2 (or more) variables, usually based on observations. Modeling is a really interesting part of mathematics, but most students never get to see the process.

The mathematics behind the CO2 model is interesting, but the most important thing in the article is that increase in CO2. We are headed for a climate melt-down if we don't do something serious about it now. We can all do something to help, from reducing our energy needs, reducing our consumption of items that destroy forests (like paper) and using public transport instead of gas-guzzling cars.

Read the article at: Earth killer - composite trigonometry CO2 graph. It includes applications of trigonometry, exponential and polynomial graphs. And it's real.

## 3. This Month's Math Tips - Divisibility

Last month we saw how to easily check if a number can be evenly divided by 2, 3, 5, 6, or 9.

We also learned that such tricks can help when we are factoring. Another place where you can use these tricks is when you are adding or subtracting fractions and trying to find lowest common denominators.

Divisibility by 4: If the last 2 digits are divisible by 4, then the whole number is divisible by 4.

For example, 528 is evenly divided by 4 because 28 is evenly divided by 4.

However, 3,257,918 is not evenly divided by 4 because 18 is not divisible by 4.

Divisibility by 11: Let's do an example first and then describe the rule.

85,217 is divisible by 11 because:

8 - 5 + 2 - 1 + 7 = 11

The final answer is divisible by 11 so the whole number 85,217 is divisible by 11.

The rule for divisibility by 11 is to work left to right, subtracting and adding alternate digits. If the final answer is divisible by 11, the number is divisible by 11.

Another example:

80,916 is divisible by 11. Working left to right, subtracting and adding we have:

8 - 0 + 9 - 1 + 6 = 22

And 22 is divisible by 11 so 80,916 is divisible by 11. Can you figure out why the divisibility test for 11 works?

So now you know the divisibility checks for 2, 3, 4, 5, 6, 9, 10 and 11.

## 4. Poll Results

Last month's IntMath poll asked if users prefer to study for a math test alone, or with friends. The response by 1000 voters was:

Alone: 72%
With a group of friends: 14%
With 1 friend: 14%

This reminds me of the time that I thought two of my students were cheating in tests because they kept getting the same answers. I separated them for the next test but they still got the same answers - right and wrong. It turned out that they studied together and had learned the same ways (right and wrong) to do the math problems. Of course, I apologized to them...

## 5. More from the Math Blog

1) Friday math movie - The Amazing Abacus
The abacus is still widely used in Japan. This movie shows how some students can multiply really quickly, without even using the abacus!

2) Learning math in Cameroon via the Web
A reader from the African country of Cameroon has written some interesting things about life in Cameroon, including studying for an engineering degree without having an engineering school in the whole country.

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