1. Do You Always Count ‘Up’? 

Dear Mathman  
I was wondering, are you supposed to count up or can you count down? I feel like I count up and to the right in my mind, but I was talking to my friend and she said she does it from right to left. I know it may not be important, but it’s got me confused. Which is the right way?  
-Emma, Linwood Primary School,  

Hi Emma,  
When you throw up a ball into the air, it may go a metre up. But of course it will then come a metre down again. We don’t say we threw it a metre down, only that we threw it a metre up, but we could, just as easily. I think it’s the same with counting.  
To some people the numbers may go upwards in their imagination, to others, downwards. They may even count along. I knew an artist who thought of the numbers as just getting fatter from the middle out! When you stack blocks on top of each other you may take note of them climbing or only take notice of them when they fall.  
The important thing to remember is that numbers don’t get bigger - they are all the same size – it’s their values that increase. And a so-called higher number isn’t necessarily more. For instance, 96 peanuts isn’t bigger than 1 car. Nor is a ‘higher’ number better. Some think that millions and millions is somehow better than three and a half. But they’re only thinking of money. What if it was germs!  
I think how you count is up to you. There is no right way to think, we’re all different, and that makes life interesting. So I would say both you and your friend are right.  
Thanks for an interesting question.  
M  
 

Dear Mathman  
We were wondering whether zero is positive or negative.  Also is it an even or an odd number? Mrs  Meehan’s standard 4 class would like to know.  

Hi class!  
First your second question. Zero is neither a positive number NOR a negative number.  We say  that a number is positive if it is greater than zero (so, zero can’t be positive), and a number is negative if it is LESS than zero (thus zero can’t be negative).  
Zero is a very special number in that it’s not positive OR negative.  
Why?  For all of the other numbers, there are both positive and negative numbers.  So if someone gives you $2, then you have +$2 in your pocket.  But if you pay someone $2, then you have -$2 in your pocket.  You have TAKEN AWAY $2. But can someone pay you -$0??  You can, but it won’t make much of a difference in how much money you have.  And if you pay someone +$0, it also doesn’t have much of an effect.  So it looks like +0 and  -0 give the same answer, and so +0 and -0 really don’t mean much and we can just use 0 in their place.  
What about even nor odd?  Let’s think about what numbers are EVEN: 2, 4, 6, and 8, among others.  What is the SAME about them?  Well, you can take some number and multiply it by 2 to get each of those numbers.  For example, how can we find 6?  We take 2 x 3 (three two times).  How can we find 8?  We take  2 x 4.  
Now let’s look at zero.  Can we multiply two by any number and get 0?  YES! We can take 2 x 0 = 0.  So that proves that 0 is EVEN, right??  So long as we think of zero as being a number. But let’s look a little further.  3 x 0 = 0.  4 x 0 = 0.  5 x 0 = 0.  In fact, ANY number times zero is equal to exactly zero, so that really isn’t a good way to show that zero is even.  
We can TRY to show zero is odd, though.  If a number is odd, then there isn’t a second whole number that you can multiply by two to get it.  For example, to find 5, you can try 2 x 2 = 4, and 2 x 3 = 6. 4 and 6 are right around 5, but there isn’t a whole counting number between 2 and 3 that you can multiply by 2 to get 5.  And we already showed that 2 x 0 = 0, so 0 can’t be odd using that argument.  

Dear Mathman  
The kids reasoned that the numbers follow an even-odd-even-odd pattern. Since they are sure one is odd then the number both before and after one must be even. They definitely agree with you that zero is an even number.  
(Thanks to Math Forum)  

3. What is 845+904=? 

Dear Mathman  
My name is Maxine. I want to know the answer to this problem. Thanks for your help.  
P.S Is there a Mathwoman?  

Dear Maxine:  
You were wondering how to add 845 and 904.  
I first write one number above the other, making sure that they line up so that the digit that is the farthest right in one number always is lined up with the digit that is farthest to the right in the other number.  So in this problem, I would write:  

                         845  
                       +904  
                        —-  

Then I start to add, starting with the ones digits, which are the digits the farthest to the right.. I add the one on the top and the one on the bottom together  (5+4=9),  so I write:  

                     845  
                   +904  
                     —-  
                     ??9  

Then go to the tens digits, the digits just to the left of the ones digits, and add them together.  So we have:  
  

                845  
              +904  
                —-  
                ?49  
Now all that is left to do is add the hundreds digits together.  The  
hundreds digit is just to the left of the tens digit.  So, we get for our  
final answer:  

                845  
              +904  
                —-  
               1749  

Good luck!  
And yes, there are lots of Mathwomen! Even in your school.