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Q&A #332


Place value and different bases

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From: Gail (for Teacher2Teacher Service)
Date: Jun 09, 1998 at 19:11:47
Subject: Re: Helping child with math

Dear Cindy,

How old is your daughter? I am a fourth grade teacher, and I find that sometimes 
students who have been very good at memorizing basic facts in the past start to 
stumble a bit during the year I have them, because they memorized without really 
understanding what they were doing. 

Many of the concepts in the upper elementary grades hinge on place value. Are you 
comfortable playing around with other bases? For example, in Base ten (our system) 
there is a ones place, a tens place, a hundreds place, etc. Really, the places are 
ones, tens, ten times tens place, ten times ten times tens place, etc.  

In base six you would have ones, groups of six, groups of six times six, groups of 
six times six times six... etc. You can use beans to represent this. Single beans 
are ones. As soon as you have six of them, put them in a little cup (for "10").  
When you have six cups (with 6 beans in each cup) you  transfer them all into a 
larger cup (a bucket).  And so on...

So if you were working in base six, you would count like this:

0,  1,  2,  3,  4,  5,  10  (read this "one zero" - it means that you have one 
                             group of six, and no ones)  
  11,  12,  13,             ("one three"  means you have one group of six, and 
                             three ones)
  14,  15,  20               and on up to 
  53,  54,  55,  100        (which means you have one group of six times six, no 
                             groups of six, and no ones).  

You can go on counting this way, reinforcing the idea of place value.

The same thing can be done with a different base. What your child will start to 
see is the relationship between the digits accroding to place value. Once that is 
clear, use the other bases to add and subtract using the buckets, cups and beans.  
It will become pretty obvious why we regroup when we add and subtract.

Let me know if this helps, or if you have more questions...   
 
 - Gail, for the Teacher2Teacher service

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