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Place Value and Different Bases
by Gail Englert

A response to the question:

How do I get my daughter the help she needs without spending a fortune on tutors?

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My daughter is generally a good student but has been starting to slip in her math during the last two years. She is not failing but she tells me she just doesn't understand. I don't understand either; I was never very good in math myself. How do I get her the help she needs without spending a fortune on tutors?

Cindy

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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 according 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 T2T service

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