Mental Math: Making Tens

Date: 09/16/2003 at 19:47:15
From: Ralph
Subject: my child's math homework

She is learning mental math strategies, butthere are no explanations 
with her homework pages.  There is mention of the "make a ten"
strategy, but no examples.  I have never heard of this, although it
might be a new name for an old concept. 

Here is a sample problem:

  89 + 24 
  Change one number to a multiple of 10: ______  
  Adjust the other number: ________ 
  Add: _____________

Date: 09/16/2003 at 20:16:09
From: Doctor Achilles
Subject: Re: my childs math homework

Hi Ralph,

Thanks for writing to Dr. Math.

I think that "making a ten" refers to the following strategy.

If you are adding 2 numbers together, you can mentally add 1 to one 
of them if you mentally subtract 1 from the other.

For example, 46+55 is equal to 47+54.

Or, a more useful example, 36+59 is equal to 35+60.  35+60 is a much 
easier problem to do in your head because you can see right away that 
the one's digit will be 5, then you just add the ten's digits 3+6, 
and get 9.  So your answer is 95.

For the problem 89+24, you can mentally change that to 90+23.  That 
comes out to be 113.

You can also add 2, 3, 4, 5, or even 10, 11, 13, or even 23, 24, 
whatever you want to one number in the problem AS LONG AS YOU 
SUBTRACT THE *SAME* NUMBER FROM THE OTHER.

For example, the problem 87+34, you can add 3 to 87 and subtract 3 
from 34.  That gives you 90+31, which is easier to do.

You can do the same thing with even more complicated problems, like 
346+175, you can add 25 to 175 and subtract 25 from 346.  That should 
give you 321+200, or 521.

Another way you could have done the same problem is to first add 5 to 
175 and subtract 5 from 346, giving you: 341+180, then add another 20 
to 180 and subtract another 20 from 341, giving you 321+200.

The way I usually do mental math is to look for whichever one of the 
two numbers I'm adding that is closest to a "round number" and then 
add or subtract from that number as much as I need to get it and then 
do the opposite to the other number.

If you're curious, when you're doing subtraction, you can also add 
something to one number, but if you do that you have to ADD the same 
amount to the other number; similarly, when subtracting if you 
subtract something from one number you have to subtract the same 
amount from the other number.  

This explanation was not designed for an elementary school student, 
but I hope it has clarified the concept for you so that you can 
explain it to your daughter.  Best of luck, and please feel free to 
let me know if you would like clarification on anything.

- Doctor Achilles, The Math Forum
  http://mathforum.org/dr.math/