In a small school district in North Dakota, elementary students make Valentine’s Day card boxes to collect cards from their friends. Some students just write their name on their boxes, others go all out. Here’s what Kylee created.
Notice how she has the planets proportionate in distance and size? Hmmmm. Wonder if she used math? Good job, Kylee!
Check numbers are a method of checking addition. Sometimes, this is called Casting out Nines. Check numbers also works with subtraction, multiplication, and division. I like to think of check numbers as a cool tool for my math toolbox. Some people use check numbers frequently, others, not so much. However, if we don’t let people know about these cool things, we’ll never know who might use them!
Let’s look at how to find check numbers, then how to apply them. We also have a presentation on check numbers for you to review. Check numbers are first taught in RightStart™ Mathematics Level D, starting in lesson 47, and Level E, lesson 4, and Math Card Games, game #A63.
Finding Simple Check Numbers
Check numbers are one digit numbers from 0 to 8. We will designate the check numbers by using parenthesis.
Let’s start with a simple two-digit number: 17
Add the digits together: 1 + 7 = 8
Check number of 17 is (8).
Now let’s try another: 49
Add the digits together: 4 + 9 = 13
Remember check numbers are only one digit, so we’ll need to take the 13 found above, and continue to add the digits together: 1 + 3 = 4
Check number of 49 is (4).
Add the digits together: 9 + 9 = 18
And again: 1 + 8 = 9
However, remember we said that check numbers are from 0 to 8? There are no 9s. Now what? Well, all 9s are 0s. So, on this example, we have 1 + 8 = 9, and 9 = 0.
Check number of 99 is (0).
Because all 9s = 0s, we have a quick shortcut to help find check number.
Let’s back up to our second example: 49
If 9 = 0, then it looks like this: 4 + 0 = (4),
which is what we had the “long” way. Neat, right?
Let’s reapply to our third example: 99
Well, that’d be: 0 + 0 = (0)
Remember the other name for Check Numbers is Casting Out Nines. If we “cast” the 9s out, which is the same as 0, our work is simplified!
Finding More Check Numbers
Let’s find check numbers with a four-digit number: 4639
Add the digits together: 4 + 6 + 3 + 9 = 22
And again: 2 + 2 = 4
Check number of 4639 is (4).
Let’s try this again using some of our newly discovered shortcuts.
Remember, 9 = 0. 4639
We can “cast out” the 9, so now we have: 4 + 6 + 3 + 0
But 6 + 3 = 9, so let’s “cast” that out too! 4 + 0 + 0 + 0 = 4
Well! That was easy! Check number of 4639 is quickly found as (4).
Another one: 7326
See anything to “cast”? How about 7 & 2 and 3 & 6? Check number is (0).
Applying Check Numbers
So now that we can find check numbers, let’s use them!
Consider the following equation:
If you’re like me, you wonder if you added it correctly and often will double check either by recalculating and/or checking on a calculator. We can check accuracy by using check numbers!
So, figure the check numbers:
. 4639 (4)
+ 7326 (0)
. 11965 (4)
Look at the check numbers! (4)+(0)=(4)!
Let’s do another:
Calculate the answer then calculate the check numbers. Did you do it right?
Should look like this:
. 364 (4)
+ 4426 (7)
. 4790 (2)
and the check numbers are correct too.
Now, let’s assume you came up with a wrong sum (which happens) and it looked like this:
. 364 (4)
+ 4426 (7)
. 4780 (1) ERROR
Notice now how the check numbers don’t add up. (4) + (7) does not equal (1). This becomes our check! We now know something is wrong and needs to be corrected.
More Applying Check Numbers
As we can see, check numbers are a method of checking and verifying addition calculations. If the check numbers are not adding up, the answer is probably wrong.
Remember that check numbers work with subtraction, multiplication, and division? We’re going to save that for another post. Meanwhile, play around and see what you discover! Stay tuned……