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"Casting Out Nines"

I was a very new teacher (in my second year, I believe), when I was lucky enough to go to a conference and hear Dr. Lola May speak. She was a great presenter, and certainly made an impression on me. I still (20 years later) have the book that was given at the conference and refer to it now and again.

It was at this conference that I first learned how to use "casting out nines" to check the answers to multiplication and division problems. I had never heard of this method when I was a student, but being a new teacher, I kind of assumed it was a method well-known to other teachers.....until I talked about it during a meeting at which our Curriculum and Instruction director was present. He overheard me explaining it to another teacher; he had never heard of it, was quite surprised and interested in how it worked, and asked me to show him a few more examples.

Over the years, I have taught it to some classes (and not to others...I haven't taught it yet this year, but plan to...though the school year will be over before we know it!), and I don't think any students have ever told me that they had already learned it. So, I supposed it isn't as well-known as I had thought (at least not around here...)

The kids really like it because it's a "trick" to check their work.  I made this little video explanation explaining how to check a multiplication problem...it's very basic and amateur, I know, (and I apologize for the blurriness at the end), but hopefully it provides clear enough directions for you to get the idea:)


The steps of casting out nines to check multiplication:
1. Going across the rows of the multiplication problem, "cast out" any 9s or combinations of numbers that add up to 9.
2. Add the remaining digits across each row, until the result is a single digit.
3. Multiply the single digits, and if the result is a 2-digit number, add the digits to get a single digit.
4. Follow the same steps in the product, until you arrive at a single-digit number.
5. If the results match, the answer to the problem is most likely correct (not 100% certain, but most likely); if the results do not match, the product is not correct.

I'll post another short video with an example or two of checking the answer to a division problem in a day or two.

Have you used casting out nines?


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