A Fun Way to Check Multiplication Problems
How often have you gone to a conference and been super-impressed by what a speaker shared? Has it happened often? It happened to me when I went to a conference as a very new teacher (in my second year, I believe), more than 20 years ago. At that conference, I was lucky enough hear Dr. Lola May speak. She was a great presenter, and certainly made an impression on me. I still have the book that was given at that conference and have referred to it many times over the years.
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 the method to many classes, and I don't think any students have ever told me that they had already learned it. So, I suppose 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 never taught them why it worked - I think that might have been too much for this age). I think it's especially handy for multiplication. Here are the steps of casting out nines to check multiplication (you can follow the example on the wheel):
1. Going across the rows of the multiplication problem, "cast out" (just cross them 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.
Casting out nines can also be used with the other operations as well, but using it to check multiplication is my favorite.
Have you used casting out nines?
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