Do you still have middle school students who DON'T KNOW THEIR TIMES TABLES?! If you teach this age, then I am sure that the answer is YES (even high school teachers can relate, am I right?!) I can be so frustrating trying to move on to higher level math, when you rstudents can't yet multiply.
SO WHAT DO WE DO??? We teach them pattern recognition. We get them to understand the multiplication chart, and recognize the patterns between the different sets of numbers. As professionals, We call this number sense.
When it comes to math, we cannot put enough emphasis on the importance of patterns. While we could easily list down all the popular number patterns into a chart that we have the students memorize, we do not want to miss an opportunity to build their number sense. We can give their brains a “hands-on” experience in working with numbers by giving them the opportunity to find patterns and figure out how certain numbers work together for themselves. The same way a composer needs to master working with musical notes and how they interact with the others, or a painter with color, we can’t expect students to become mathematicians without presenting them with chances to figure out how numbers relate to each other.
So at the beginning of the year, I spend a week with my 7th and 8th graders just looking at a multiplication table. The come up with patterns, share them with each other, then go back and look for more. EVentually the whole class is able to create this chart on their own, in a a short amount of time. Students who have not yet memorized no longer get stuck on 7x8, because they rely on patterns to get their quickly.
Here are a few patterns my class was able to discover when they were asked to examine the multiplication table:
In every row, anytime the ones place hits zero, the ones place pattern repeats itself.
The 4’s row is every other 2. The 6’s row is every other 3. The 8’s row is every other 4....
The 6’s row is just the 5’s row plus an extra group of 6.
I didn’t show the multiplication table to the students to have them memorize it. They didn’t need to. As their number sense continues to develop and they become more flexible in their thinking, they will be able to get to the answers on their own. While memorization can be a helpful tool for many, it should take a back seat to students becoming versatile thinkers who can recognize patterns and get to the answers on their own. Pattern recognition is crucial. Flexible thinking is crucial. Number sense is crucial.
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