Math Circles at Home: The Opposite of Times Tables

When my children were in primary school, I found that multiplication times table tests were far less common than when I was their age. At least, teachers were less likely to give them. Other parents, however, worried that their kids wouldn’t get enough ‘practice’ and wouldn’t be ‘fluent’ in single digit multiplication. So they’d time their children completing times tables at home.

This, to me, encouraged flippancy, not fluency. In the short term, flippant memorization of multiplication facts might work, but in the long term it’s a disaster.

There is a place for (fluent) mastery of multiplication facts. So, if not times tables, what then?

Do math with your children instead. Give an actual problem to be solved, where the practice of ‘multiplication facts is built in. Try this:

Numbers can be partitioned in many different ways:

7 = 3 + 4 = 1 + 1 + 5 = 2 + 2 + 2 + 1 = 1 + 1 + 1 + 1+ 1 +1 + 1 = etc.

For a given number, take the numbers in one of its partitions and multiply them. Out of all the possible partitions of that number, what’s the biggest product you can get? Can you come up with a rule that guarantees the largest product?

In this investigation, you’ll find you have to do a lot of multiplication, more than if you completed a times table. But now you will multiply with a goal in mind. You’ll need to organize your work, make conjectures, consider simpler cases, connections between cases, and, most importantly, you will be doing this work with a purpose.

And all those things are sorely missing when you do times tables.