If your child is anything like mine, they struggle to truly commit their multiplication tables to memory. For the last couple of years, I have operated under the assumption that repetition would eventually do the trick and this has proven to be mostly true. My daughter can come up with the correct answer to most multiplication facts given that she has time to think it through. Enter Classical Conversations. She is determined to be a Memory Master and this feat demands that she be able to recite the multiplication tables through 15 x 15 in a very short amount of time with absolutely ZERO ERRORS. This is a tall task for most adults. Since she is doing very well with all the other memory work, math has become a bit of a thorn in our side. But I’m determined to do everything I can to help her achieve her goal. It was with this in mind that I came up with the following system.
The idea behind this is that it is significantly easier for kids to skip count than it is to recite the entire multiplication fact. CC operates under this assumption as they only require children under 10 to skip count in order to become Memory Masters, whilst older children must move on to giving the entire fact in their recitation. What I am finding with my own CC Masters class is that many of the students can skip count proficiently, but moving on to the full fact really throws them for a loop. So I developed the following progression:
I begin by having my girl recite the skip counting for each number we are working on. For example, let’s say we are doing 12’s, she would begin by reciting: 12 – 24 – 36 – 48 – 60 – 72 – 84 – 96 – 108 – 120 – 132 – 144 – 156 – 168 – 180. We continue with just the skip counting until she can do it reasonably quickly and consistently accurately. At that point we move on to what I’ve affectionately deemed the “transition chart.” I am inserting a photo of the chart below.
We begin with her simply pointing at the second multiplicand as she continues skip counting. So she would point at 1 as she says “12”, then point at 2 as she says “24”, then 3 and “36”, etc. Once she can complete this task without difficulty, we move on to her saying the number as she points to it and then immediately saying the answer. So it goes like this: point to number 1, say “1”, then say “12”; point to number 2, say “2”, then say “24”; point to 3, “3”, “36”; etc. When she can do this well, we move on to the final step: She points at each number as she recites the entire fact: points at 1, says “12 x 1 is 12”; points at 2, says “12 x 2 is 24”; points 3, “12 x 3 is 36”; etc.
You will notice that on the conversion chart the 12 x is written in small print only once. This is intentional. I find that it is the actual recitation of the fact that confuses my students. They seem to be able to keep the numbers in their head for skip counting, but once they verbalize the fact itself, it jumbles the answer in their mind. I encourage my daughter therefore to try to recite the 12 x part without even thinking about it, as rote as possible. I then encourage her to simply “read” the second multiplicand without thinking about it. Since she is pointing at the multiplicand, this makes it easier. This way her mental energy is focused on keeping track of the answers in her head, not on remembering which fact she is on. It seems like a small detail, but it has made a huge difference.
I hope your kids will find this simple tool as helpful as mine have. Until next time, Happy Learning!