A friend of mine asked me an interesting question about multiplication facts. I thought I should share it with you.

How do you make sure that when a child learns multiplication facts by heart, he/she understands the underlying calculation?

I recently read two articles related to learning combinations of numbers (Baroody, 2006), and multiplication of one-digit numbers in particular (Kling & Bay Williams, 2015). According to these articles, it seems that mastering multiplication facts should be seen more as a *journey* than a step of memorization.

- Phase 1 – The child uses modeling and/or counting strategies to solve a multiplication. He/she may use manipulative, fingers, a visual representation (e.g. to solve 6 x 4, a child draws 6 groups of 4 dots, and skip counting the dots; Fig 1, Kling & Bay-Williams, 2015)
- Phase 2 – The child starts using reasoning strategies, deducing an answer from known facts and relationships (e.g. to solve 6 x 4, the child may solve 5 x 4 = 20, and add one more group of 4; Fig 1, Kling & Bay-Williams, 2015)
- Phase 3 – The child provides fast, and accurate, answers (e.g. the child knows that 6 x 4 = 24; Fig 1, Kling & Bay-Williams, 2015)

I like the approach of a *journey*. I remember as a child being pretty stressed out by learning all the time tables by heart. But building it up from reasoning strategies sounds so helpful.

Solving 7×8? Well, I am not quite sure. I could skip counting by 7. Or since I remember 7×7 = 49, I just have to add another 7. The answer is 56 !

So at home, when my child starts remembering some multiplication facts (my child is not there yet, it is by grade 3, that she will have to “know from memory all products of two one-digit numbers”, CCSM 3.OA.7), I will likely

- keep providing opportunities to explore multiplication with modeling and representing word problems, so that she can strenghten her own reasoning strategies.
- come up with some games to practice time table. Two quick examples, I just like the idea of practicing multiplication facts often, but for a very short period of time
- Rolling 2 dice, and multiply the 2 numbers, just a few times in a row but several times a week
- Asking for “Passwords” on the door worked very well for us to practice pairs to 10 (see my previous post here), so we may come up with something similar with time tables.

While implementing these activities, I would make sure she sees some combinations as “safe bases” (e.g. multiples of 5, multiples of 10), and check regularly that her reasoning strategies are solid and in place. According to Kling & Bay-Williams (2015), it is fundamental to help the child retain the facts.

I am such a fan of letting children exploring concepts on their own, and allowing them to build up mastery from there. And home is a great place to do so, and support all the good stuff they learn at School.

References

- Baroody, A. J. (2006). Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them.
*Teaching Children Mathematics*,*13*(1), 22-31. - Kling, G., & Bay-Williams, J. M. (2015). Three steps to mastering multiplication facts.
*Teaching Children Mathematics*,*21*(9), 548-559.

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