Do you need drill to learn multiplication facts?

Continuing on the same lines as my previous post, what about multiplication facts and drill?

Well, the principle is similar: show them first the concept and patterns.

Then can come some plain drill.

But, I want to share with you a few more detailed points.

  1. The main "patterns" in various multiplication tables of course follow from the concept of multiplication. For example, table of 2 is counting by 2's. You get table of 4 by doubling the answers in table of 2. You get table of 8 by doubling the answers in table of 4.

    Table of 10 is counting by 10s. Table of 5 - just take half of what the 10 ×

    Here are some resources to give you ideas about these kind of patterns and little "tricks".

    * Michele's Math
    * Times Tables' factsheets

  2. We ALSO need them to know the tables "backwards".

    Let me explain.

    It's not enough to know that 8 × 7 is 56, when someone asks what is 8 × 7. The students ALSO need to know that 56 is 8 × 7, when given just the answer 56.

    This is very important. Students need this fairly soon when they start learning division. Later on it will be important when simplifying fractions or factoring.

  3. Since it's important to know the tables backwards, I do not feel it's enough if the child is able to "figure out" the multiplication problems. I feel they need to memorize them, period, and not just be able to count or use some other method to find the answers.

    It's fine initially, and indeed very helpful, if the child figures out 8 × 8 by first going 8 × 2 and doubling that twice.

    But this fact also needs memorized so that later on, when she comes to the problem 64 ÷ 8, it won't take her 10 seconds to find the answer.

    Now you might ask why is that important? Because of long division, for example. It's going to be a pain to learn long division if you don't know your division facts by heart.

    Here's another reason: soon the student is going to have fractions to simplify. If you know your division facts, then simplifying 35/56 will be a breeze, otherwise a pain.

See how it all builds on the previous topics? You need to get a good foundation, and multiplication facts "both ways" is part of that foundation.

I have posted online the entire guide to effective oral drilling from one of my books.

The guide explains how the teacher and student can achieve memorizing multiplication tables in this manner where they know the answers and they know which answer goes with which multiplication problem.

Check also a list of online games that practice times tables. These are great after you've done some basic drill and the child needs reinforcement (practice!!!).


Anonymous said…
I think your idea is very sound, but the hardest part is to decide when it is appropriate to move to drill, that is not focusing on drill prematurely. Any comment?
Maria Miller said…
I would start the drill after the student has worked through enough problems just using the definition that the student either sees the need for memorization, or has already memorized a few facts just from doing many problems.

This is the idea I have included in my Multiplication 1 book.

For example, let's say you teach the concept of multiplication, teach multiplying by one and zero and two (doubles), teach the idea of number line jumps and a few word problems.

During those topics the student of course does quite many multiplication problems.

Then, after those topics are fairly well mastered, it might be time to go through the tables systematically and do some drill.

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