How to Conquer the Times Table, Part 4

photo by Karen via flickr

Photo of Miss Karen (and computer) times 3, by Karen, via flickr.

If you remember, we are in the middle of an experiment in mental math. We are using the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible. So far, we have studied the times-1 and times-10 families and the Commutative Property (that you can multiply numbers in any order). Then we memorized the doubles and mastered the facts built on them.

Square Numbers

Now is a good time to think about the square numbers. Your son or daughter may have heard of square numbers before, but if not, the topic will come up soon. Square numbers will haunt them all through high school, so they might as well get used to them now: A square number is simply a number that makes a square.

  • Here is your second memory task: Learn the squares!
by fdecomite, via flickr

1 \times 1 = 1
2 \times 2 = 4
3 \times 3 = 9
4 \times 4 = 16
5 \times 5 = 25
6 \times 6 = 36
7 \times 7 = 49
8 \times 8 = 64
9 \times 9 = 81
10 \times 10 = 100
11 \times 11 = 121
12 \times 12 = 144

Take all the time you need for your student to master these, because the square numbers are important. Remember to take turns. Let your child quiz you to see if you remember what is seven squared.

Hands-On Learning

Get out blocks or graph paper so you can actually see the squares.

  • Make one row of one block for the first square number: 1 \times 1 = 1, and we say, “One squared = one.”
  • Two rows of two blocks makes 2 \times 2, or two squared, which is four.
  • Three rows of three blocks is 3 \times 3, or three squared. How many blocks is that in all?
  • Four rows of four blocks…
  • Five rows of five…
  • Six rows of six…

Go ahead and build all the square numbers. Make a great pyramid of blocks, one square number on top of another. Or make a poster of graph paper square numbers and hang it on the wall. Be amazed at how quickly the squares grow from tiny to huge.

Square pyramidal number, from Wikimedia Commons

Next-Door Neighbors

Once you know the square numbers, simple addition (or subtraction) will help you find some of the hardest-to-remember multiplication facts. For example, 6 \times 7 is a neighbor to 6 \times 6 and 7 \times 7 :

6 \times 7
= 6 squared + one more 6
= 7 squared − one 7

And 7 \times 8 is a neighbor of 7 \times 7 and 8 \times 8:

7 \times 8
= 7 squared + one more 7
= 8 squared − one 8

How many next-door-neighbor numbers can you find? How many ways can you calculate them? The more different ways you know, the more likely that you will be able to reason out an answer when your math-fact memory goes blank.

This leaves us with only 13 facts to cover:


This is the fifth post in my Times Table Series. To be continued…[Go to part 5.]

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2 thoughts on “How to Conquer the Times Table, Part 4

    1. Thank you! I’m honored that you included me.
      Unfortunately, I don’t have the time right now to do a good job on responding to blog awards — although it’s a good reminder that I’ve promised myself I was going to update my blogroll one of these days. So many new math bloggers, so little time to read them all…

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