Q&A #494

Teachers' Lounge Discussion: Multiplication tables

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From: Gail

To: Teacher2Teacher Public Discussion
Date: 2000082115:37:20
Subject: learning multiplication tables

I have copied the responses to earlier questions that were similar to

"Transitioning from manipulatives to use of symbolic concepts/notation
is always a problem.  You're probably already doing this, but don't
forget to have your students record the multiplication sentence
whenever they build with manipulatives.  Also, have students talk and
write about what the manipulative models mean.  One successful method
we've seen of helping students internalize the multiplication facts is
to build arrays (like 2x3 as a 2 by 3 array) using manipulatives (like
tiles) as well as recording the arrays on grid paper and recording the
multiplication sentence.  As you get to facts like 6x8, many students
see these as 3x8 doubled because they can visualize the arrays.  (This
also extends nicely to 1-digit and 2-digit multiplication.)  Playing
games which use the multiplication facts (even things like "war") also
help students internalize the facts."
 -Jenny, for the Teacher2Teacher service

"I have several suggestions for you to look to find your answer.

--Consider visiting the Internet Math Library, an annotated catalog of
mathematics and mathematics education web sites.  The Library features
a description of each entry, hierarchical categories for browsing, a
searcher on each browse page, and selected sites for each category's
starting points (look for Math Topics: Arithmetic/Early: Basic
Operations: Multiplication)



--Teach some of the tricks on the Beat the Calculator! page

--Calculation Tips & Tricks

Parents, teachers, and students have written to Dr. Math asking for
help with learning their multiplication tables.  Here are some of the
best answers from those archives:

--Learning Multiplication Facts-- Dr. Math FAQ

Let us know how this helps you and your students."
 -Roya, for the Teacher2Teacher service

"What sorts of strategies have you already tried with her?  Have you
helped her make a multiplication table?  There are many patterns to be
found, once the table is constructed.  How about using counters to
work out the facts, and record them?  (i.e. 4x 7 is 4 groups of 7, or
7 groups of 4 depending on how you look at it).  You can also build
rectangles using graph paper.  Make side of the rectangle as long as
one of the factors and the other as long as the other factor. 
Complete the rectangle, and count the number of squares inside the

This is not really a "trick".  Have you had your student look
carefully at the products that occur when you are using the one digit
factors (1X1 through 9X9)?  There are several patterns to be found,
and many relationships between the products themselves.

For instance, if she knows the twos, the fours and twice as much.  The
same with the three and sixes, and the fours and eights.

If you have not already done this, make a 10 by 10 grid. Above the
grid put the numbers 0 through 9, and do the same down the left side.

Your student should find a cell (one "square" in the grid), and then
multiply the factor at the end of that row with the one at the top of
that column.

When the grid is finished, have her look for patterns in the grid. 
She may want to color all the like products the same color, or she may
want to shade all the evens, or all the odds.

You might want to "help" her notice what happens to the size of the
products as you move around in the grid.  Are they larger if you move
in a certain direction?  Is there any way to predict where the largest
products will be found?  She will find some surprises, and they will
help her understand multiplication, and remember the products.

I find that some of my elementary students who are having trouble with
multiplication facts haven't really internalized the idea that they
rapidly adding, because what they have been shown to do is to memorize
a set of facts.  There is no understanding behind the facts.  It is
almost like learning a to sing in a foreign language, but learning
phonetically, rather than learning the words themselves.  There is no
way to construct meaning, and there is no way to use what has been
learned in another situation,
because it has no meaning.

That may be what your son's struggles are stemming from.  If so, you
could use manipulatives, like counters, washers, or beans, to help him
build sets of the facts.  For example, Building the sevens family
would be making one set of 7, then two sets of 7, then 3, and so on. 
Having your son look at the size of each successive amount, and noting
what that many "looks like" can help a student build a frame of
reference for the facts.  The same sorts of activities can be done
with the other "families".  There are also mental math activities that
can help your son gain proficiency.  For example, if he learns that
the fours are twice as large as the twos, (same for sixes and threes,
eights and fours, etc.) he can use that knowledge to compute the
products that way, too.  So 9 X 4 is twice 9 X 2, and 8 X 6 is twice 8
X 3."
I hope this is a start for you.  Please write back if you would like
more suggestions.  :-)
-Gail, for the Teacher2Teacher service

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