
The ideas in this drill guide are taken from Multiplication 1 ebook.
Effective oral drilling to learn multiplication tables
Free guide for the teacher from HomeschoolMath.net
This kind of drilling is aimed at memorizing a certain times table. It should be used only after the child has already studied multiplication concept to some
extent and understands the concept itself.
When you are doing drills to memorize, explain to the child that the goal is
to memorize the facts, to recall from memory, and not to get the answers
by counting or some other method. Just like your child probably has
memorized your address and phone number, now she/he is going to memorize some
math facts. You can easily see if the student is trying to count because
producing the answer takes much more time. You should expect the answers
from the child immediately when you are drilling. If he/she doesn't know
the answer by heart (from memory), then tell him/her the right answer. Usually short
drill sessions are best. You can drill for example for five minutes at a
time, or ten, depending on the child.
Try to have at least two sessions within
a day though, as your schedule permits. Brain research shows us that
forgetting happens fast, and that new information is retained far better if the
first reviewing session is done within 4-6 hours of the first time
learning. (By the way, this principle applies to anything new you are
learning.)
Paper-pencil activities where
the child is left alone, do not work really well for memorizing the facts - the
child may get the answers by counting and not from memory. So it will take
time from the teacher/parent. If you can, utilize older siblings in the
drilling task too. Computers are great drillers since they won't get tired
and you can usually choose a timed session where the child is then forced to
produce the answers quickly. Children can actually enjoy the memorization process when they notice they are
truly learning the facts and are able to go through the drills
successfully. Computer programs and computer-based drilling
can be very rewarding to children and let them enjoy memorizing times
tables. See http://www.homeschoolmath.net/math_resources_2.php for a list of free interactive online multiplication activities. The method below has several
steps from 1 to 5. You can work on only a few of the steps in one session,
again, depending on the child's concentration and ability. Memorizing
the table of 3 - in steps
Have a table to
be worked on all ready written on paper. We will use here the table of
three as an example.
1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18 7 x 3 = 21 8 x 3 = 24 9 x 3 = 27 10 x 3 = 30 11 x 3 = 33 12 x 3 = 36
-
The first task is to memorize the list of answers, so to speak.
Study first the skip-counting list up until the midpoint (3, 6, 9, 12, 15, 18).
Have your child say it alound while pointing to the answers one by one with
a finger or pen - thereby using many of his senses simultaneously. After he
has gone through if a few times, ask him to repeat the list from memory.
Try require the answers from your child, and not give them to her too easily, because ONLY by straining her mind will she make the effort to eventually memorize these facts. The mind is like muscles: it needs exercise to become stronger.
Require her to memorize this list both upwards and downwards. Continue this way until she can 'rattle off' the first list of 3, 6, 9, 12, 15, 18.
With some tables, like table of 2, table of 5, or table of 10, point out the
pattern in them. The pattern in table of 9 is more subtle but still
usable.
- Then tackle the last part of the list: 21, 24, 27, 30, 33, 36. Do the same things you did with the first part of the
list.
- Lastly, work with the whole list of answers. Practice the list UP AND DOWN until it goes smooth and easy.
This part may be enough for one day. But review it later in the day.
-
Next, practice
individual problems randomly. You can ask orally ("What is 5 times
3?") or point to the problems
on the paper, or use flashcards. However, I would recommend saying a
question aloud and simultaneously pointing to the problem the child can see,
because again, using multiple senses should help fix them in the mind better.
The goal at this stage is to associate each answer 3, 6, 9, 12, 15, 18, 21,
24, 27, 30, 33, 36, with a certain multiplication fact (such as 7 x 3).
You can also mix earlier tables that she already knows with these new
problems, and drill both with flashcards.
-
The last step is to do this the other way round so that YOU say the answer, say 21, and the
student has to produce the problem (from table of 3). Have the table handy, hide the problems, and point to the answers in random order.
This one you can work the other way around: the student says answers, and
you produce problems. Answer wrong sometimes, too, to check her out.
As an extension, you can say answers from several tables that you've
studied, and the student gives the corresponding problem. Sometimes
there are several answers: for example 36, 30, 24, and 20 are in several
different times tables. This is an especially good exercise as it
prepares to division concept and factoring.
See an example of drilling tables of 2, 3, 10, and 5 and drilling tables of 4, 11, and 9
The
memorization won't probably happen overnight. On subsequent days, you
can mix these drills 1-5 (and hopefully you don't need to concentrate on
steps 1 and 2). This kind of drilling takes a little time and effort from the teacher, but it
can be very effective. And, homeschoolers can obviously do some of it
while going about other tasks, or while traveling in the car, etc.
While you are doing this table by table, you can also try to teach the process to your child, so that she will learn how to do memorization herself. She can hide the answers and try to produce the list in her mind.
Other helpful ideas
-
Hang a poster
with the 12x12 or 10x10 grid on the wall. Remind your child to glance at it a
few times a day. It can work wonders for visual learners!
-
Hang beside it
another, initially empty, poster, to which the child fills in those facts he
has mastered.
-
Recite the
skip-counting lists or multiplication facts aloud just before going to bed.
This can turn them into mastered facts by the next morning.
In my ebook Multiplication 1, the tables are not studied in just ascending number order, but in a specific order: first table of 2, then table of 4, table of 10 (very easy), table of 5 (easy), then some review. Then, table of 3, table of 6, table of 11 (very easy), and table of 9 (which has a pattern) - and then some review. Lastly are studied the 'hard ones', table of 7, table of 8, and table of 12.
Along with that, in each lesson there is a 12x12 grid to fill where all the facts not yet studied are colored full. Each time a new table is studied, those still colored places get less and less, which can encourage the student a lot. And, with each new table, the facts in it that the student already knows, are explicitly pointed out. With the last tables there are but a few new facts to memorize.
|
FREE math homework help on www.PhatMath.com
-
40 Math forums for grades K-12 & College
-
Post/view math problems & solutions
- Blogs for students, parents, teachers
|

Over 150 hand-crafted quality math worksheets covering all 6th grade topics.
See our samples!
|
|