Kiss those Math Headaches GOODBYE!

Posts tagged ‘Times Tables’

Times Tables, Learning the Threes


What’s more important for early math than knowing the times tables?

Not much, right?

Since the times table facts are so fundamental, and because many students struggle with them, I’d like to share a strategy I came up with today for
learning the 3s. This technique works particularly well with students
who struggle with memorizing apparently random facts. (We know these
facts are not random, but if learned with nothing more than flash cards,
they can appear random.)

The strategy involves three stages, each stage bringing the child closer
to being able to QUICKLY access the desired multiplication facts. Here are the stages, in order they should be taught.

STAGE ONE:  “Patty-Cake Threes”

What I do here amounts to a “patty-cake” approach to learning the threes, which works like this.

The student and I sit facing each other with our hands up. We hit our right hands together and say “one,” then hit our left hands together and say “two.” Then we
hit BOTH HANDS TOGETHER and say, “THREE.” When saying the “one” and “two,” we utter the numbers quietly. But when we say “THREE” and all successive multiples of three, we say these numbers loudly, almost (but
not quite) shouting.

After three, we continue:  “four, five, SIX … seven, eight, NINE, ten,
eleven, TWELVE … ” and so on. So this gives children a fun way to
hear — and get a feel in their body for — the multiples of three, in the proper
order.

Patty Cake

Image by davie_the_amazing via Flickr

STAGE TWO:  “Finger-Drumming”.

After the child has the rhythm of the number three, from the “patty-cake” approach, we do “finger-drumming.” To “finger-drum” the multiples of 3, the child makes a fist with one hand, and shakes it, saying with each shake, “one, two, THREE!” And when saying “THREE,” the child extends one finger from the fist. The child continues: “four, five, SIX,” and at “SIX,” he extends another finger, so he has two fingers out.

Then you ask the child, for example, “What is three times two?” Answer: the number he just said, “six.”

In this way, the child can “finger-drum” out all of the multiples of three. To
reinforce the times tables as you go, ask questions like:  “What is 3 x 4? What is
3 x 5? etc.” Each time you ask, the child must “finger-drum” till s/he gets the
correct answer. This flows very nicely from the “patty-cake” approach as it
builds on the rhythmic feel for counting in threes.

STAGE THREE:   “Finger-Skip-Counting”   The third stage follows “finger-
drumming.” To begin finger-skip-counting, the child must have done enough “finger-drumming” so s/he is quite familiar with the multiples in the correct order.

To “finger-skip-count,” 3 x 4, for example, the child holds out a fist and
runs through the multiples of 3, like this:  “Three (extending one finger), Six (extending two fingers), Nine (extending three), Twelve (extending four fingers).”  You ask, “So what is 3 x 4?” And the child answers:  “3 x 4 equals 12.”

I found it helpful to first just challenge the child with the multiples from 3 x 1 through 3 x 5. Once s/he develops competence there, proceed to “finger-skip-counting” the multiples from 3 x 6 through 3 x 10. Finally do 3 x 11 and 3 x 12.

Put all together, these three stages offer a fun and rhythmic way for children
to learn their multiples of three. I’m curious to find out if I can use a similar
approach for the 4s, and I’ll find out soon.

I can’t be sure, but it seems like children could probably learn their 4s
by jumping rope, or doing other activities with a rhythmic nature.

If any of you have used an approach like this one for learning the times
tables, feel free to share it.

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Multiplication Facts


QUESTION:

Is there a particular order that is most beneficial to learning times tables? For example, I have heard that learning 1, 5, 10, 11, 2, 4, 8, 12, 3, 6, 9 is a good order. What say you?

MY REPLY:

There are many “schools of thought” on what makes the best order for teaching the times tables.

I encourage everyone out there who has a favorite order to share it with us in the comments. And feel free to explain why this is your favorite order.

Here is my preferred order — and a few notes on why:

1, 2, 4, 10, 5, 11, 3, 6, 9, 8, 12, 7

IMPORTANT NOTE: I teach the facts for the multiplicands 1 – 6 first. Only after
students have those down do I advance to the multiplicands of 7 – 12.

i.e.: When teaching the x 4 facts the first round through, teach 1 x 4 through 6 x 4. On the second round through, teach the 7s through 12s, i.e.: 7 x 4 through 12 x 4.

Using this staggered approach helps students avoid getting befuddled by the size of numbers they encounter early on. This approach builds success and confidence early on.

A few notes on my order:

1st) I teach x 2 second. That’s because you can teach multiplying by 2 as simply “doubling” the number, a concept almost all kids understand. The “doubling” approach gives teachers a good way to talk if you’re going to use manipulatives to reinforce the concept.

In suggesting that you use manipulatives, I mean that you may want to use counters such as tiddly winks, paper clips, pennies, etc. To demonstrate a fact like 2 x 7, you would first lay out a row of 7 counters, then underneath them put out another row of 7 counters, and you would have the student count them all up.

2nd) I put x 4 third because you can teach multiplying by 4 as doubling a number TWICE. e.g.,: 4 x 3: 3 doubled is 6. And 6 doubled is 12, so 4 x 3 = 12.

Again, it would be a good idea to use manipulative counters to demonstrate this concept. Here you would lay out four rows of three counters, to show the fact that 4 x 3 = 12

3rd) I teach x 5 right after x 10 because multiplying by 5 gives you a number that’s exactly half of what you get when you multiply by 10.

When teaching the 5s tables, use the trick that multiplying by 5 is the same as multiplying by 10 and cutting in half. (And, for even multiples of 5, first cutting the number in half, then tacking on a 0 at the end.)

e.g.: for 4 x 5: Half of 4 is 2. Tack on a 0, and you get 20 4 x 5 = 20 [yes, it is that easy!]

4th) You can teach multiplying by 8 in several ways, depending on what works for your children. One way is to see that multiplying by 8 is doubling a number three times. e.g., for 6 x 8: 6 doubled is 12. 12 doubled is 24. 24 doubled is 48. So 6 x 8 = 48

Another strategy for 8: Multiply by 10, then take away 2 x the number. e.g., for 6 x 8: 10 x 6 = 60, and 2 x 6 = 12. 60 – 12 = 48, so 6 x 8 = 48

5th) Multiplying by 12 offers you a great chance to introduce the distributive property for multiplication. That’s just fancy language for saying that when you multiply, say, 6 x 12, you can look at it like this: Since 12 = 10 + 2, 6 x 12 can be viewed as: (6 x 10) + (6 x 2) = 60 + 12 = 72

Most children can get used to this quickly, if they are taught it EARLY ENOUGH.