by Josh Rappaport
Can you think of any info more important for early math than knowing the times tables?
Not many things, right?
Since the times tables are so critical for math success, and since many children struggle while trying to learn them, I'd like to share a fun, active strategy I came up with this past week for teaching children the 3s.
The strategy involves three stages, each stage bringing the child a step closer to multiplication-memory-mastery. Here are the stages, in the order I suggest they be taught.
STAGE ONE: "Patty-Cake Threes"
What we do here amounts to a 'patty-cake' approach to learning the threes, and it works like this.
The student and I sit facing each other with our hands held up, chest high, palms forward. At the very same moment, the child and I extend our right hands and gently clap them together. At the moment of the clap, we say "one" in unison, but in a fairly soft voice. Then we pull back our right hands and extend our left hands. When our left hands meet, we say "two" at the moment of the clap, again saying the number-word softly. Then we pull back our left hands, and push forward both of our hands. At the moment of the double clap, we say, "THREE!" But this time, when we say the number "THREE," we say the word more loudly, to show that this number is one of the numbers we "care about" since it's a multiple of three.
After three, we continue on: "four, five, SIX ... seven, eight, NINE ... ten, eleven, TWELVE ... " and so on. This process gives children a fun way to hear — and get an introductory feel for — the multiples of three.
STAGE TWO: "Finger-Drumming".
After your child has learned the rhythm for the multiples of three, from the 'patty-cake' approach, we start in with Stage Two: "finger-drumming." To 'finger-drum' the multiples of 3, the child makes a fist with one hand, and shakes it downward (using the same movement in the game "Rock, Paper, Scissors.") With each down stroke of the shake, the child says a number, and says them in order: "One, two, THREE!" But when the child says "THREE," she extends the index finger from her fist. The child continues: "... four, five, SIX," and at "SIX," she extends her middle finger in addition to her index finger, so now she has two fingers extended.
In this way, the game turns the body into something of a multi-sensory human calculator. So, for example, by the time the child says, "TWELVE," she should notice that she has four fingers extended from her fist. In this way, your child should see, hear and feel — that 3 x 4 = 12.
When you child gets to 3 x 5, all fingers of her hand are extended, meaning that the fist is gone. This is fine. At this point she keeps those fingers extended and starts to 'finger-drum' with her other hand. When she extends the first finger from her other hand's fist, that represents 3 x 6. Extending a second finger represents 3 x 7, and so on.
Once your child does the 'finger-drumming' process three times, start to ask her questions like: What is 3 x 6? Your child should be able to 'finger-drum' her way to the answer, for she should say "EIGHTEEN" just as she extends her sixth finger.
STAGE THREE: "Finger-Skip-Counting" This next stage follows "finger- drumming," but it is more challenging because in this stage the child does not say the intervening numbers; she says ONLY the multiples of three.
To begin 'finger skip-counting,' the child must have done enough "finger-drumming" so s/he is quite familiar with the multiples of three in their correct order.
To 'finger-skip-count,' 3 x 4, for example, the child holds out her fist and states the multiples of 3, like this: "Three" (extending one finger), "Six" (extending two fingers), "Nine" (extending three fingers), Twelve (extending four fingers)." You ask, "So what is 3 x 4?" And the child answers: "3 x 4 equals 12."
[Tip #1: When starting 'finger-skip-counting,' it's often helpful to allow children to whisper the intervening numbers. This helps keep them on track. Then challenge your child to whisper those in-between numbers more and more softly, eventually reaching a point where she doesn't need to whisper them at all.]
[Tip #2: Also, I've been finding it helpful to first have your child do only the multiples from 3 x 1 through 3 x 5. Once s/he develops competence at this skill, proceed to 'finger-skip-counting' the multiples from 3 x 6 through 3 x 10. ]
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, as I have a number of children who are learning their times tables.
I'm just guessing, but it seems like children could probably learn their 4s by jumping rope, or doing some other activity 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.
Josh Rappaport lives and works in Santa Fe, New Mexico, along with his wife and two teenage children. Josh is the author of the Algebra Survival Guide, and the companion Algebra Survival Guide Workbook, both of which will soon be available for homeschoolers as a computer-based Learning Management System, developed and run by Sleek Corp., of Austin, TX.
Can you think of any info more important for early math than knowing the times tables?
Not many things, right?
Since the times tables are so critical for math success, and since many children struggle while trying to learn them, I'd like to share a fun, active strategy I came up with this past week for teaching children the 3s.
The strategy involves three stages, each stage bringing the child a step closer to multiplication-memory-mastery. Here are the stages, in the order I suggest they be taught.
STAGE ONE: "Patty-Cake Threes"
What we do here amounts to a 'patty-cake' approach to learning the threes, and it works like this.
The student and I sit facing each other with our hands held up, chest high, palms forward. At the very same moment, the child and I extend our right hands and gently clap them together. At the moment of the clap, we say "one" in unison, but in a fairly soft voice. Then we pull back our right hands and extend our left hands. When our left hands meet, we say "two" at the moment of the clap, again saying the number-word softly. Then we pull back our left hands, and push forward both of our hands. At the moment of the double clap, we say, "THREE!" But this time, when we say the number "THREE," we say the word more loudly, to show that this number is one of the numbers we "care about" since it's a multiple of three.
After three, we continue on: "four, five, SIX ... seven, eight, NINE ... ten, eleven, TWELVE ... " and so on. This process gives children a fun way to hear — and get an introductory feel for — the multiples of three.
STAGE TWO: "Finger-Drumming".
After your child has learned the rhythm for the multiples of three, from the 'patty-cake' approach, we start in with Stage Two: "finger-drumming." To 'finger-drum' the multiples of 3, the child makes a fist with one hand, and shakes it downward (using the same movement in the game "Rock, Paper, Scissors.") With each down stroke of the shake, the child says a number, and says them in order: "One, two, THREE!" But when the child says "THREE," she extends the index finger from her fist. The child continues: "... four, five, SIX," and at "SIX," she extends her middle finger in addition to her index finger, so now she has two fingers extended.
In this way, the game turns the body into something of a multi-sensory human calculator. So, for example, by the time the child says, "TWELVE," she should notice that she has four fingers extended from her fist. In this way, your child should see, hear and feel — that 3 x 4 = 12.
When you child gets to 3 x 5, all fingers of her hand are extended, meaning that the fist is gone. This is fine. At this point she keeps those fingers extended and starts to 'finger-drum' with her other hand. When she extends the first finger from her other hand's fist, that represents 3 x 6. Extending a second finger represents 3 x 7, and so on.
Once your child does the 'finger-drumming' process three times, start to ask her questions like: What is 3 x 6? Your child should be able to 'finger-drum' her way to the answer, for she should say "EIGHTEEN" just as she extends her sixth finger.
STAGE THREE: "Finger-Skip-Counting" This next stage follows "finger- drumming," but it is more challenging because in this stage the child does not say the intervening numbers; she says ONLY the multiples of three.
To begin 'finger skip-counting,' the child must have done enough "finger-drumming" so s/he is quite familiar with the multiples of three in their correct order.
To 'finger-skip-count,' 3 x 4, for example, the child holds out her fist and states the multiples of 3, like this: "Three" (extending one finger), "Six" (extending two fingers), "Nine" (extending three fingers), Twelve (extending four fingers)." You ask, "So what is 3 x 4?" And the child answers: "3 x 4 equals 12."
[Tip #1: When starting 'finger-skip-counting,' it's often helpful to allow children to whisper the intervening numbers. This helps keep them on track. Then challenge your child to whisper those in-between numbers more and more softly, eventually reaching a point where she doesn't need to whisper them at all.]
[Tip #2: Also, I've been finding it helpful to first have your child do only the multiples from 3 x 1 through 3 x 5. Once s/he develops competence at this skill, proceed to 'finger-skip-counting' the multiples from 3 x 6 through 3 x 10. ]
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, as I have a number of children who are learning their times tables.
I'm just guessing, but it seems like children could probably learn their 4s by jumping rope, or doing some other activity 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.
Josh Rappaport lives and works in Santa Fe, New Mexico, along with his wife and two teenage children. Josh is the author of the Algebra Survival Guide, and the companion Algebra Survival Guide Workbook, both of which will soon be available for homeschoolers as a computer-based Learning Management System, developed and run by Sleek Corp., of Austin, TX.
At his blog, Josh writes about math education, offering tips and tricks. Josh also authors Turtle Talk, a free monthly newsletter with an engaging "Problem of the Month." You can see a sample issue here or subscribe at this site. Josh also is co-author of the "learn-by-playing" Card Game Roundup books, and author of PreAlgebra Blastoff!, a "Sci-Fi" cartoon math book featuring a playful, hands-on approach to positive and negative numbers.
In the summer Josh leads workshops at homeschooling conferences and tutors homeschoolers nationwide using SKYPE. Contact Josh by email @ josh@SingingTurtle.com or follow him on Facebook, where he poses two fun math Qs/day.
