2x2 is 4, 2x3 is 6, 2x4 is 8. We all remember these chants from elementary school. Every 2nd and 3rd grade teacher works hard to teach their students the times tables. The only problem is, the traditional methods used across our nation in most elementary schools simply don't work -there are just too many students and too much to do. If you think they do, ask your child for the answer to some random basic facts, such as 6x7 or 7x9 - if they have to stop and think, they don't know them. Even older children -5th and 6th graders - don't really know the basic facts of multiplication. Now, 2nd graders are supposed to already know their basic facts up through the fives, but they never do, so it normally falls upon the 3rd grade teacher to pick up the slack. And since most fail to actually get their students to really know the basic facts, it falls upon the 4th grade teacher to pick up that slack when they are trying to teach more complex math, which requires absolute, dead cold memorization of the basic facts. As an elementary school teacher for 25 years, I have developed a method that not only works, it works well and is very effective. This method is very useful too for homeschool parents. Check out homeschool websites and homeschool associations for more ideas. You might also want to do a Web search for math curriculum (what the school teaches) and for math skills.
If you are the parent of a child in a public school or private school, this is an excellent way to make sure that your child learns these important basic facts that the teacher may not be very successful with. You do it at home, and it really doesn't require that much time. Explain the importance of learning the basic facts of multiplication to your child, and be helpful and encouraging. Set aside a few minutes each night to work on this program. If you take the time to follow my method, you will be giving your child a gift - the advantage of being ready to learn how to do higher skill math, such as algorithms, division, and even beginning algebra skills, with much less difficulty and anxiety.
Virtually all students know the 0s (0x1, 0x2, 0x3, etc.) This is called "The Zero Property of Multiplication."ÃƒÂ‚ Â‚ Â‚ÃƒÂ‚ Â‚ Â‚ÃƒÂ‚ Â‚ÃƒÂ‚ Â‚ Â‚ÃƒÂ‚ Â‚ Â‚ÃƒÂ‚ Â‚ÃƒÂ‚ Â‚ Â‚ÃƒÂ‚ Â‚ÃƒÂ‚ Â‚ Â‚ÃƒÂ‚ Â‚ Â‚ÃƒÂ‚ Â‚ÃƒÂ‚ Â‚ Â‚ÃƒÂ‚ Â‚Any number x 0 = 0. They will likely also know the 1s (1x2, 1x3, 1x4, etc.) This is called "The Identity Property of Multiplication." Any number x 1 = the number. Be sure to explain this to your child.
Consequently, we will begin with the 2s and 3s as a package, then add the 4s and 5s, and finally the 6s through the 9s.
Things You Will Need
3x5 index cards
Ruler or some straight edge
Plain copy paper or notebook paper
Prepare the Materials
Use the marker to write the basic facts on the index cards so that they can be folded to hide the answer.
Write each of the basic facts on a separate card:
2x2 = 4 2x3 = 6 2x4 = 8 2x5 = 10 2x6 = 12 2x7 = 14 2x8 = 16 2x9 = 18
3x2 = 6 3x3 = 9 3x4 = 12 3x5 = 15 3x6 = 18 3x7 = 21 3x8 = 24 3x9 = 27
4x2 = 8 4x3 = 12 4x4 = 16 4x5 = 20 4x6 = 24 4x7 = 28 4x8 = 32 4x9 = 36
5x2 = 10 5x3 = 15 5x4 = 20 5x5 = 25 5x6 = 30 5x7 = 35 5x8 = 40 5x9 = 45
Be sure to leave extra space between the = and the answer. Use a ruler or some straight edge to draw a line between the = and the answer, and fold the card on the line so that the answer is facing backwards.
Next, get a sheet of paper and draw a circle on it. You may want to trace around a plate or a saucer. Make it as large as space will allow. You can cut out the circle, or just leave it on the paper as it is.
Number it like a clock, but go only from 1 to 9.
Start Working on the 2s and 3s
Start by reciting the 2s with your child together. You and your child will say "2x2=4, 2x3=6, 2x4=8," etc.
Then have your child go off to a quiet place and practice the 2s with the cards. The child should just hold up the unfolded cards and read from them aloud, in order. Make sure the cards are unfolded, because it is important for the child to see the whole fact: 2x6= 12.
Next, get with your child and fold the cards so that the answers are in the back. Hold the cards up, in order, and have the child say the basic fact and give the answer aloud. Whether the answer is right or wrong, unfold the cards so the child can see the whole fact: 2x4= 8. Have your child read the whole basic fact aloud from the card to reinforce learning and memorization. Move on to the next card. If your child seems to pause or stop to think on any of the facts, put those cards in a rubber band, and set them aside as facts to be studied more. Repeat this process until there are no errors or hesitation in answering. Be careful not to push the child too hard or too long. Do this over a period of time.
Once the child is able to get all the facts correct in order, without stopping to think, mix up the cards so that they are NOT in order. Once again, go through all the cards, with the answers folded back, and then unfold the card so the child can read the whole basic fact. As before, if your child seems to pause or stop to think on any of the facts, put those cards in a rubber band and set them aside as facts to be studied more. Repeat this process until the child can answer each fact (with the cards folded and out of order) without stopping to think. Your child should read the fact from the card and give the answer immediately, without stopping to think. As always, after each card, unfold the card so the child can read the whole fact aloud.
Now it's time to get out the clock. Explain to your child that you are going to test the basic facts. Explain that you will point (with your finger or with a pencil) to a number on the clock, and the child is to say "2 x (whatever number you point at) = (and give the answer.)" For example, if you point to 4, the child should say 2x4=8. Point to different numbers on the clock and have your child say 2 x (whatever number you point to) = (and give the answer.) Do this three or four times, making sure to include each number on the clock. As you do this, make a mental note of any that your child seems to pause on, and go back to that number later. If your child is having trouble with any of the facts, pull those cards, and have the child study them more. Then, repeat the "clock test" until the child can go through all the numbers, three or four times, without hesitating or stopping to think about any of them. When you are satisfied that your child has "mastered" the 2s, do all of this again with the 3s until your child has demonstrated with the "clock test" that the 3s have been "mastered." Remember - this is to be done over a period time - perhaps even two or three days or more, depending on how well your child is doing. If you push too hard or go too long, your child will become frustrated. Make certain that you praise or even reward your child for effort and success throughout this process.
Finally, go through the same process exactly, but do it this time with the 2s and 3s mixed together. Go through the cards, 2s and 3s, unfolded, in order, and read them together to practice. Then show the cards (folded) to your child, and set aside any that the child pauses on. Set these aside in a rubber band to be studied more. When the child is successful, mix the 2s and 3s out of order, and with the cards folded, go through them. Set aside those that need to be studied more, and try again. When success comes, give the "clock test" again, first with the 2s and then with the 3s. Repeat this "clock test" three or four times. When you are satisfied that the child has "mastered" the 2s and 3s mixed together, move on to Step 3.
Start Working on the 4s and 5s
Your child will likely have anxiety when faced with the 4s and 5s. These facts seem to be "big"and "hard." Before you begin this part, encourage your child by explaining that once the 4s and 5s are done, the hardest part is done, and that it will be much easier after that. This is the truth, too, as you will read in Step 5.
In Step 3 you will do exactly the same thing you did in Step 2, but this time do all of it with the 4s and 5s. Go back and review the process to follow in Steps 1 and 2 to be sure you remember how to do it correctly. Follow the process until the child has demonstrated "mastery" with the "clock test" on the 4s and 5s.
Remember to stretch this out over a period of time so as not to frustrate your child.
And don't forget - make certain that you praise or even reward your child for effort and success throughout this process.
The Finishing Touches on the 2s Â‚ - 5s
We're almost finished with the "hard part" of memorizing the basic facts of multiplication.
In Step 4, you will follow the process you did before, but now you will mix the 2s through the 5s together. Refer back to Steps 1 and 2 if you need to.
Your child will definitely be stressed out now - to do all the facts from 2s through 5s seems like a daunting task indeed. Remind your child of what has been accomplished so far, and give assurance that the child will be able to do this within a day or two.
Encourage your child by explaining again that this is the hard part, and that it will be easy from here on out. Remember - this is the truth, as you will see in Step 5.Once your child has memorized the 2s through 5s, the 6s through 9s are actually easy - easier than learning the 2s through 5s. Make sure your child understands this. Understanding this will serve as motivation for learning the 2s through 5s, and will help relieve anxiety about learning the 6s through 9s - the part that most children think will be "really hard."
The Home Stretch: 6s through 9s, and All of the Basic Facts
At last, we have reached the final stages. Now, at this point it is important for you to know something, and to make sure your child knows it:
Now that your child has memorized the 2s through 5s, there are only TEN more basic facts to learn! That's right - just ten more to go!
Here's why: all that needs to be learned are what I call "the doubles and up." Here's what that means: it isn't necessary for the child to learn 7x4, because 4x7 has already been learned. There's no need to learn 9x3, because 3x9 has already been learned. See what I mean? Here are the remaining basic facts to learn:
6x6 = 36 6x7 = 42 6x8 = 48 6x9 = 54
7x7 = 49 7x8 = 56 7x9 = 63
8x8 = 64 8x9 = 72
9x9 = 81
See? Just "the doubles and up" are left! Write these facts on index cards, and use the same process as before to master these ten basic facts. This should not take long at all, since there are only ten of them, and the child will feel a great sense of relief once the "clock test" shows that they have been mastered. Make certain that you praise or even reward your child for effort and success throughout this process.
Next comes the part where you mix ALL the facts together - the 2s all the way through the 9s. You will follow the process you did before, but now you will mix the 2s through the 9s together. Refer back to Steps 1 and 2 if you need to.
Finally, give the "clock test" on all the facts. Mix them up. Do the 4s, then the 8s, and so forth. Then, do them all again, mixing them around. Do the 5s, then the 9s, then the 2s, and so on. Repeat this three or four times. Remember - keep a mental note of any facts that the child still seems to have a little trouble with, and put them in a "study some more" rubber band. Over a period of days, working a little each night, practicing and taking the "clock test," to check for mastery, your child will have completed the task of memorizing The Basic Facts of Multiplication.
Now it's time for a real celebration! A prized reward of some type would be perfectly appropriate at this time.
To maintain the learning, the "clock test" should be given every few days, with extra study as needed.
And that's it! You have helped your child achieve a goal that is difficult to do alone in school and by himself or herself at home. You have given your child a gift that will serve well and be of great benefit in the future. Be proud of yourself and your child.
I hope that this article will help you in your efforts.
Tips & Warnings
Tips and Warnings:
Make sure that you work with your child in a quiet area, with little distraction.
Don't work too long at one time.
If your child goes off alone to study, be sure a quiet, comfortable place is available.
This is a process that may take several days, maybe a couple of weeks, and it is okay to skip a day now and then.
Don't "push" your child, or show any sign of impatience, anger, or disappointment.
Stay positive and encouraging. Remember - this may seem easy to you, but it doesn't to the child.
Be sure that you continue to check for "mastery" regularly, and encourage more study and practice as needed. This way, your child will not "forget" the basic facts. It may take weeks or even months (depending on the child) before your child has once and for all truly memorized the basic facts.
Make certain that you praise or even reward your child for effort and success throughout this process.