The reason we have problems with the multiplication table is that we are too good at pattern matching. Start with a 9x9 grid. 45 of these are duplicates. 1,2, and 5 are trivial to remember. That leaves 21 things to remember. Of these 7x8 is probably the most difficult for me, and it is probably that the pattern seems broken. 21 things to remember is not a lot, and you could argue that 3, 4, 6 are fairly easy too. That would cut it down to 6. Perhaps some of the problem is that we teach these difficult ones the same way we teach 2, 4, 6, 8, and expect our considerable pattern matching abilities to see a similar pattern in 7,14,21,28,35,42,49,56,63 but there is not a recognizable pattern.
3 4 6 7 8 9
4 12 16
6 18 24 36
7 21 28 42 49
8 24 32 48 56 64
9 27 36 54 63 72 81
I think we are in a transitionary phase in mathematics, like the one that occured when the printing press was invented. When the printing press was invented, and the long journey to literacy started, I suspect there was loud opposition to reading because it was ruining our memory. I see a lot of this same issue in Mathematics. Many believe memorizing a spelling word, or a formula is somehow related to creative ability. When I was a student, 45 years ago, it was necessary to learn and memorize the multiplication table, but in 1975 when calculators went below $10, the need for this ended. We subject children to years of memorization, calling it mathematics, and wonder why most people hate Mathematics. We make students do long division, something that they will never use. We totally complicate the teaching of fractions. and many high school students do not know how to add 1/5 and 2/5, because we complicated it too soon. Calculation is a separate skill than pattern matching. While I understand the arguments which teachers use to justify that these skills are important, they all seem to revolve around the fact that someday they may not have a calculator, and then where will they be, or they will fail a test that does not allow calculators. These are not rational arguments. I do not know the answer to this problem, but I suspect it will disappear when the people like me who had to memorize the multiplication table are gone.
When teaching multiplication to my students, I want them to understand the concept before memorizing facts. I have them use arrays, numberlines, skip counting, draw pictures, etc. while I'm teaching multiplication. While we are working on these strategies in class, I will have the students memorize using flashcards at home. You can have the students use index cards to make flashcards if they don't have any.
Another motivation for students is "Banana Split Multiplication." As you are studying multiplication, have the students take quizzes to show mastery of their facts. When they show mastery of a group of facts, they get a bowl. As they master more groups, they can earn a spoon, banana, scoops of ice cream, toppings, etc. At the end of the year, the students get to eat whatever they have earned. I have seen a teacher display the student's progress through laminated cutouts of each thing that the student earns. After they master the group of facts, the student gets to put the next thing on their display.
It's good for students to learn that multiplication is simply a faster form of addition. Once they see that relationship, multiplication will make more sense to them. Specifically, you can use a skip-counting game, where each person adds the factor to the previous answer and you go around the room to some specified product.
For Algebra teachers whose students are struggling with multiplication, you can add a variation that will connect this to linear equations: If you are working on 3's, the first time around, the first student starts with 0, the next student 3, then 6, 9, etc. until the first round ends. That's your times table for a factor of 3. The next round, the first student starts with 1, the next student will add 3 to get 4, 7, 10, etc. Third round starts with 2. Then, you can show them how this represented y=3x, y=3x+1, and y=3x+2.
I had once a girl who was horrible on multiplication, but crazy about horses. So if we have 4 horses, how many horses legs are there? If there's another paddock with 5 horses, how many legs then? If food requirements are 2 hay bales and 8 gallons per day per horse, how much do you need for both paddocks? If it costs $3 a bale, how much do you spend each week in hay? etc.
She knew her tables cold within a week.
Of course, this means tailoring the curriculum to a student's interest. Which means finding out what the student is interested in, which can be difficult, if not impossible if there's 30 kids in the class. Maybe assign similarly interested kids to a few different groups, one for horses, one for vampyres, etc? If 4 vampyres each need 5 quarts of blood per day, how many victims......:)
Music helps with memorizing rote facts. There are things out there like "Multiplication Rap". You can also teach them some of the tricks for certain numbers (like 9s, with the digits of the answers adding to 9) If they aren't good with skip-counting, that's another thing to reinforce to help them remember. And sometimes, if they get to a certain age and still don't know those math facts, they really aren't likely to learn. Then some accomodations need to be made so that they are allowed to use tables or calculators, or they won't be able to go further in math. A lot of kids can understand concepts for higher math but just can't remember all the facts, and shouldn't be penalized for that.....but that's just my opinion.
I think that it would be a bit more difficult to teach older kids multiplication tables. I personally feel that it should be up to the teachers of the younger grades (perhaps 2nd-4th) to teach the kids multiplication and not make it harder on not only the teachers of the upper grade levels but also the kids themselves. It means a lot more work for them as a student.
Unfortunately in today's education system, teachers are not as concerned about actually having the student learn something. Many are just there for a paycheck. That being said, it sounds like you truly want the students to learn, and here is my suggestion for teaching older kids multiplication:
As much as they probably don't like it, I think that daily practice, quizzes, homework, etc is the best way to get them to learn. Daily repetition will make it easier for them to learn and have it stick in their long-term memory. It's similar to learning a new language.
Hope this helps!
There are many ways to teach old and young kids their time tables. One popular and easier way is to sing a song about it. There are a lot multiplication songs you can find online or make up by yourself. After singing the song constantly, you should be able to memorize the time tables. Another way is to recite it. Have the time tables written down on a separate sheet of paper and say them out loud while looking at the paper. Then say it with out the paper. A tip is to start with the twos and work your way up.
When I was younger my mom taught me the times table and before I knew it I had it down by heart. When I was in 1st grade she started teaching me the times table and to remember I wrote it down and sang it in a sing songy voice. Before I knew it I had 1-10 tables memorized by heart and reviewed it when I sat in a car or anywhere I went. After that I learn the times table of 11-20 and with these its super easy to know multiplication and there is no need of a calculator.
I learned my multiplication facts simply by rote memorization. Every night, my dad would quiz me on a set for ten to fifteen minutes. Then after my 12s, he would begin to mix them together until I finally got them all right.
My dad also taught me a lot of patterns and gave me a lot of hints within the multiplication facts:
- Anything multiplied by 0 is always 0
- Anything multiplied by 1 is always that number
- Anything multiplied by 2 is double
- Anything multiplied by 10 is that number plus a 0 at the end
- If one way is "too hard" (ex. 7x4), then "flip it around" because it's the same and you already learned it (4x7)
- Everything multiplied by 9 will result in an answer that adds up to 9 (there is also a great hand trick from 9x1 up to 9x10) - Hold both hands spread out in front of you, palms facing you. when you do 9x1, put down the first finger. Every finger before that finger stands for the number of tens. Every finger after that finger stands for the number of ones. So 9x1 has 0 fingers in front and 9 fingers in back, so 9x1=9. For 9x2, put down the second finger, and 1 finger is in front and 8 are behind, so the answer is 18. Keep going until 9x10 when there are nine fingers in front and 0 fingers behind.
I recommend having students memorize a set of facts each day then quiz them on it the next day. Have them keep a chart where they can add a sticker for each quiz they get, say 80% or higher. If they don't, then they have to repeat that quiz for the next day. This keeps going until they get the whole set (up to 12s), then they get a big prize (like ice cream or a big candy bar). Then they have to take a couple quizzes with all the facts mixed together, and then they can get another prize if they pass those too.
I was forced to memorize the table by my father. I hated every minute of it and would try to hide from him by climbing up to the top bunk bed. Forced, repetitive memorization is perhaps the worst thing I ever had to do.
But in all honesty, I am glad for it now. The tables facts must come as automatically as your name if only because it makes calculations and mental math so much easier. Memorizing the tables thoroughly helped me easily do division, algebra, and even calculus. I'm not saying every child has to go on to study calculus, but we should make it so that every child has the tools for it if they decide to do so.
I volunteered at a summer school and not a single third to fifth grader could confidently say any of the multiplication facts. And then we wonder why they have trouble in middle and high school maths. Its madness. Some things in math just have to be boringly memorized so that the interesting and creative problem solving can come later.
Make a little song to help the students, when i was in first grade everyday at the end of the day my teacher would teach us the multiplication song and make us sing it. By a month most of the students in my class knew it.
i think a good way of making them (us) learn timetables is by using rymes or songs
mabye make every one choose their favorite song and sing the times table to the rythme
Yes! Rhymes and songs work remarkable well when helping children
memorize those pesky times tables. Check out wwwTheTimesTable.com.
here there is a book and songs/rhymes designed to help children
memorize the multiplication tables quickly. I created it for my child who
was having trouble memorizing and it worked so well that I tested and
perfected it . After 6 years it was published (2012) and is now being used
in schools all over. Please check it out if you get a chance.
Thanks and have a good one.
wanna myltiply any number by 11.
Its so easy, take any number, say, 36
place 3 and 6 in the ends and their sum in the middle
you get 396.
To find a square of the number that ends with 5:
take a number, say, 65. Its square is
simple its 6*,next number ie, 7 =42.
place 25 to th answer it will be 4225.