Teaching MultiplicationDoes anyone have any good ideas for helping older kids memorize their times tables?
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.
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
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.
I use songs that myself and some other teachers have made up based on tunes the students know. I sometimes have the kids get together to make these up. If they own a number song or rap they tend to remember it better. Older kids are thrilled to do something fun and seem to enjoy this. I also get them visualizing the groups. Flashing cards on a screen because they show groups of numbers and they get into the habit of visualizing the numbers. Example: 3 five of hearts. Another thing I like to do is to give them a certain set of facts and let them be number detectives. They get to try to find relationships between the numbers and see what they notice about them. I feel like repitition, visualization and ownership helps so much with these concepts.
Find what they like. A teacher should always know their students so use whay they like to your advantage. For example, If they like cookies, you would give then one for multiplying 1x1 to 1 x 10.
use a calculator
Bring them a times table book and tell them to memorize this and if they don't then they will be grounded for a week and they cannot use computer. That should do the trick!!!!!!!!!!!
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
I loved teaching math facts to my 5th graders! There are so many great tricks and fun methods!
Many students are relieved to discover that they only need to multiply half of the multiplication table. If you fold the table in half diagonally from top left to bottom right, one half is all you need. Then when they don't know 8 x 4, they can be reminded that they have memorized 4 x 8!
Purchase a big tub of dice and have students pair up to practice their facts by tossing down the two dice and the person who comes up with the answer first gets a point. Add additional dice for a bigger challenge. If you don't have the funds for dice, teach the students to make a cube out of paper and number it.
Teach your students to make paper fortune tellers. When they are complete they can write multiplication problems on the outside flaps, ex. 4 x 5 and when the person answers 20 they operate it 20 times. Then on the inside there will be another math facts equation to solve. When they give the correct answer, they will discover the fortune on the inside.
Of course there are so many fun tricks as well, and songs make memorizing much more fun! There are also many great websites that help students visualize the math facts such as Wolfram, The National Library of Virtual Manipulatives, and fun game sites for practicing as well. It does take practice, but it can be both fun and challenging.
easy answer: just don't teach it. it's not important. use a calculator. That's all you ever need. Or give them skittles
practice makes perfect! i think it helps a lot by practicing...
also there is this trick i learnt for the multiplication of 9: hold out your 10 fingers... for 1x9, put down the first finger and the remaining fingers give 9. for 2x9, put down the second finger and you have 1 finger on the left side and 8 on the right so its 18 :) this can be used up till 9x10
Does anyone have any good ideas for helping older kids memorize their times tables?
It's all about helping students make connections. There are easy problems to solve so start with those. I always start with the basic rules like anything multiplied by 1 is that number and anything multiplied by 0 is 0.
The next step is doubles. Most kids know how to do this with addition so study X2. Then go to X 5 and X 10. Make sure they know the patterns. Anything x 5 ends in a 5 or a 0. Anything x 10 you just add a 0 at the end...no matter what number you multiply by 10, just add a 0. Then work your way from there.
Fun patterns to see help students memorize facts.
x 2 is double the number
x4 is double double (4 x 6 is double 6 (12) and double 12 (24)
x8 is double double double
x 6 is x 3 and double it.
Help students make the connections and see the patterns with numbers and it becomes not just about memorizing the times tables but understanding the numbers themselves.
I am listing a link that was taught to me on a bus as a 3rd grader. I was a slow bloomer in the multiplication facts area. I had the lower numbers memorized but struggled with the 6-9 facts. A woman was on the bus as we were traveling cross country and she shared a method very similar to this with me. By the end of the summer I could multiply. By mid-year I even managed to memorize them.
From my experience, if your a student, you have to remember them by hard, probably up to multiplications of 13. Do practice remembering it everyday. The easiest to start is with multiplication of 2, 4, 5, 9(able to use fingers) and 10. 5 is easy for those who just know how to read analogue time. So the rest of the multiplications can later memorise, slowly, bit by bit. As long as the student practice it everyday.
So as for the teachers, if your class is small or you are a personal tutor, do make an effort to test them before leaving the class. Make sure they get it right, then they may leave. Some students may know the importance of memorising them as when they see their classmates being able to leave with correct answer, they will tend to go back home and memorise them.
So overall, it's all in the mind, make them memorise hard and remember, practise makes perfect! Just a little note to students for inspiration purpose: This is your first step in remembering large size of numbers, as you get older and continue to be you want to be, there's still more to come. So have fun with it!! Have a nice day =)
In reply to #8
Kids always like to play any games so you have to mix maths with gameplays. You put 3 kids in every corner of the class and if they answer three times correct they can change the corner and if they made one round they get no homework at that day
The value of multiplication tables in not in just being able to calculate the different values in the table by multiplication, repetitive addition, or by any other method. Multiplication are useful only when we learn them by heart so well so that they one comes out with any required value in the table almost as a reflex action. This kind of ability and skill can be acquired only be repetition.
We can make this process of repetition more effective and interesting, but there is no alternative to it.
Teaching multiplication is a difficult task for us teachers here. Rather than let them memorize the multiplication table. I encourage them to use their fingers. And its nice to know that they learn easily. You can multiply two digit number to a 2-digit number using the fingers.
8 and 8 are on the floor playing nint. 64 some riddles for each fact
for 9 facts ones decrease by one 9 to 0 and the tens increase by one 0to 9
Take a look of this easy trick:
9x2=18 ; 1+8=9
9x3=27 ; 2+7=9
9x4=36 ; 3+6=9
9x5=45 ; 4+5=9
9x6=54 ; 5+4=9
9x7=63 ; 6+3=9
9x8=72 ; 7+2=9
9x9=81 ; 8+1=9
Iterative addition is also a good teaching method, using real examples.
E.g.: We are three person in this house and each of us has 2 eyes, so, how many eyes do we have?
For consecutive digits: 5,6,7,8