Maths
Learning To Multiply
Maths is an exact science - there is only one answer, you can't get it nearly right.
Counting, adding and subtracting are the first necessity.
- Adding is merely counting on numbers ie. 5+4 = 5 count on four = 6789 = 9.
- Subtraction can be reverse counting, but it is easier for a child to think how many more to reach the number.
ie. 9 - 5 = how many numbers do I count to reach 9 from 5 = 6789 = 4. - To put that in equation form is. 9 - 5 = what? Or 5 + what? = 9.
Most children can get this far without too much difficulty, but some will be slower than others. Why? One reason is well known in teaching and teachers try to teach audial, visual, and kinaestheticaly ie. hear, see, and do. The hear and see are easy to teach, the teacher stands at the front of the class and says listen to me, and speaks and writes on the board, fine for children who are predominantly audial and/or visual. Unfortunately some children are predominantly kinaesthetic ie. I need to do something. These children are left behind, they don't understand from that style of teaching. I don't know how you teach a large group of children kinaesthetically. I am not a Schoolteacher, but I can teach. In fact because I am not a schoolteacher and have not been 'Trained' I can teach a small group of children (3) quicker and better than a schoolteacher. In fact I can and have taught children of age 10 - 11 who could not multiply at all, to being reasonably profficient in six lessons on one digit numbers.
Multiplication is the next hurdle, and this is a very definite decider between succeed or fail, bright or dumb. Learn your times tables, boring, boring, boring. Some children can do this, because they are able to concentrate on it or they get help outside of school or they are obedient or they are determined. Boring maybe, but they learn it, but the top ones do not answer what is 6x7 by the times tables, they have memorised 6x7=42. There are 36 equations from 2x2=4 to 9x9=81. If you child learns the times tables they will have to learn another 28 equations because 7x6=42 as well as 6x7=42. The requirement is to be able to multiply, the times tables are a means to that end. Is there another way?
What does a child want? Fun. A challenge. To learn. To be interested. Quick moving. Hands on. That is how children want to be taught.
- To learn, to know they will succeed.
- A challenge, to have a time limit to success.
- To be interested, children hate boring teaching/teachers.
- Quick moving, fast, faster, fastest, stop wasting my time.
- Fun and games, games are fun, games are a challenge, games are interesting.
- Hands on, I want to be involved, I want to be doing.
Is there another way? Yes there is, working in a small group of three, or two, or singly. Memorisation is the key. If children are given a fast, fun, challenging, hands on, means of learning, they will memorise the answers because they want to. Do you think they will learn to memorise if they find it boring and unintelligent and don't want to?
You can explain things to some children and they will understand it straight away. You can explain it to other children and they will never understand it, especially attention deficit children. So you have to have them do it.
The most daunting times tables to learn are the higher numbers 9, 8, 7. So how do we deal with these numbers? First we learn how to multiply by 9, (not the 9 times table). Multiplying by 9 is very easy and there are a number of ways of doing it. See 'A SIMPLE WAY TO LEARN TO MULTIPLY" And I explain there why it is not necessary to learn to multiply by 7 and 8. 'Maths Games' will show you how to make learning fun
HOMEWORK
The word most children dread, it means more boring school stuff to do at home when you already don't know how to do it. Let's face it, to give children work to do at home that they don't know how to do is punishment, not practise. We all know that practise makes perfect, but giving children homework they can't do emphasises failure, and accentuates bad teaching.
Instead of homework we will substitute Practise.
An interesting point - My children would lie on the floor watching TV and doing their homework, mother would say "you can't watch TV and do your homework at the same time" The boys would say "Yes we can Mum". Dad would say "Yes they can because I can do that." Children face distraction all the time at school. Of course they switch to homework in the adverts. My wife cannot stand distraction of any kind when she is doing something like studying or writing, Whereas distraction doesn't usually bother me I can phase in or out as I please.
There is another problem in teaching, besides the audial, visual, kinaesthetic ways of learning/teaching, that isn't so well understood. And that is the temperament type, which comes from personality typing. There are a few ways of personality typing but the most popular is the Carl Jung, Myers-Briggs one.
It is pretty obvious that people who did well at school are more likely to become teachers Those children are the SJ temperament. S for sensing ie. I hear you, I see what you show me. J for obedient and orderly. Those children go to the top of the class, ideally suited to the school system. 54% of teachers are SJ. So over half of the teachers are likely to be of that one of the four temperaments. 34% of teachers are NT, N for intuitive ie Don't give me lots of facts, challenge my mind, otherwise I will dream off. T for thinking, logical, right or wrong, Only 9% of teachers are NF temperament, F for feeling, compassion, what is best for the child, rather than what is right or wrong. And the most appalling of all 3%of teachers are SP, S for sensing and P for Put off and play. Now get this, when the children were asked who were the best teachers, they chose the SPs. The SPs tried to make everything fun, didn't worry too much about sticking to the curriculum and other does and don'ts, the few who made it through the school system sufficiently to be able to become a teacher soon ran foul of the administration and system, they didn't match up. The administration are likely to be SJ, Obedience and orderly, so put off and play wouldn't go down very well, so what about SP children? The statistics are taken from American research on teaching.
Incidentaly I am a INTP if you know about the Carl Jung, Myers-Briggs Personality System
ADD/ADHD If you want to know more about this SEARCH - Kiersey - on the internet for the articles below - Keirsey Temparament and Character.
- Essays on Aspects of Temperament and Behavior
- News Alert: Ritalin Class Action Suit
- TOO MUCH DOPE FOR TOO MUCH PLAY AND TOO LITTLE WORK
- The Great ADD Hoax
- THE EVIL PRACTICE OF NARCOTHERAPY FOR ATTENTION DEFICIT
- Abuse it -- Lose it
- Drugged Obedience in the School
- Learning in Style: Artisans in Action
Recommended Books
- Children the Challenge
- Talk So Kids Will Listen and Listen So Kids Will Talk
- Talking back to Ritalin
- Just Say No To Addicts
Maths Games
COMPETITIONS - 2 Players
One player works out equation in his head, the other uses a calculator. Best out of ten.
Give the answer, players compete to give the equation. Best out of ten.
Throw two dice, players compete to multiply numbers, first correct answer receives a rubber bullet as reward. When ten bullets are handed out they shoot at a small target and get a pebble for every hit.
Deal two number cards, players compete to multiply numbers, awarded a ball as reward for first correct answer. When ten balls are awarded they shoot at basketball net and get a pebble for every score.
Spin for a number with spinner, then another number. Players compete to multiply numbers. Awarded a ring for every correct answer. When ten rings have been handed out they try to ring an upturned chair leg. A pebble for every success.
Use a set of magnetic numbers each, call out equation and they have to arrange numbers and answer. Best of nine correct answers gets a go at the skill games, which are timed. Various awards.
RACES - 2 Players
Two boxes with magnetic numbers in them, they have to run up and get a number and place it next to sign, then run up and get another number from box and place next to sign to form an equation and write down the answer. First to get five correct answers gets a go on the deadly triangle.
Signs __ x__=
Fishin
Cardboard fish with washer on top and a multiplication underneath, two different colours. Players have to fish with a magnet on the end of a rod and line , write down the multiplication and the answer.
Best of seven gets a pebble.
If they hook the wrong colour fish they lose a point.
Two question cards with multiplications on them, one each. Players have a dice each, and have to throw a six to get a go at answering a multiplication. First to get five correct answers gets a pebble.
Simple Way To Multiply
Only two times tables to learn x2 and x3
I will presume you know that 1 times any number is that nunber and ten times just has a 0 added on it.
TO MULTIPLY BY 5 - Hold out your hands and you will see 10 fingers (normaly).
- Going from the left label them 1 to 10.
- When these fingers are multiplied by 5 the last figure goes 5 0 5 0 5 0 the labeled fingers are numbered 5, 10 ,15, 20, 25, 30, 35, 40, 45, 50.
- If you are asked 5x8, don/t start counting from 5, 10.... the first finger you count on the right hand is number 6, and 6 is 30 so count from there.
Quick eh!
TO MULTIPLY BY 9 - Hold out your hands, fingers labelled from left 1 to 10.
- 9x3 - bend or cover the 3rd finger, those to the left are 2 but in tens ie 20
- Those to the right are units ie 7 so you have 27.
- 9x7 - bend the 7th finger, 6 to the left, 3 to the right ie 63.
- Simple eh! Who would want to go through that complicated rigmarole of the times tables they teach at school.
- (I did not know about this when I taught Myself As a young boy, I multiplied by 10 and subtracted one of the number ie. 7x9 = (70-7) = 63
Now you can become proficient at multiplying by 5 and 9 by testing yourself by throwing a dice, (have a second dice with 123 marked as 789)
Now let me let you into a secret. The kids who are brilliant or good at multiplication do not use the times tables, they used them to learn the equations, memorised them, and answer from memory.
Now we will go to the two higher NUMBERS 7 AND 8.
- These are more difficult so we will forget them except that we will memorise 7x7 = 49, 7x8 = 56 (and 8x7), 8x8 = 64. WHAT! How can you forget 7 and 8 says the schoolteacher?
- We allready know what 1,5,9,and 10 times 7 and 8 is, we don't need to duplicate it, the others we will learn. Stick white paper onto a dice and mark them with the multiplications and test the student on those numbers.
This leaves us with 2,3,4, and 6
LEARN 2 AND 3 TIMES - best to do it like you did the 5 multiplication.
Then throw the dice, get a friend and make it into a competition, make it fun, Give him a cookie for 20 correct answers, or a minute on a skill game.
TO MULTIPLY BY 4 - multiply by 2 and double the answer ie 4x6 so 2x6 = 12
+12
=24
TO MULTIPLY BY 6 - Multiply by 3 and double the answer ie 6x7 so 3x7 = 21
+21
=42
Test with a dice again.
You need to be able to add two digit numbers to do this, if you can't, learn how to, you need to be able to add before you multiply.
You need to be able to count before you add or subtract.
I do not know of any way to be able to divide before you can multiply so you need to get proficient at multiplying before you can divide.
Another way to multiply by the more difficult numbers is to break them down.
- Lets take 7 x 8 = 56
- Break down 7 to 2 and 5
- 2 x 8 = 16 and 5 x 8 = 40. And 16 + 40 = 56