This is not an article about autism but autism is my point of departure because I have always been intrigued by the genius of mind of autistic persons and how they have been portrayed in cinema and books. Their ability to identify patterns in numbers specifically, otherwise hidden from civilian eyes, is, for me, a fascinating glimpse into how the human brain functions and what it is capable of achieving.
Where numbers are the basis, patterns are the key. Logical problem solving translated in numbers.
Remember how easy 11x Tables were once you got the pattern to their solution?
We all know that adding a zero to the end of a number solves any multiplication problem of 10. And to solve a multiplication problem of 5 you simply divide the number in half, then x 10. Most people I know are also aware that percentile problems work in reverse too.
Do remember the 9x Table Finger Trick? I used to love this one. For those of you that don’t know it works on bonds of 9 up to 10; you put your hands out in front of you, say you’re working on 9 x 3 … you then fold down the 3rd finger, the answer will be the number of fingers to the Left of the folded down finger and the number of fingers to the Right of the folded down finger (2 + 7 = 27). Try it.
I was reflecting on all the maths shortcuts I’ve learnt over the years when considering school homework recently. Would it be considered “cheating” to exercise any of these shortcuts? I don’t think so as long as the basics, the mathematical foundations, are laid. (I remember having to learn the 17x table; this was one of the most difficult things I had to do. Now I can’t forget it and it is a great party trick since apparently not many other people are familiar with bonds of 17…) To me it’s like the moment when you realise that there is a good and different opinion to one you have been carrying for so long – a paradigm shift, a revelation of sorts. It is refreshing, energising and exciting all at once. And, of course, everybody has a different learning style – so why not?
To be perfectly honest, I don’t think I’ve ever been asked to actually calculate bonds of 99 or 999 but if I was called upon to do so at least I would know how to …
Is the learning outcome to learn the math sequences off by heart, or is it to instill problem solving abilities? I am not an educator so I’m not advocating what is right or wrong. Just have some thoughts running through my mind in this regard at the moment.
Here are some shortcuts you may or may not know. Have fun with them!
Square of numbers near to 100
Trick: Calculate the difference between the number and 100. Subtract or Add this number to 100 (if the number is greater than 100 add, if less than 100 subtract). Write down this number . Calculate the square root of the number that is the difference. Write down this number to complete the answer.
100 – 96 = 4
96 – 4 = 92 (Write this down)
4 x 4 = 16 (Write this down)
Answer = 9216
100 – 108 = 8
108 + 8 = 116 (Write this down)
8 x 8 = 64 (Write this down)
Answer = 11 664
Legs alive for number 5
To calculate the answer to any multiple of 25; add 00 to the end of the number and divide by 4.
To calculate the answer to any multiple of 125; add 000 to the end of the number and divide by 8.
What are you worth?
Let’s get practical. We’ve all tried to work this out before. You can do this without a calculator. Take your salary, drop the last three zeros and then divide by the number two. This number is your hourly rate if you work an average of a 40-hour week.
Beat those repeating fractions into decimals!
This is so easy you could most probably perform this trick at the end of an all-day braai!
- Choose a number (a repeating fraction of course). We’ll use 0.54545454.
- Find the number that repeats (54)
- Figure out how many places that number has (2)
- Divide the repeater by a number with the same number of places made up of nines (in this case, 99)
- So, 0.54545454 = 54/99 = 6/11.
The best tip I ever got? Every multiplication has a twin e.g. 8×5 equals 5×8. You only ever have to remember half the table.
Here are some multiplication tips for your kids or students:
|FOR KIDS AND SCHOLARS|
|Bonds||Basics||E.g. 100 (Read L-R, don’t BODMAS)|
|1||The answer is always the number||1 x 100 = 100|
|2||Double the number||2 x 100 = 100 + 100 = 200|
|3||Double the number then add the original number to the sum||3 x 100 = 100 x 2 + 100 = 300|
|4||Double the number, and double it again||4 x 100 = 100 x 2 x 2 = 400|
|5||Multiply the number by 10 and divide by 2. For larger numbers, halve the number and move the decimal point||5 x 100 = 100 x 10 / 2 = 500 5 x 4500 = 4500 / 2 = 2250 = 22 500|
|6||Multiples in even numbers always end in the same number||6 x 100 = 600, 6 x 2 = 12, 6 x 24 = 144|
|7||Multiply by 6 then add the original number||7 x 100 = 100 x 6 + 100 = 700|
|8||Double the number. Double the sum. Double the sum again.||8 x 100 = 100 x 2 x 2 x 2 = 800|
|9||Multiply the number by 10, then subtract the original number||9 x 100 = 100 x 10 – 100 = 900|
|10||Add a 0 to the end of the number||10 x 100 = 100 + “0” = 1000|
|11||Up to 9x: Repeat the number||11 x 9 = 9 next to 9 = 99|
|2 Digit problems: Add the 2 digits, insert between the original 2 digits. (If the numbers in the middle add up to a 2 digit number, just insert the second number and add 1 to the first)||11 x 10 = 1 + (1 + 0) + 0 = 1_1_0|
|3 & 4 Digit problems: Add pairs of numbers and insert between the first and last number.||11 x 100 = 1 + (1 + 0) + (0 + 0) + 0 = 1_1_0_0|
|15||Multiply the number by 10. Add that number to half the sum.||15 x 100 = 100 * 10 + 500 = 1500|
If you’ve actually read this entire article – bravo! Here’s a game you can play wherever you are, whoever you’re with right now…
Step1: Think of any number.
Step2: Double the number.
Step3: Add 9 with result.
Step4: sub 3 with the result.
Step5: Divide the result by 2.
Step6: Subtract the number with the number with first number started with.
The answer is always “3”.
Can you read the matrix yet Neo? 🙂