Snap snap

Assalamualaikum, hello peeps.

So… Exam, revising, flipping through notes and everything. Some finished theirs, I’m left with one paper which I’ll be having next week. Pressure’s off :)

Anyway, just want to share some pictures I took. Roll it.

Alright, I guess that’s all for now. Selamat Hari Raya Aidiladha everyone.

Salam.

Bring it; your Human Calculator!

Hello everyone! Hello Dr. Leong!

This is one of my coursework for ED1411 (Creative Mathematics in Children) and I hope everyone who reads this post will find it useful for them.

At first I find it very hard to come up with an interesting topic yet is useful to share with everyone. Then I remember that I own a book by Scott Flansburg, thanks to my mom who gave me that book. The book is about working out maths problems; not just working them out using the usual old methods but with brilliant strategies which I will share with all of you in a bit.

Before I share the interesting things, I think I should first introduce Scott Flansburg, the author of the book. Maybe none of you know who Scott Flansburg is. He may not be as famous as Bill Gates but I think he is a maths genius. He’s now 46 years old (I think!) and was born in New York. He’s been featured on many radio stations in the US and television talk shows. Well he’s now teaching others to overcome their “mathsfobia” (fear of maths)

Okaaaaay, enough with Scott. Let’s start with one simple question. How many of you out there think that maths is important in our daily life? Some might say not so important cause like what Scott Flansburg said, “After all we do have calculators to do maths for us, right?”

You see, now that we have so many new inventions, we are becoming lazy. I guess we don’t even use our brain anymore to calculate simple maths and instead use the calculator.

So I am going to share some strategies introduced by Scott so that everyone will have a different mindset about maths. Like me, after learning these strategies I find maths very easy (before, I let the calculators do the job!)

Okay, the first one is Distributive Property of Numbers.

Look at the following problem: 24 X 99 = ?

You might want to take a calculator to solve that. That’s okay but let’s not use the calculator that you buy from the store but use the calculator you were born with: your brain!

Look at the numbers and think. Isn’t 99 real close to 100? So 99 is actually 100 minus 1, right? So we now have: 24 X 100 minus 24 X 1 = ?

Of course you all know that 24 X 100 is 2,400 and 24 X 1 is 24. So we have 2,400 - 24 and that gives the answer 2,376.

It can still be difficult to work out 2,400 – 24 for some people, so we use a little different step.
Let’s convert 2,400 to $24.00 (we know how people likes money haha) then convert 24 to 24cents. Now look at 24cents, it is real close to 25cents. Now $24.00 minus 25cents would give us $23.75. Since we use 25cents instead of 24cents, we have to add 1cent back to the $23.75 and that would give us $23.76. Therefore now we have our answer which is 2,376!

Let’s try another one: 24 X 52 = ?

Do you realise that 52 is close to 50? And you know 50 is half of 100. So if 24 X 100 is 2,400 then 24 X 50 would be half of 2,400. What’s half of 2,400? Yup, 1,200. Okay, since we only work out 24 X 50, we still have to add 24 X 2 because 52 is 50 + 2. The easiest way to work that out is just by doubling each number of 24. Double of 2 is 4 and double of 4 is 8. Then 24 X 2 = 48.

Now we can add 48 to 1,200 and that’s 1,248!

Easy righttt! Hehe. Looks like we’re bringing out the Human Calculator in You!

Alright, the second strategy is Addition.

Look at the following example:

   225
   124
   221
+115

The first column is the hundreds, the second column is the tens and the third is the ones. This strategy starts in the hundreds column by adding the 2 and the 1. That gives us 300 (200 + 100). Then we add 300 to the next number which is 2 so that will give us 500 (300 + 200). Finally, we add 500 with the last number, 1, which will give us 600 (500 + 100).

Now we move on to the next column. The first number, 2, stands for 20. We add the number we calculated in the first column which is 600, with 20. That gives us 620. Then we add again with the next number, 2 (which is 20) and we get 640. Then the next number, 2 (which is also 20) and we get 660 and lastly the number 1 (which is 10) and we get 670.

Now we can move on to the last column. We add the first number 5 to 670 and we get 675. Then we continue to the next number, 4 and add that number to 675 to get 679. Then the next number is 1, so we add again and get 680. Lastly we add the final number which is 5, to 680 and we get 685!

Now the third strategy will be on Multiplication. This strategy sounds complicated but it is actually easy as long as you remember the steps. So take a pen and a paper, let’s work together (and I insist!)

Let’s work with the following problem:

   621
x 584

We will work out our answer and write down answer from right to left. First, 1 X 4 is 4. We write that down as the last digit of our answer. Then we cross multiply 2 and 4 and we get 8. Wait a second now before you right that number down. We cross multiply 1 and 8 first to get the number 8. Then we add 8 which we obtained from 2 X 4 with the other 8 which we get from 1 X 8. This will give us 16. Now we can write down the number 6 next to 4 which we have written earlier on. The number 1 from 16 will be used later on.

Now we multiply 6 and 4 and add it to 5 X 1 and then add to 2 X 8. So we get 24 + 5 + 16 which gives the total 45. Remember the number 1 from 16? Now we can use that number to add to 45 and we get 46.

Next step is to write 6 (from 46) next to the two numbers we have written down before which is 64 and we have 664 now. Again, the number 4 will be used later on.

Now we are going to multiply 6 and 8 and add it to 5 X 2, giving us 48 + 10. That’s 58. Then remember the 4 we were going to use later on? Add that number to 58 and we get 62. Now write down the number 2 (from 62) next to the number 664 which we have written before. Now we have 2664. Again, the number 6 will be used later on.

Okay lastly we multiply 6 and 5 to give us 30. Add the number 6 which we were going to use “later on” to 30 and we get 36.

Write down 36 next to the numbers we wrote just now, we have 362,664. Guess what? You got the answer.

Now try this using the strategy you have just learned (don’t be lazy to try):

   733
x 367

Now check your answer with you calculator, if you get the right answer you don’t even need the calculator anymore.

The fourth strategy is the Complementary Multiplication.

We’ll be working on the problem:

   96
x 94

We’re going to start with how far from 100 each number is. Now calculate the difference of 96 from 100 and the difference of 94 from 100. That’s 4 and 6 right? Now multiply both numbers and we get 24. This is the last two digits of our answer.

   96   4
x 94   6
   90   24

How do we get 90? Easy, we just subtract the 4 from 94 or 6 from 6. So the answer is 9,024.

Still don’t understand?

Let’s try:

  93      7
x 91    9

7 X 9 is 63. That’s our last two digits. Now we subtract 9 from 93, or we subtract 7 from 91. What do we get? Yes, 84.

Then the final answer is 8,463!

If the product of the difference numbers (e.g 4 X 6 for the first problem or 7 X 9 for the second problem) is over than 99, add the hundreds unit to the right digit of the first part of the answer.

Example:

   76
x 88

76 is 24 units away from 100 and 88 is 12 units away from 100. So 24 X 12 is 288 (this is over 99). Our first part of answer would be 64 (76 – 12 or 88 – 24). Now add the number 2 (from 288) to 64 and we get 66. So the final answer would be 6,688.

If the numbers to be multiplied are over 100, we don’t subtract the difference but add them instead.

Example:

   103  7
x 107  3

As usual, we multiply the difference, 7 X 3 = 21. Then usually it’d be 103 – 3 or 107 – 7 but this time since it’s over 100, we add 103 + 7 or 107 + 3. Now we get 110. The final answer is 11,021.

So how do you find the strategies so far? Amazing how we can find so many ways to work our maths problems right?

Now we move on to the fifth strategy (Squaring) which is the quickest and simplest way to square a number below 100 and above 51. We simply need to know how far from 100 is the number you are going to square.

For example, we try the 96²

96 is 4 units away from 100. Now we subtract 4 from 96. We get 92.

The second part is simply squaring the difference (the number 4) and put the number behind the number 92 we obtained earlier on. So the answer is 9,216!

If the squared number of the difference is larger than 99, for example the square of 88, simply add the hundreds unit to the second digit of the first answer.

  88²
-12
  76

    76
+144
 7744

This following part is the last one I’ll share which seems to be my favourite one.

If someone asks you “what is the square of 65?”, you might just say you don’t know the answer or you take a calculator and start to punch in the numbers. I mean, I’d do that before..

Here’s a simple method Scott found out for squaring number which ends with 5.

Let’s use 65²

We know the square of 5 is 25, so we write down

65²
25

Then, to get the first part, you will need to add 1 to the first digit of 65 and that is 6 + 1 = 7. Add the number 7 to the equation:

    7
x65²
  25

Now multiply 7 and 6, you get 42. Add the answer to 25. We get 4,225. That’s the answer! Don’t believe? Check with your calculator.

Okaaay, I really hope you are not tired after this. At least you gain something and now you can use these strategies and work your brain more often rather than using the calculator all the time.

I will share more in the next posts on other things so do check if you have the time.

For the time-being, I hope Dr. Leong will give me gooood marks for this. If you remember, I was going to do something on shapes but then I found that topic a little more challenging to make it interesting. Nevertheless, i find these strategies way interesting and useful in teaching children.

Alright, till next entry.

Salam.

Under the waterfall

Assalamualaikum. Hey.

I came accross some quotes today, from a book featuring Scott Flansburg. I'll talk more about him in my next post since i'll be doing a coursework based on his work.

One of the quotes, "Whether you think you can or cannot become successful, you will be right!"

That's my favourite one for today. Like it alot.

Till then, i'm going to post one of my coursework tomorrow, here.

Salam.

The new beginning

Assalamualaikum. Hello all.

As a start, i'd like to share my.. not so impressive tessellation but it's my very original idea. It took me a month to think of what to tessellate. Even drawing faces can be hard especially when you try to avoid gaps to make a complete tessellation.

I handed in the work to my lecturer already, took few pictures of it though. Thought it'd be nice to share as a start.

Enjoy :)

Will post next entry real soon.

Salam.