The best way to teach math?

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I came across a really interesting question today, as I was talking to one of my friends. He asked me, if you came across a human being that had not yet been introduced to the concept of mathematics, what would be the most optimum way of teaching the person from scratch.

I think it’s interesting, because this is basically the concept of math in pre-school. We have some kids, that might be able to count to 10, less or more but really do know how what it means to take one number and add it to another. What is the best way to teach people math, that’s the question.

My personal suggestion is to start out using practical examples to teach the kids, the foundation of mental math. If you had to learn just one math concept, it would in my opninion have to be mental math. The idea of figuring out problems in your head is a lot more important than any other math concept.

So that would be my entry, teach the person to add 1 and 1 in his head and then move on from there. How would you go about it?

2 digit multiplication – Multiplying 2 digits by 2 digits

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It’s been a while since I came up with another general “tip” for mental math. I thought I’d like to share one of the things that I have been practicing lately and that is to do 2 digit by 2 digit multiplication. Continue reading →

Mental math practice trumps mental math tricks!

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Hey guys,

Lately I have been doing a lot of thinking about mental math. I’ve been playing some math games and I can definitely feel like I’m getting better at quickly figuring out math problems.

You may have found my website in the attempts to figure out how to do impressive mental math feats that amazes your friends or family and I have written about some tricks earlier like: Mental Math trick – Multiplying by 11 or even Mental Math – Multiplying numbers between 10 and 20.

Those methods are great and I plan to definitely keep adding more later. What I just wanted to touch on a bit in this post is that mental math tricks are well enough, but you have to PRACTICE if you want to improve your number sense or mental math capability.

My first post on mental math squaring for instance included the very mechnical way of multiplying, which actually just uses the fact that because we are multiplying the same number we get some similar products. Like if you were squaring 76 you are actually doing 70*6 and 6*70 which greatly reduces the stress on the brain!

I later learnt a new way from The book of Mental Math, which will be in a new article soon. I already mentioned the mechanics in my 3-digit easy squaring post but I’ll add another post on it later.

I hope you are practicing math every day, with yourself or your family and that you enjoy the increased number ability that the practice leads to.

Scott Flansburg – The Human Calculator

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On this site I have been talking a lot about Arthur Benjamin, because I felt like his massive squares were quite amazing. Arthur has his flaws as well as any other human, I particularly don’t like his “Which number did you leave out trick” nor do I like that he’s used the same script for the last 20 odd years!

Scott Flansburg is another remarkable math individual that I came across recently through searches and I discovered that he had much the same philosophy I had when I started this website. Get people interested in math by presenting it in a cool and fun way!

Scott presents his own show all over the world and although his “tricks” seem to be limited to a few different ones, he’s doing them with REMARKABLE speeds. For instance ask him to divide a 3 digit number by a 1 digit number and he immediately blurts out the result to some 7 places – that’s pretty cool!

This is the video that made him famous a long time ago: Scott Flansburg – The Human Calculator on Discovery Channel (Youtube video)

A global improvement in number sense has to come from below

Scott speaks to a lot of younger audiences and I really like him for that. He tries to show them from an early age that math isn’t about being boring or difficult, but actually easy and fun! In most of his shows he actually teaches a lot of basic stuff like left to right addition like I wrote about earlier was a necessary skill to do mental maths quickly.

He makes the stuff simple and fun, whilst really conveying math in a fun and educational way. This is the way we need to operate to get the young kids involved in math, if we can get the entire youth population in the world going, then we could potentially see a dramatic shift in the condition of math today.

About Scott Flansburg

Scott isn’t a savant like Daniel Tammet, he merely has some kind of anomaly in his brain that means his math and number sense is greatly increased. Now he travels the world, setting world records in adding the same number to itself most times within 15 seconds, teaches kids and adults about mental math.

You can visit his personal website here: Scott Flansburg – The Human Calculator

My mother sucks at mental math

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Lately I’ve been practicing mental math, inspired by Arthur Benjamin’s mathemagics. I’ve got his book Secrets of Mental Math and I’m really getting excited about actually using my brain to do the advanced mental maths that I should have learned in school.

My mother noticed that I started doing this but expressed no interest in hearing about it or learning it herself. She just figured it was another one of my “silly projects” – well, i told her what is 57*57? Her response was a little shocking, she took a LONG time and even used some paper to jot down some numbers, but came to the result of 2,549 – I asked if she were serious with that answer, she said yeah – was it wrong?

When I look at 57 my immediate reaction is to do (50*64)+49 but that doesn’t even matter. The bigger problem I realized was that her wrong answer, was so far away from the correct one, that she should have realized before she spoke that it wasn’t even possible for the result to be around that number. Maybe my brain is already improving because of my maths training, but it’s pretty quick to realize that 50*50 is 2500 so 57*57 has to quite a bit more, you could even think that 60*60 is 3600 so 57*57 is between 2500 and 3600 with a considerable bias towards the 3600.

Granted my mother has never been much of an academic or bothered too much about school, and it has been some 30 years since she last had math but I was still slightly disappointed.

Lack of Mental Math skill is a global problem

Then later on the television I saw a quiz show where the player was asked: How many percent is 10 of 50. It’s shockingly bad when the player can’t even begin to reason towards a correct result. I won’t bore you with the actualt result because its so easy even a first grader should be able to figure it out…okay maybe not first grade, but definitely by the time you are introduced to percentages.

It’s a global problem that we suck at mental math. Computers and calculators do the jobs for us and so we lose the training aspect of maintaining a skill. This is why i created mental math now – my humble effort to spread the love of mathematics and try to make people think a little once in a while.

Be the change

This website will never speak about calculus or advanced maths that you actually do need a graphical calculator for. As interesting as it may be, I just think that it’s not really that great for every day use. Mental math is a lot more fun, useful and applies directly to every day aspects. Like going to the supermarket or doing your tax returns!

How is your personal math life, do you know anyone like my mother – or the quiz player? Comment below!

The way to memorize large numbers in mental math

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Hey guys,

I just started learning how to memorize large numbers with loads of digits using the Major Mnemonics System.

this helps me do mental math problems, and I hope to become good enough to use it in 4 and 5 digit squares to make them easier ;)

Here is the chart:

(Source: http://en.wikipedia.org/wiki/Mnemonic_major_system)

0 s, z, soft c “z” is the first letter of zero. The other letters have a similar sound.
1 d, t d & t have one downstroke and sound similar (some variant systems include “th”)
2 n n has two downstrokes
3 m M has three downstrokes and looks like a “3″ on its side
4 r last letter of four, also 4 and R are almost mirror images of each other
5 l L is the Roman Numeral for 50
6 j, sh, soft “ch”, dg, zh, soft “g” a script j has a lower loop / g is almost a 6 flipped over
7 k, hard c, hard g, hard “ch”, q, qu capital K “contains” two sevens
8 f, v script f resembles a figure-8. V sounds similar. (some variant systems include th)
9 b, p p is a mirror-image 9. b sounds similar and resembles a 9 rolled around
Unassigned Vowel sounds, w,h,y These can be used anywhere without changing a word’s number value

Examples:

TITAN = 112

COCOA BEAN = 7,793

MY ELEPHANT IS BLUE = 35,921,095

Easy huh? Now comes the hard part, memorize the tables and practice!

Here is a video of Arthur Benjamin explaining how it works, and how it’s done! He’s a great mental math artist and mathematician!

The video is copyright from The Great Courses.com – but is offered for free on their website as a promotion for Arthur Benjamins: Secrets of Mental Math course, which is highly recommendable.

How to set up your own mental math blog!

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Mental Math Now – How to set up your own blog

I’ve received a question on how to set up your own blog, maybe for mental math or maybe for something else. Here’s my quick and easy guide to do that.

Disclaimer: The links in this article, where available, are affiliate links. This means that any purchase made using those links will generate a small commission for me and the site. Thank you for your support!

The easiest way – Externally hosted blogs

I’m a huge fan of WordPress, so naturally my number 1 site for getting started with blogging is on:

www.wordpress.com 

Positives

WordPress.com literally takes a minute for your blog to be up and running.

The wordpress software is excellent and allows for high customization.

Multiple blogs managed under one username

Negatives

Plugins are not supported, this means that you lose access to visual or practical plugins that really make your blog better.

You’re under wordpress.com ownership, if they decide to shut you down you pretty much have no rights

Not your own domain (although it is possible to set up redirects and so on)

Other mentions in the category

Google’s own blog framework: www.blogspot.com

Tumblr.com: Heavy emphasis on sharing, reblogging and social media – I’m not a huge fan because you so easily get spammed by the people you follow posting cartoons, gifs and what not.

 

Doing it the right way – hosting your own blog!

Contrary to what you might think, setting up your own blog with a personalized domain isn’t difficult and requires no technical knowledge whatsoever.

Step 1 – Buy a domain with hosting from GoDaddy

 

You can get a domain hosted for as little as $5 per month. Use the banner here to check it out.
GoDaddy - World's #1 Domain Registrar

Step 2 – Wait for the hosting and domain to be operational

This step won’t take long. Just keep a note on your email inbox and the GoDaddy Site

Step 3 – Install WordPress

To install WordPress go to your GoDaddy account and chose Hosting from the top left menu.

Once in there you should see a huge WordPress logo in the top right corner of the screen, click through the instructions and it will install WordPress for you.

Step 4 – Login and begin to customize

Themes

WordPress supports themes to change the appearance and functionality of your blog, you can look in the directory under THEMES from the left hand side of the wordpress menu. I personally am not a huge fan of many of these themes, but if you wan’t to spend money then this is the place to go!

I use premium themes myself, they look nicer and have a better backend which enables me to customize my blog even more and run more efficiently. I have used two services primarily in the past:

WooThemes: Might seem pricy at first, but you get so many themes with the membership that you can start hundreds of unique blogs, they feature a really strong backend, a great, helpful community and really stunning visual themes. If you don’t want to spend money you can use one of their two free themes, but be careful – they are used so much on the web that visitors might not enjoy it.

ThemeJunkie: Smaller site than Woo, but a bit cheaper. One year is about $50 which includes 19 nice themes, all updates and new themes. Their support is fantastic and the themes look great.

Plugins

Having plugins on your site will greatly enhance the experience for the user. I don’t use that many plugins, but that’s because I like to keep my blog simple. You can go to the Plugins menu in wordpress and simply start searching. Sorting by popularity will bring out some of the most popular plugins.

Some absolutely essential plugins:

Google Analytics – Incorporates google analytics, allowing you to track visitor information, number of hits and much more.

Contact form 7 – allows you to make your own forms, comes bundled at GoDaddy

Sexy Bookmarks – I don’t particularly enjoy huge social media plugins, but I feel like Sexy Bookmarks does it in a very clean and elegant way – highly recommended.

Google XML Sitemaps - Creates a site map that will get your page better indexed by google

Yoast SEO or other SEO plugin. SEO stands for search engine optimization, with this plugin you can help yourself get better rankings with google and get noticed more!

Not essential but pretty cool:

WordPress Editorial Calendar – Plan your posting schedule with this nifty little plugin.

Outside WordPress:

You can download Windows Live Writer and write blog posts directly in a more familiar text editor environment. I prefer it to the bulky wordpress admin panel, maybe you will as well?

That’s it – time to get blogging!

Thank you for reading and enjoy your new blog! – It’s a super fun experience and if you do create a math blog don’t hesitate to post the URL either as a comment or using the contact form.

Mental Math Tip: Multiplying by 11

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Hey guys,

Here’s a neat little mental math trick you can do when you are facing a multiplication problem where one of the numbers is 11.

Suppose a problem like:

57 * 11

Now, it’s entirely feasible to use a tip i frequently use and often mention:

10 is such a nice number in mental math, particularly when you are doing multiplication problems because multiplying anything by 10 just means adding a zero. Thefore you could attack this problem like:

57 * 10 = 570

570+57 = 627

But there is a faster way:

Pull the number multiplied by 11 apart and mentally place a 0 in between. We’ll change this zero later if neccesary.

57 – 507

Add the digits of the non-11 number and add a zero.

5+7 = 120

add the number to your first number; remember to use the correct ordering:

507+120 = 627

Note: Even though the correct method is to add 0 to the 5+7 = 120 step, it can sometimes be easier mentally by just visualising 12. You just have to be sure that you remember that the 1 in 12 is actually hundreds and the 2 is actually tens, be sure to remember this so you don’t accidentally do: 

507+12 != 519

It’s easy to spot your mistake just by thinking that 507*10 = 570, but still its a very easy mistake to make.

I hope you enjoyed another tip here from MentalMathNow.com – See you later!

Making mental math easier by breaking numbers down into simple one-digit addition problems!

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When doing mental math, always make it easier for yourself – this is the key concept and applies to all kinds of math.

Imagine a problem like:

6592 + 8624

Those numbers aren’t very nice, and we can even see carries coming, so what do you do to keep it simple?

Step 1. Attack the problem from left to right – if you are totally new to this, you could read my introduction here.

Step 2. Break the problem down into parts that are easier for you brain.

From the other post I told you that 42+56 is just 40+56+2 and that’s the philosophy I’m going to continue with here;

Start by adding the thousands, the hundreds, the tens and the singles:

600+800 (check hundreds for carry, if they make less than 9 think the result, else add 1: Say out loud: 15 Thousand!

500+600 (check tens for carry as above) say TWO HUNDRED

92+24 = 92+20+4 say (and) SIXTEEN

Do you see how thinking left to right improves the speed and accuracy of the calculations? With this method you know from step one that the answer is somewhere in the ballpark of 15 thousand, whilst with traditional math you’d only know that the answer ended in 6…that’s not too great!

I hope you continue to enjoy – See you later!

Mental Math Trick: Multiplying two numbers between 10 and 20

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This is a short guide on how to multiply two numbers between 12 and 20.

It also works on 10 and 11 but as probably know:

- Multiplying by 10 is just adding a 0 to the end of the number.

- Multiplying by 11 is also very easy and I’ll cover that a bit later!

- Note: 15*15 is a special case that’s covered in my mental math trick: 2-digit square article:

Crushing 2-digit squares

Cliffnote: (any square ending in 5 will always be:

First digit TIMES the first digit PLUS one with 25 added to the end

For the above example 1*2 = 2, add 25 to it and get the result: 225!

So the pain starts at 12, but don’t despair – it’s actually quite easy!

Lets take an example: 12*14

Add the ones from the smaller number to the entire big number:

2+14 = 16

remembering that we are dealing with tens we add a 0 to the end:

160

Finally multiply the ones and add them to the number we first got:

160+8 = 168

Now you should be ready to solve the following quickly in your head:

11*15

12*16

18*19

 

Remember that this method isn’t always easier, it can sometimes be beneficial to use other methods that we have gone over.

I hope you enjoyed this mental math guide, please share and enjoy it!