Quick and dirty vid on problem solving:
Soon there will be a few more pages devoted to this and more "story problems" on my site.
Right now you can go here for a little bit more: CRHOM Problem Solving.
That page is just the tip of the iceberg. So much to do so little time...
Tuesday, December 22, 2009
Saturday, December 19, 2009
How maths makes the world go round
Always amuses me that people that speak the same language can speak it with subtle differences...like putting an "s" at the end of math and thinking me odd for calling it "the mathematics" instead of just mathematics...anyhow took this from a blog note there is the link to the place I got it, I don't claim to have written it but I do claim fair use. You can take anything off my website or this blog as long as you provide a live link back to the source...
How maths makes the world go round
http://refreshingnews9.blogspot.com/2009/10/how-maths-makes-world-go-round.html
Whether you’re searching for oil, the lost chord or a better kind of carrot, mathematics is the key, says Ian Stewart
Maths makes it: genetic breeding yields a better class of carrot
Like many amateur guitarists, I’d always wondered how to play the opening chord of A Hard Day’s Night. Over the years, I spent hours trying to reconstruct it, but there was something very odd about it: no matter how hard I tried, I could never get it quite right.
In the end, the key to the mystery turned out not to be music, but mathematics. Five years ago fellow Beatles fan and mathematician Jason Brown of Dalhousie University analysed the chord using a method called Fourier analysis, which splits sounds into their basic components. It turns out that the Beatles used a piano as well as their guitars.
It’s not just music that has benefited from a little mathematical knowhow recently. On the sports pages, there has been a bit of fuss about a new type of football, which actually travels in the direction intended. What the reports don’t say is that the design is based on a field of maths called computational fluid dynamics, which uses complicated equations to work out how the air flows past the ball, equations which take into account not just the pattern of the panels, but even details of the seams.
That’s the strange thing about maths. Save for the odd occasion when you want to split the bill at a restaurant, it seems infinitely removed from everyday life. So it comes as a surprise to discover just how much maths is lurking in everyday objects – such as footballs.
We know that maths and technology go hand in hand: the inner workings of Google’s search engine, for example, rely on several areas of advanced maths, such as network theory, matrix algebra and probability theory. The researchers there are highly incentivised to make their work as accurate as possible: improve the maths behind the equations, and oodles more cash floods in from more effective advertising.
But let’s think about something more down to earth: a supermarket vegetable aisle, for example, and in particular, the carrots. The carrot is the second most popular vegetable in the world, after the potato. There are hundreds of varieties, differing in colour, taste, resistance to disease, and ability to survive for weeks in a lorry while being lugged across half of Europe.
All of these types of carrot have been specially bred. One method is to cross-breed different varieties and see what you get; a more modern innovation is genetic engineering. Both rely heavily on maths: it’s used in the statistical calculations required to decide which breed is best, and in the design of the trials that provide the necessary information.
Now, I’d be the first to admit that when you are buying carrots, you don’t need to do that sort of maths. But someone has to, otherwise there wouldn’t be any carrots for us to buy. Old-fashioned breeds don’t work when you have to sell millions of carrots every day. No maths, no veggies.
Anyway, once you’ve lugged that bag of carrots over to the car and dumped it in the boot, you notice that you’re nearly out of petrol. No problem: the supermarket sells that, too. You don’t need to know any maths to stick the nozzle in your car – but without a lot of very difficult maths indeed, there wouldn’t be any petrol in the pump.
Early in September, British Petroleum announced the discovery of a massive new oilfield in the Gulf of Mexico, but you don’t find oil seven miles down by drilling wells at random: you have to know where to look.
Given an accurate map of the rock under the ground, geologists can recognise places where oil may be trapped. But how do you make that map? You make loud bangs at the surface and listen to the returning echoes. By doing the right maths, you can then work out where the different layers of rock are.
It’s a complicated problem, because the echoes from all the different layers of rock interfere with each other. It’s a bit like trying to work out the street plan of a city by shouting loudly and listening to the sounds that bounce off the walls. It has taken decades of work by specialist mathematicians to come up with methods that are practical and accurate: one big oil company now does a quarter of a million of these complex calculations every day.
For centuries, maths has been the main driver of science and technology, and the results have transformed our world. My wife and I have a new grandson, and a few months ago we were able to watch a DVD of him before he was born, made using an ultrasound scan. This employs sound that is so high-pitched that the human ear can’t perceive it. And it works much like oil exploration: the equipment listens to the echoes, and uses maths to reconstruct the shape that must have produced them.
Modern medicine uses many different scanners – CT scans, PET scans, ultrasound. Their common feature is that they use maths to calculate the shape of whatever is being scanned, by analysing the signals that the equipment is designed to detect. The mathematical basis of CT scans was worked out more than a century ago by Johann Radon, a pure mathematician who had no idea that his work – suitably tweaked – would routinely save lives long after he was dead.
Today, medical researchers are developing mathematical ways to detect cancer more accurately. Under a microscope, cancer cells look different from healthy cells, but it takes a trained eye to tell the difference. The mathematics of fractals – very complex geometric shapes – is just what the doctor ordered, helping to capture the difference between the shape of a healthy cell and a cancerous one.
As if that wasn’t enough, maths plays a big part in keeping the environment healthy, too. An example is climate change. Even to detect it, you have to compare what is actually happening with what would have happened if the planet had been left to its own devices. But we can’t rerun the planet’s history, so we have to deduce what would have happened without human intervention. One way we can do that is to model the climate mathematically.
So yes, our fancy electronic gadgets – mobile phones, DVD players, digital cameras, the internet, satnav – rely on a lot of maths. And yes, we use it to make sure that aircraft stay up, Formula 1 cars drive very fast, and gigantic towers don’t collapse. But we seldom realise the extent to which maths has invaded every corner of our lives. It shows up in politics, in opinion polls and focus groups. It controls traffic lights, gets crowds safely into and out of sports stadiums, designs the lenses in our spectacles.
And the reason we don’t notice it is that, entirely sensibly, the maths is kept behind the scenes. If I’m buying carrots, I don’t want to have to learn about the mathematics of genetic trials. If I’m putting petrol in my car, I don’t need to know how to solve the inverse problem for seismic waves. But if I want to understand how my world works, I do need to appreciate that the maths is there. Otherwise, I’ll think that the subject is useless. And if too many of us do that, soon there won’t be enough mathematicians to keep everything working.
Professor Stewart's Hoard of Mathematical Treasures. Published by Profile (RRP £11.99) is available from Telegraph Books at £10.99 + £1.25 p&p. Call 0844 871 1515 or visit books.telegraph.co.uk. He will be speaking at the Royal Society on November 5 at 6.30pm.
How maths makes the world go round
http://refreshingnews9.blogspot.com/2009/10/how-maths-makes-world-go-round.html
Whether you’re searching for oil, the lost chord or a better kind of carrot, mathematics is the key, says Ian Stewart
Maths makes it: genetic breeding yields a better class of carrot
Like many amateur guitarists, I’d always wondered how to play the opening chord of A Hard Day’s Night. Over the years, I spent hours trying to reconstruct it, but there was something very odd about it: no matter how hard I tried, I could never get it quite right.
In the end, the key to the mystery turned out not to be music, but mathematics. Five years ago fellow Beatles fan and mathematician Jason Brown of Dalhousie University analysed the chord using a method called Fourier analysis, which splits sounds into their basic components. It turns out that the Beatles used a piano as well as their guitars.
It’s not just music that has benefited from a little mathematical knowhow recently. On the sports pages, there has been a bit of fuss about a new type of football, which actually travels in the direction intended. What the reports don’t say is that the design is based on a field of maths called computational fluid dynamics, which uses complicated equations to work out how the air flows past the ball, equations which take into account not just the pattern of the panels, but even details of the seams.
That’s the strange thing about maths. Save for the odd occasion when you want to split the bill at a restaurant, it seems infinitely removed from everyday life. So it comes as a surprise to discover just how much maths is lurking in everyday objects – such as footballs.
We know that maths and technology go hand in hand: the inner workings of Google’s search engine, for example, rely on several areas of advanced maths, such as network theory, matrix algebra and probability theory. The researchers there are highly incentivised to make their work as accurate as possible: improve the maths behind the equations, and oodles more cash floods in from more effective advertising.
But let’s think about something more down to earth: a supermarket vegetable aisle, for example, and in particular, the carrots. The carrot is the second most popular vegetable in the world, after the potato. There are hundreds of varieties, differing in colour, taste, resistance to disease, and ability to survive for weeks in a lorry while being lugged across half of Europe.
All of these types of carrot have been specially bred. One method is to cross-breed different varieties and see what you get; a more modern innovation is genetic engineering. Both rely heavily on maths: it’s used in the statistical calculations required to decide which breed is best, and in the design of the trials that provide the necessary information.
Now, I’d be the first to admit that when you are buying carrots, you don’t need to do that sort of maths. But someone has to, otherwise there wouldn’t be any carrots for us to buy. Old-fashioned breeds don’t work when you have to sell millions of carrots every day. No maths, no veggies.
Anyway, once you’ve lugged that bag of carrots over to the car and dumped it in the boot, you notice that you’re nearly out of petrol. No problem: the supermarket sells that, too. You don’t need to know any maths to stick the nozzle in your car – but without a lot of very difficult maths indeed, there wouldn’t be any petrol in the pump.
Early in September, British Petroleum announced the discovery of a massive new oilfield in the Gulf of Mexico, but you don’t find oil seven miles down by drilling wells at random: you have to know where to look.
Given an accurate map of the rock under the ground, geologists can recognise places where oil may be trapped. But how do you make that map? You make loud bangs at the surface and listen to the returning echoes. By doing the right maths, you can then work out where the different layers of rock are.
It’s a complicated problem, because the echoes from all the different layers of rock interfere with each other. It’s a bit like trying to work out the street plan of a city by shouting loudly and listening to the sounds that bounce off the walls. It has taken decades of work by specialist mathematicians to come up with methods that are practical and accurate: one big oil company now does a quarter of a million of these complex calculations every day.
For centuries, maths has been the main driver of science and technology, and the results have transformed our world. My wife and I have a new grandson, and a few months ago we were able to watch a DVD of him before he was born, made using an ultrasound scan. This employs sound that is so high-pitched that the human ear can’t perceive it. And it works much like oil exploration: the equipment listens to the echoes, and uses maths to reconstruct the shape that must have produced them.
Modern medicine uses many different scanners – CT scans, PET scans, ultrasound. Their common feature is that they use maths to calculate the shape of whatever is being scanned, by analysing the signals that the equipment is designed to detect. The mathematical basis of CT scans was worked out more than a century ago by Johann Radon, a pure mathematician who had no idea that his work – suitably tweaked – would routinely save lives long after he was dead.
Today, medical researchers are developing mathematical ways to detect cancer more accurately. Under a microscope, cancer cells look different from healthy cells, but it takes a trained eye to tell the difference. The mathematics of fractals – very complex geometric shapes – is just what the doctor ordered, helping to capture the difference between the shape of a healthy cell and a cancerous one.
As if that wasn’t enough, maths plays a big part in keeping the environment healthy, too. An example is climate change. Even to detect it, you have to compare what is actually happening with what would have happened if the planet had been left to its own devices. But we can’t rerun the planet’s history, so we have to deduce what would have happened without human intervention. One way we can do that is to model the climate mathematically.
So yes, our fancy electronic gadgets – mobile phones, DVD players, digital cameras, the internet, satnav – rely on a lot of maths. And yes, we use it to make sure that aircraft stay up, Formula 1 cars drive very fast, and gigantic towers don’t collapse. But we seldom realise the extent to which maths has invaded every corner of our lives. It shows up in politics, in opinion polls and focus groups. It controls traffic lights, gets crowds safely into and out of sports stadiums, designs the lenses in our spectacles.
And the reason we don’t notice it is that, entirely sensibly, the maths is kept behind the scenes. If I’m buying carrots, I don’t want to have to learn about the mathematics of genetic trials. If I’m putting petrol in my car, I don’t need to know how to solve the inverse problem for seismic waves. But if I want to understand how my world works, I do need to appreciate that the maths is there. Otherwise, I’ll think that the subject is useless. And if too many of us do that, soon there won’t be enough mathematicians to keep everything working.
Professor Stewart's Hoard of Mathematical Treasures. Published by Profile (RRP £11.99) is available from Telegraph Books at £10.99 + £1.25 p&p. Call 0844 871 1515 or visit books.telegraph.co.uk. He will be speaking at the Royal Society on November 5 at 6.30pm.
Thursday, December 17, 2009
Wild About Math
This is a very cool blog, you can end up spending quite a bit of time here if you enjoy math, or things related to it:
WILDAABOUTMATH
I sent him a short email showing why cross multiplication works and he was kind enough to put up a couple links and my vids on his site. I consider it an honor because he has put a lot of effort into his blog and it is a fun place to go. You should check it out when you get the chance. Careful: you can spend a few hours before you know it...
There are lots of math sites and blogs out there. Some are better than others. I have to start going through them along with the websites I frequent and provide links and information on why I like and use them. This should save you time.
Meantime I am looking for even more sites that are good and will start spending the time to contact sites I like and use so we can share links, which I am told is an important part of building free web traffic and getting good ratings with the search engines.
I also am learning about affiliating with various companies to help offer their products and services to people who come to my site...however I am pretty picky because there is so much raw unadulterated CRAP out there for teaching math or "helping" you teach or learn math that is expensive and useless. I am determined to make it so that if you heard about it on this blog or on my site it is not just a good product or service but a FANTASTIC, most extremely excellent product or service. Then the next trick is getting it at a good price. I have decided NOT to rip on the crappy stuff; we'll focus on the positive.
There are a couple rip offs and scams that I will steer you clear of and a couple teaching methods that do about as much harm as good in my experience. I have to do it in such a way as I don't get sued...lol.
Meantime stuff I like is hard to affiliate with...but I'm working on it. Mortensen Math products and Math U See come to mind...
You will start seeing more stuff for sale on my sites and soon there will be a marketplace tab at Crewton Ramone's House Of Math where you can get all manner of math stuff...just fun stuff like math t-shirts or ties and jewelry...as well as books and software and etc. I have even located some cool PDF's for low cost where you can get 90 sheets of math print outs, everything from simple graph paper to fractions and cut out's for math activities...they have previews so you can see what I'm talking about...
Just takes time to build it all. But with winter break coming up I should have more free time to get it done...key word "should." Check out Crewton Ramone on FaceBook...
WILDAABOUTMATH
I sent him a short email showing why cross multiplication works and he was kind enough to put up a couple links and my vids on his site. I consider it an honor because he has put a lot of effort into his blog and it is a fun place to go. You should check it out when you get the chance. Careful: you can spend a few hours before you know it...
There are lots of math sites and blogs out there. Some are better than others. I have to start going through them along with the websites I frequent and provide links and information on why I like and use them. This should save you time.
Meantime I am looking for even more sites that are good and will start spending the time to contact sites I like and use so we can share links, which I am told is an important part of building free web traffic and getting good ratings with the search engines.
I also am learning about affiliating with various companies to help offer their products and services to people who come to my site...however I am pretty picky because there is so much raw unadulterated CRAP out there for teaching math or "helping" you teach or learn math that is expensive and useless. I am determined to make it so that if you heard about it on this blog or on my site it is not just a good product or service but a FANTASTIC, most extremely excellent product or service. Then the next trick is getting it at a good price. I have decided NOT to rip on the crappy stuff; we'll focus on the positive.
There are a couple rip offs and scams that I will steer you clear of and a couple teaching methods that do about as much harm as good in my experience. I have to do it in such a way as I don't get sued...lol.
Meantime stuff I like is hard to affiliate with...but I'm working on it. Mortensen Math products and Math U See come to mind...
You will start seeing more stuff for sale on my sites and soon there will be a marketplace tab at Crewton Ramone's House Of Math where you can get all manner of math stuff...just fun stuff like math t-shirts or ties and jewelry...as well as books and software and etc. I have even located some cool PDF's for low cost where you can get 90 sheets of math print outs, everything from simple graph paper to fractions and cut out's for math activities...they have previews so you can see what I'm talking about...
Just takes time to build it all. But with winter break coming up I should have more free time to get it done...key word "should." Check out Crewton Ramone on FaceBook...
Wednesday, December 16, 2009
"Ten Apples Up On Top..."
Ever since I started this little adventure of blogging and building Crewton Ramone's House of Math I have talked about having links to products I know work (for teaching math) or that I actually use and have had good experiences with.
Here is a super simple one:
For teaching little kids how to count and get a one to one correspondence this book is great. Don't just read it to them, have them count and point with their fingers...get creative. Do simple addition and ask how many more one animal has than the other. Count a lot on just about every page, add up the apples--"How many do they have together?" "Who has the most apples?" etc. There are times when this book takes a half hour to get through...if you just read it it takes less than ten minutes.
Talk about the pictures, count by tens at the end and count by 7's when they all have 7 apples up on top. There is a page where the lion has 3 the dog has 4 and the tiger has 7...make it into a little problem 3 + 4 = 7 but also show them 3 needs 4 to be 7 and 4 needs 3 to be 7 etc. MAIN THING: HAVE FUN.
Add this book to your library if you have young children. As you can see it's a very low cost tool that can make a big difference if used properly. Eventually maybe I'll have a detailed page that shows some of the things I do, page by page, but I'm pretty sure you can handle it. Great before bedtime or as a playtime activity where you get out the blocks and follow along...
EAT SLEEP MATH.
Here is a super simple one:
For teaching little kids how to count and get a one to one correspondence this book is great. Don't just read it to them, have them count and point with their fingers...get creative. Do simple addition and ask how many more one animal has than the other. Count a lot on just about every page, add up the apples--"How many do they have together?" "Who has the most apples?" etc. There are times when this book takes a half hour to get through...if you just read it it takes less than ten minutes.
Talk about the pictures, count by tens at the end and count by 7's when they all have 7 apples up on top. There is a page where the lion has 3 the dog has 4 and the tiger has 7...make it into a little problem 3 + 4 = 7 but also show them 3 needs 4 to be 7 and 4 needs 3 to be 7 etc. MAIN THING: HAVE FUN.
Add this book to your library if you have young children. As you can see it's a very low cost tool that can make a big difference if used properly. Eventually maybe I'll have a detailed page that shows some of the things I do, page by page, but I'm pretty sure you can handle it. Great before bedtime or as a playtime activity where you get out the blocks and follow along...
EAT SLEEP MATH.
Tuesday, December 15, 2009
Cross Multiplication
Introduction:
Building on that short foundation:
Remember, I am condensing hours and hours into less than 20 minutes. If you miss something or you don't "get it" watch them a couple times...
Two vids on Cross Multiplication. More explanation with words and maybe some pictures coming your way soon. Meantime go to Crewton Ramones's House of Math for more.
Also if you think this is cool, wait till you see the vids I make on algebra: problems like (x+1)(x+2) = x2+2x+2, I use exactly the same blocks.
More beginner multiplication at CRHOM.
Building on that short foundation:
Remember, I am condensing hours and hours into less than 20 minutes. If you miss something or you don't "get it" watch them a couple times...
Two vids on Cross Multiplication. More explanation with words and maybe some pictures coming your way soon. Meantime go to Crewton Ramones's House of Math for more.
Also if you think this is cool, wait till you see the vids I make on algebra: problems like (x+1)(x+2) = x2+2x+2, I use exactly the same blocks.
More beginner multiplication at CRHOM.
Monday, December 14, 2009
New Video on Subtraction With Addends
Here is a quick Video explaining the concept of "Small Addition" when doing subtraction.
Go to my website for more.
Go to my website for more.
Friday, December 11, 2009
New Video on Making Change.
If a picture is worth a thousand words...then a video is...
Watch the vid a couple times if it goes too fast. Soon you will be able to make change in your head, fast and easy.
For a bit more go to my subtraction page. My website is slowly but surely growing. Currently I'm in video production mode. Will be adding some videos this week on problem solving, multiplication and cross multiplication...which I keep seeing around the web as a "trick" because they only see the numbers and don't understand what they are counting.
That will take about 3 vids to cover, ten another one on subtraction and some more on algebra...so much to do...
Watch the vid a couple times if it goes too fast. Soon you will be able to make change in your head, fast and easy.
For a bit more go to my subtraction page. My website is slowly but surely growing. Currently I'm in video production mode. Will be adding some videos this week on problem solving, multiplication and cross multiplication...which I keep seeing around the web as a "trick" because they only see the numbers and don't understand what they are counting.
That will take about 3 vids to cover, ten another one on subtraction and some more on algebra...so much to do...
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