Archive for the ‘Area’ Category
Maths is Awesome Activity
DYI Construction Set
Skills: Geometry, measurement, symmetry, area, angles.
Year Level: Year 7
You will find more info here.
This idea is gobsmacking. We live in a consumer world so the thought of making your own construction set is foreign to us.
Building your own cardboard construction set involves:
* Lots of maths
* Every pupil made 20 construction pieces now you can make something huge for a maths display. eg. giant parabola, π, √2
think really BIG.
More info here at Building Blogspot.
The Maths-is-Awesome Activity:
Skills:Geometry, measurement, cylinders, area, symmetry and creativity.
Year Level: Year 4 – whatever
Ask students to build their own cardboard armour and helmet. Give prizes in the category of Scariest, most Mathematically-Complex, Star Wars Potential, Most Historical, Most Creative and any other category that crops up. You can source cardboard from your nearest Self-Storage Warehouse.
Mathspig was at Womadelaide Music Festival 2013 and saw the Box Wars at work. The Box Wars guys, Joss, Josh and Hoss, started in Melbourne and now travel to Music Festivals around Australia. Boxwars builds sculptures, armour, props and sets and airplanes , tanks, cannons and the rest.
They stage battles of destruction … but destruction isn’t always the outcome.
If you want to interest kids especially boys 8 – 12 years of age in maths, get them building armour.
Mathspig saw dozens of them at WOMAD and they so loved their armour they wouldn’t take it off in 39Cº.
Sometimes it is just lots and lots of fun. Here is a recently staged BOX WARS in Canberra. You only need watch a few minutes of the video to get the idea.
Meet Salman Khan. He has put free maths on-line.
This article on Salman appeared in The Sunday Times, UK, 12 JUN 2011.
Salman, 28, started putting tutes online for his 12-year-old niece, Nadia, and things grew. So far the Kahn Academy’s claim to fame are:
* Over 2,400 videos including hundreds and hundreds of 12-minute maths tutes
* Over 63,000,000 lessons delivered.
* Bill Gates kids use the site.
* A staff of 1 with funding from The Bill and Melinda Gates Foundation.
* Tutes on Biology, Chemistry and Physics too.
You can look up the maths tutes by topic @ The Khan Academy.
Or search topics on Youtube eg. Introduction to Conics Khan
Why Does Mathspig like The Kahn Academy? Because it’s:
Salman gives digital chalk-and-talk tutes like a teacher. He hand draws the equations and graphs. He uses a calculator from time to time, but he tends not to use whizz bang spreadsheet graphs or perfectly presented textbook equations. It’s a bit wobbly and it’s all coming from Salman’s head.
And students like this approach. It makes maths look do-able.
Mathspig thinks you are just GORGEOUS!!!!!!!!!
Australia’s Year 7 – 12 Maths Curriculum is already on-line and free, funded by McDonald’s. See What are maths teachers for, sir?
The tutes on Maths Online are produced by Aussie Maths teachers and they are very good. Mathspig, of course, imagined the quadratic function tutes might look something like this:
There is a lot of maths in weddings including how are you going to pay for the damn thing.
But Mathspig became interested in Kate’s Wedding Dress train.
I mean how hard is it to drag a wedding train down the red carpet at the Royal Wedding.
Unfortunately, there was no data available for coefficent of friction of silk on wool carpet.
Mathspig did her own experiment to come up with a drag coefficient (See details at the end of the post).
2011 Kate’s Wedding Train = 2.7 m/8ft 10 in
1986 Sarah Ferguson’s Train = 5.2m / 17 ft
1981 Diana’s Wedding Train = 7.62 m / 25 ft
1947 Princess Elizabeth Train = 4 m / 13ft 1 in
(Now Queen Elizabeth. Wedding Dress below)
Dragging that bridal train down the Red Carpet!!!!
As you can see (below) it takes some effort to drag those wedding dress trains.
If the train is TOO HEAVY it is hard work for the bride (See Diana below) walking up the steps.
IF it is TOO LIGHT it can blow up in the wind like a yacht sail and carry the bride off.
If it is TOO SLIPPERY then coming down the steps the train will just keep going and bundle up at the brides feet.
Some trains are wider than 1 m like Kate’s so the drag would be even higher. Some red carpets are narrow. Nevertheless, these calculations are a good approximation.
Some Brides over do the train.
.As an 8 year old boy weighs around 24 kg some long trains would equal dragging a short train down the aisle with the page boy sitting on it for a ride.
According to OK magazine the longest wedding dress train measured over 2488 m or 8,164 feet and was created by Lichel van den Ende. It was presented and measured in Zoetermeer, The Netherlands, on December 22, 2009.
UPDATE: 21 March 2012 ABCNEWS
According to the ABC News, Romania has set a new World Record for Wedding train length. The 1.85-mile ( 3 km) long ivory train was modeled by Ema Dumitrescu, who appeared in a hot air balloon floating over Bucharest. The Guinness Book of World Records officially named the train the longest one in the world. It required 15,420 feet of taffeta, 18 feet of lace and 147 feet of lining.
NOTE for Science Students: Mathspig used 4 m square of silk shantung folded into 1 m square and weighing 375 kg. She then dragged this square down her own carpet and recorded the drag on kitchen scales in gram. The drag per m square was 450 gm or 0.45 kg. The difference between static and kinetic friction was minimal because the brides walk is not smooth.
Then Mathspig used 2m square of silk folded to form 1m square. It weighed 180gm and had a drag per m of 200 gm. This seemed too light for a wedding train.
There are 22 million people in Australia. We Aussies might have the reputation of being tough individuals who can open stubbies with our teeth and wrestle crocodiles. But we Aussies aren’t rugged folk. We cling to life in the cities and we couldn’t survive for 3 days in the desert without a latte. If we got lost in the wilderness we’d only survive if we could light a fire by rubbing 2 iPhones together.
We Aussies are ever so slightly spooked by the greatness and vastness of our Red Centre. There aren’t many people out there. You can drive for days without seeing a Macdonald’s. And, anyone you meet in the red centre is, according to some movies, an unshaven, axe-wielding psychopath. No wonder we stay put in the cities. Being city dwellers, however, we can’t quite grasp the size of Australia. So how big is Australia?
The area of Australia is 7, 686, 850 sq km. You’ll find more info @ Nationmaster
Here mathspigs are some interesting comparisons using areas in sq km although the unit doesn’t matter, of course ass long as you keep using the same one. These calcs ignore the shapes. It is astraight area calculation.
Australia = 11.0 Texas’s
West Australia = 3.63 Texas’s. I can’t imagine saying bigger than West Australia. Maybe it had something to do with the size of those cowboy hats.
Australia = 25.5 Italys
Australia = 28.6 New Zealands
Australia = 856 Yellowstone National Parks
In fact, one of our National Parks Kakadu is 20,000 sq km. This makes it the second largest National Park in the world (Greenland wins!) and
Australia = 3, 843, 425 Monacos
This statistic is particularly amusing. The population of Australia is approx 22 million. Divide this figure by the number of Monacos and we have 6 people per princedom. Every family in Australia could, theoretically, have it’s own principality!!!!
Golf courses range from 140 – 250 acres but 250 acres = approx 1 sq km. This is St Andrew’s, Scotland, 18th hole pictured.
Australia = 7, 686, 850 Golf Courses
Turing Australia into 7 million plus golf courses would please some. We have a lot of water traps and sand bunkers. And Australia is, mostly, FLAT.
Australia = 22,345,494 Disneylands
Imagine Australia being turned into 22 million theme parks. It would be amaaaaazing!!!! We would get one Disneyland for each of us!!!!!
Australia = 18, 302, 023, 810 Basketball Courts.
Unfortunately, we can only manage one player for every 832 basketball courts, which would not make for much of a game.
Now mathspigs, if you are interested in a career in stage/film lighting or even architecture you will need this maths.
USA uses Foot-candles. Can you imagine the pickup line ‘You brighten up my world like a footcandle’? A foot-candle is the brightness of a candle 1 foot away. Now think of a bubble around the candle. Brightness is mostly measured using one square foot or one square metre of that bubble:
1 LUMEN = 1 Footcandle/ft squared
1 LUX = 1 footcandle/m squared
Don’t get too hassled by these units. As a rough rule:
1 candle = 1 LUX
From graph you can see by 3m a Birthday Cake is not very bright even in a haunted house or crypt.
Challenge: Draw a graph of the brightness of your own Birthday Cake!
Big Challenge raw a graph of your Teacher’s Birthday Cake!!!!!! Ahhhh!!!!
1 candle = 1 LUX
Now compare the brightness of 1 candle to the brightness of other sources of light:
Family Living Room = 50 LUX
Toilet = 80 LUX
Office = 320 – 500 LUX
Indoor lighting Range = 50 – 1,000 LUX
Outdoor moderate sun = 32,000 LUX
Outdoor FULL SUN = 130,000 LUX
If you want sufficient light to live your everyday life you’d need 80 candles just to go to the toilet!!!!!!
Girls.. you may think diamonds are your best friend, but not at the moment. According to this article from The Australian (27/7/09) sales for the world’s largest diamond-producer are down by 57% at the moment. The price of diamonds should be dropping and indeed they are.
According to the most recent graphs I could find (below) from the Certified Diamond Exchange #mce_temp_url# diamond prices have dropped significantly from last year. And they are still dropping. Diamonds come in many sizes and shapes. So diamond graphs must compare similar diamonds eg. Large Fancy, Small round etc. The y-axis shows the price of the diamond compared to the Jan91 price which is set at 100.
Oooo!!! Aaaaeeee!!! Mathspigs Note: Cutting diamonds involves maths.. angles, symmetry, % and a lot of NERVE!!!
How big are BIG diamonds Or THAT ROCK YOUR WEARING EQUALS HOW MANY PAPERCLIPS?????
Let’s do some maths mathspigs!!!!! Diamonds are measured in carats. 5 carats = 1 gram. Now keep in mind that one paperclip weighs one gram. So we need some boxes of paper clips to do this exercise. Here are some examples of the largest diamonds in the world. More at: #mce_temp_url# Convert these to grams and hence paper clips and feel the weight. Would you want any of these diamonds hanging around your neck??????
The Blue Hope Diamond is believed to carry a curse because two of the families who owned it died. It weighs 45.52 carats.
The Koh-I-Noor (Mountain of Light) weighs 186 carats and is a part of the crown jewels.
The Excelsior diamond originally weighed 995 carats but it was cut into 10 pieces. The largest diamond it produced was 158 carats.
The Taylor-Burton diamond weighs 240.8 carats.
The Cullinan I or Star of Africa Diamond is the world’s largest cut diamond weighing 530.20 carats. It is a part of King Edward VII’s Sceptre and is housed in the Tower of London which means Mathspig has seen it, sort of. To view the Crown Jewels in the Tower of London you must stand on a moving walk way that really whips along so you see a crown for about 3 seconds!!!!!!
Angles, Symmetry and %’s.
As the school will not give you diamonds to cut – you could ask, but!!- we will make 2-D images. We will do the top of the diamond looking down. (The images here show the top and the underneath projections.) Start with a circle, an oval (ellipse in maths) or a rectangle and see how you would make some cuts. It is a good idea to locate the middle of your diamond. This will help with the symmetry. Then use a protractor to calculate the angles you used. This means you can do the same pattern again.
SUPER BLING CALCULATIONS FOR ADVANCED MATHSPIGS: Calculate the area in the middle of your diamond. This would be the part of the diamond you did not cut. The bigger this area the bigger the cut diamond will look and, of course, you are not wasting the gem by cutting it into little bits. Then calculate the total area of your shape. Now find the % of diamond left uncut. The bigger this % the better your gem cutting skills.