Archive for the ‘Exponential Functions’ Category

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MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig …………………………………………………. with Kerry Cue

July 10, 2015

Mathspig m&m maths intro

Hellooooo My Little Sweeties,

There is so much maths you can do with m&ms, it’s hard to believe there is any other sort of maths.

You can study:

Countingtimes tables, set theory, Bar graphs, Fractions, % and decimalsMean, median, modeand parabolas (using a really cool peg-powered catapult).

But my favouritest ,developed by Patrick Len, is using m&ms to demonstrate half life in radioactive substances and therefore write an exponential equation.

m+m ACTIVITY:

m&ms  table

Throw a fixed no. m&ms on a table. Mathspig chose 128 m&ms for a very good reason. Eat the ones with the m showing. Count remainder. Throw again. Eat the ones with the m showing. Count remained. Keep doing this. You will end up with results like the following. (Not identical as chance is involved)

mathspig   m&m maths exponential fn  2

Wow! m&m’s and exponential equations. How yummy is that!!!!!!

More yummy maths:

m+m maths 1: find the volume using m+ms!

m+m maths 2: Guess, NO, calculate the number of m+ms in a jar!

m+m maths 3: how many m+ms will kill you?

m+m maths 4: How many m+ms will kill my dog?

m+m maths 5: how many m+ms will kill my cat?

m+m maths 6: How many m+ms will kill my pet rat?

m+ms maths 7: how many m+ms will kill my pet mouse?

Mmmmmmm! Can’t talk. Face full of chocolate.

Bye bye

Mathspig

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Popular Culture and MEAN GIRLS Maths

November 15, 2013

Lindsay Lohan may not be seen as the pin-up girl for Maths.

Yet her character Cady in the Mean Girls TV Series, not only does ‘math’ in 12th grade, she joins the the maths geeks as a mathlete and adds the term ‘The Limit does not exist’ to pop culture.

Her teacher is Mrs Norbury (Tina Frey).

Here is the good:

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Here is the bad:

Do girls still do this? Pretend they are dumb to impress a boy?

FYI Aaron!!!!!!!!!

n factorial = n! = 1x2x3x4x5x6x7x8x9x10 ………………………

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Here is the Whoa! This is real maths … on the tellie:

And here is the maths from openstudy that Cady did in her head while thinking about not calling people stupid or fat:

The limit doesn't Exist  openstudy.com

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10. Design Cool Techno Stuff

August 29, 2013

Here are some google glasses that actually look cool.

google glasses

Here’s what Google Glasses can do.

Instead of using the Google Maps on your phone the Google Glasses put the map onto the glass lense so you can see where to go and where you are going. Theoretically.

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The Maths

Google Maps uses GPS or Global Positioning System satellites and simple maths of TRIANGULATION or, in the case of the 3D model, 3D TRILATERATION to accurately locate your position on earth.

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You will find excellent explanations of how GPS works at the Nova Scotia Dept of Education website and by Diana Cooksey 
MSU GPS Laboratory website.

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Simple Explanation:

GPS satellites broadcast two signals which allows the GPS program in  your phone or device to calculate your distance from the satellite. GPS needs data from 3 satellites to locate your position on earth.

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2D Model:

Let’s assume your phone can calculate how far you are from a radio tower.

Tower 1:

Your phone can calculate how far your are from the tower but you could be anywhere on the first circle.

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Tower 1& 2:

Your phone can calculate your distance from two towers and locate you at one of two points where the circles intersect.

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Tower 1, 2 & 3:

Now you phone can accurately find your position at the intersection of 3 circles.

GPS_2D

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3D Model:

Your phone can calculate how far you are from a satellite.

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Satellite 1:

You could be anywhere on the first sphere.

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Satellite 1 & 2:

You could be anywhere at the intersection of the two spheres. These spheres intersect along a circle.

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Satellite 1, 2 & 3:

The 3rd sphere will cross that circle at 2 points. As one position is not on earth it can be discarded.

3D GPS

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Error Alert:

All measurements have an inbuilt uncertainty (scientists call it an error) because the accuracy of instruments is limited. Measuring across such long distances makes for significant errors. One problem for GPS is signal interference.

GPS Error

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Mr Google

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New Techno Frontiers in the Maths Classroom

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1. If you teach maths wearing Google glasses you can INSTANTLY  record students bad behaviour in class on your computer. Wow! Evidence.  THE FORCE BE WITH YOU,  Mathspiggies.

OR

2. You can record a maths lesson using Google Glasses. It is already happening, my Sweeties. Have a look at this.

 

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Grow, baby, Grow!

August 6, 2013

 If we double the rate of population growth in Australia, what will the population be in 38 years?

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Pop growth rate per year:…..r = 3.6 % = 0.036

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pop calc Aus 2

 

You can check your calculations here @ Wayne’s World Population Calculator.

 

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10. 6 degrees of separation

July 9, 2013

You are, according to mathematicians, 1 degree of separation away from anyone you know. Then two degrees from people they know and son on.

Professor of mathematics Jason Brown explained in the Chronicle Herald, California, how the 6 degrees of separation theory works:

pic 19 holding_hands_six

 For example, suppose that you are or have been acquainted with, say, 400 people. Each of those may know 400 others, giving rise to about 400 times 400, or 160,000 people, you may know in two steps.

Again if each of those individuals knows 400 people, you would only be three steps away from about 400 times 160,000, or 64 million people, and so on.
six-degrees

This is exponential growth.

Assuming we each know 400 people.

x = total number of people involved.

n = degrees of separation

 

x = 400n

If n = 6

x = 4006

x = 4 x 1015

As the population of the earth is only 7 Billion or 7 x 109, it seems likely that we can be linked to anyone else on earth in less than 6 degrees of separation, 4 maybe.

 pic 18sixdegsep

6 degrees of separation Myth busted.

 

Exercise:

Here is an awesome Middle School Maths PDF from PBS MATHONLINE based on Rumours.

It is an excellent introduction to exponential functions.

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Harry Potter Needs Maths

February 1, 2012

What has Harry Potter to do with Maths?

Watch this video of Harry Potter and the Half Blood Prince: Death Eater Attack.

You can click on the link here or below (Video will only play on You Tube site):

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A recent article in The Guardian, UK, explained the link between Harry Potter and Maths:

‘(Alex)Hope, managing director of the visual effects firm Double Negative said: “In Harry Potter [and the Half Blood Prince], the opening sequence has Death Eaters flying across the river Thames, destroying the (Millennium) Bridge between St Paul’s and the Tate Modern.’

“The way you create that is people who understand computational fluid dynamics, they know how water moves. They take the physics that’s used in modelling rivers and the flow of water and apply that in our world. People doing it need an artistic sensibility as well. An understanding of maths and science is fundamental to many of the disciplines in our industry.”

Fluid Dynamics is the study of fluid flow. You can look at this picture (below) and see the similarity to the Death Eaters water-flowy appearance.

Here is a experiment showing lamina Vs turbulent flow in water. Mathspig did experiments like this at university in Chemical Engineering. Equations can be scary, mathspigs, but not necessarily.

Here is a water flow equation for a sharp edged weir with a V notch out let from AQUATEXT:

Q = 0.266 x cB x (2g)0.5 x H1.5

where;

Q = water flow rate, m3/sec

B = width of the weir at the flowing rate

c = discharge coefficient, average 0.62

g = gravitational constant, 9.81

H = Height of the water over the weir, measured behind the weir edge, m

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Here is a real flood caused when water was released from a real weir or dam.

In 2011 operators of the Wivenhoe Dam in Queensland (above) had to release water to stop the dam collapsing during severe floods.  8,000 properties were flooded.

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More @ News Limited 


Combine the flow maths for a weir (equation above) with computer graphics and you have a realistic flood film sequence!!!!!!

Or maybe a really unrealistic but terrrrrrrrifying sequence:

Aghhhhhhhhhh!!! We’re all gonna die or …. like …

have a really amazing white water raft ride, maths dudes!!!!!!!


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Maths Girls a Go Go II

September 8, 2011

Vi Hart ( pic below) calls herself a mathemusician. She graduated  with a degree in music from Stony Brook University, NY, two year ago, but has always maintained an interest in maths. Last November she posted Doodling in Maths Class on You Tube, which as the New York Times explained ‘ married a distaste for the way math is taught in school with an exuberant exploration of math as art’. It went viral. Her youtube videos have collected over 1 million hits already.

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The question for maths teachers is this:

Why didn’t Vi study MATHS at uni when she:

* is smart

* loves maths

* is mathematically creative

Was she booooooooored by high school maths?

Vi’s videos should be a must see for all maths teachers. They are fun and they encourage girls to take on the maths challenge.

Vi Hart: Infinity Elephants

Fun Jnr Maths Exercise in Fractals

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Vi Hart: Binary Trees

Fun Introduction to Exponential Functions

You will find more videos @ Vi Hart Website.