Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology

Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.

Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology

Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.

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:

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)

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

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:

Here are some google glasses that actually look cool.

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.

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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.

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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.

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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.

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:

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.

This is exponential growth.

Assuming we each know 400 people.

x = total number of people involved.

n = degrees of separation

x = 400^{n}

If n = 6

x = 400^{6}

x = 4 x 10^{15}

As the population of the earth is only 7 Billion or 7 x 10^{9}, it seems likely that we can be linked to anyone else on earth in less than 6 degrees of separation, 4 maybe.

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.