Archive for the ‘direct proportion’ Category


3. How far can a bio-fuel Mini drive on 1 kg of human fat?

September 30, 2014

man vs mini 5b

Of course, in heavy traffic you are burning up the bio-fuel/fat getting nowhere.

Fuel Consumption (F) can plummet, even for the Mini, from 3.4 kg/ 100 km to 6.8 kg/100 km to 8.8 kg/100km. You may as well get out of the car and walk!!


In Biodiesel

Consumed walking

In FAT including Human Fat


Outdoor Maths Adventures: Grade 3 – 5

June 30, 2014

Outdoor Maths 1 Mathspig 2

This fab idea comes from Juliet Robertson, an outdoor education consultant in Scotland. Her blog Creative star learning is one of the most inspiring outdoor maths blogs you will find.

Outdoor Maths 2 Mathspig

Outdoor Maths 3 mathspig

Outdoor Maths 4 Mathspig

Outdoor Maths 5 Mathspig

Outdoor Maths 6 Mathspig

Outdoor Maths 7 Mathspig

Outdoor Maths 8  Mathspig

Check out Mathpig’s protractor joke here.

Outdoor Maths 9 Mathspig

Outdoor Maths 10 Mathspig

Another fab idea from Juliet Robertson.



Outdoor Maths Adventures: Middle School

June 30, 2014



Outdoor maths middle school 1 mathspig

Lego Man soccer fields will vary in size depending on the height of each player picked by each student. This does your head in. It is really challenging maths!


Outdoor Maths Middle School 2 Mathspig

McGill Uni link here.

Outdoor Maths MIddle School 3 Mathspig

Don’t forget to throw in Mathspig’s lame protractor jokes.

Outdoor Maths Middle School 4 mathspig

You’ll find full calculations at the Maths is Fun blog.

Outdoor Maths Middle School 5 Mathspig

You’ll find more fab outdoor junior and middle school maths activities at the terrific Maths and Movement blog.

Outdoor Maths Middle school 6 Mathspig

Some students will discover their co-ordinate point is not on the grid. Students should then work out that they will need a different scale for the y-axis. You can get more inspiration at the Stand Again blog.


Get Ready for the Lego Olympics

February 23, 2012

Get ready mathspigs. You need one Lego Man, Girl, Vampire or Alien each for this exercise. Now we are going to set out the Lego Olympics Athletics track.


But this story of the Olympics begins with Carl Lewis, one of the greatest athletes of all time who won 9 Olympic Gold medals in 100m, 200m, relay and long jump.








Carl Lewis

Mathspig needs to find out how big the Lego Olympics track would be. How? Easy.

Carl Lewis will be our standard Lego Man.

I chose Carl Lewis because he kindly gave me his autograph once when I sprinted in high heels across a ballroom floor at a sports dinner in Melbourne and beat all other journalists.  It was my personal best in high heels, I think.


Lego Olympics to Scale2016……….


This means everything at the Lego Olympics  will be


of the real Olympics.










The  Lego Bird’s Nest Stadium @ Beijing will be 1/50th of the real Bird’s Nest Stadium. (Not the scale shown here). Pictures by Johor Bahru.









The Lego Beijing Water Cube Swim Centre will be 1/50th of the Real Water Cube.


Now mathspiggies over to you. The first thing to do is calculate the Lego Olympic measurements (table below). 



Then mark out a Lego Olympics 100m sprint to scale and/or

draw a Lego Olympic track (in chalk, perhaps) and/or

step out a Lego Olympic marathon track and/or

make a pole vault pole to scale for your little Lego Man.

Or bring in a Lego Man/Girl/Pirate and step out the Marathon Track (840m to scale).

This little guy has to run 840 m!!!!! Wow!







100m Sprint



400m Sprint


42 km marathon


Olympic Pool



Olympic Pool



Olympic Rowing Course


Equestrian Jump Height


Approx Pole Vault Pole Length


Javelin Length





Olympic Stadium

Straight Segment

Semi-circle Radius inner Lane

Lane Width





Little Lego Men Need lotsa Lego Maths

February 1, 2012



There is a lot of maths in Lego, mathspigs, but rather than smash up bridges not to mention toes with 40 kg weights, here are some other cool ways to do LEGO MATHS.

You can make yourself into a Lego Figure like Mathspig, but first ….





Ideally, students would measure their own Lego Man. Otherwise, use the dimensions shown and fill in the chart. 

To calculate your Lego man conversion factor:

   Lego Conversion Factor =   Your Height mm/ Lego Man height mm

eg. Mathspig Height = 172 cm

Mathspig Lego Conversion = 1720/ 38.2 =  44.6

A full size Lego Mathspig is 172 cm, therefore a full sized lego Mathspigs legs would be:

Mathspig Lego Legs = 14.0 x 44.6 = 624.4 mm = 62.4 cm



Lego Man Dimensions


Your Real Dimensions


Your Lego Man Dimension



(Not including the round thing

ie. the stub)


Head Height

Top to chin







Shoulder to hip

(Swivel pt)



Leg Length

Hip to Floor



Now you could draw or photo shop a real picture of yourself to these dimensions or – this is so cool – just make a Lego Man Pic of yourself @ Reasonably Clever


Zombie Maths 2: Direct Proportion

December 13, 2011

Welcome to the Zombie Olympics.

This could take some time.

Another way of calculating a Zombie’s velocity

or speed is to use direct proportion.

ZOMBIE eat hockey team ..

EAT Gym Team too… very young

… very tender

mmMMMM …… YUM!


12 minute Maths Guru

July 4, 2011

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:

1. Free.

2. Quick

3. Clear

4. Low-key







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.

Go, Salman.

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:


Jumping Hair Gel or Sticky Maths

May 17, 2011

Eurovison 2011

Here are JEDWARD, the ex X-Factor, UK,


identical twin contestants who have morphed into super


hair-gelled stars of Eurovision 2011.

Jumping Hair Gel, there is a lot of maths in hair products!!!!!



  There are all sorts of instruments for testing hair gel.

 It must be tested so that the same product is produced each time.

  This piece of equipment tests the ‘stiffness’ of hair gels. You can find a lot more hair product test equipment at the manufacturers.


The hair gel and mousse market is worth $US 581 million in USA alone.


  Hair gel contains polymers (long chain molecules) and alcohol. The alcohol dries off leaving the polymer clinging to the hair strand which consists of  long stands of proteins. The hair gel seals in the moisture making the hair firm. 


This piece of equipment tests the stiffness of hair gel on hair. Cosmetic chemists make up the product formulas, test the products and produce graphs like the one below.


Note: Hair gel becomes more floppy in humid conditions. RH is relative humidity.

You will find this graph and more information at the Styling Technology website.




You can see from this early photo that Jedwards’ hair is growing fast.

So, mathspigs, when will their hair be taller than Jedward?


We can work it out!


Jedward Height (according to Jedward) = 5ft 11 inch = 180 cm


Measuring Jedward on the Left in photo above:


Jedward Hair Height in pic= 1.7 cm


Jedward hairline to chin length in pic = 3.2 cm


Jedward hairline to chin in real life = 19.1 cm*


Jedward hair height in real life = x cm


*This measurement is the 50 percentile or median of hairline to chin measurements for adult males.

Jedward hair height = 10.1 cm


Jedward Height = 180 cm


When will Jedwards’ hair be taller than Jedward?


We must know something about hair growth.According to Tom Dawson of Procter & Gamble, the hair growth cycle for young, healthy scalps,involves  hair typically growing for three years then stopping  and remaining dormant for three months. You’ll find more information at the Happi website (Household and personal products industry)


Hair growth rate = 1.25 cm per month


But hair grows on average only 11 out of12 months:

Assuming Jedwards hair just keeps growing


and hair gel just keeps getting stronger then


Jedwards hair would be as tall as Jedward


in 12 years time!!!!!! 


Ahhhhhhhh!!!!!! That’s spooky.


But Baby, my Feets too Big!!!!!

September 22, 2009

Confused_tnsThose Hippie Statisticians at The Australian Bureau of Statistics (ABS)  are Navel Gazing Again!!!! . Here are the statistics for the height of students belly buttons above the ground for Year 4 – 12 students. ABS  #mce_temp_url#





height chart Correction


tom & kate


policeman_stop_tns Stop!!! WARNING!!!

Before we do any maths with students height mathspigs, be warned. Students can be teased or embarrassed by their height. Mathspig has always argued that a lampost is tall but does not have much of a personality. And a bee is very small but you’d be crazy to tease one. Nevertheless we will use celebrity heights and average student heights instead. 

Here we go!!!!!




 Look at the data. It is useless. THIS IS THE POINT. You have to make sense of data not just sprout numbers. Foot sizes actually shrink!!!! There is insufficient information. The ABS random sample size used was too small. So baby your feet might be too big… but we can’t tell from this data.









 Q2: Does the ‘average’ Aussie student have divine proportions?Da_Vinci_Vitruve_Luc_Viatour

 The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci around the year 1487. This sketch supposedly represents the perfect proportions in man. Measure Height and Belly Button Height of Vertruvian man. Divide his Belly Button Height by his full height.

We will call this the DIVINE FRACTION. 

How do Aussie Students compare? You have the data needed to calculate the DIVINE FRACTION for each year level.



Q3: How do the average heights of our  students  compare to students in other countries?

If we could took a very, very large number of student heights they would produce the graph below. It is a NORMAL DISTRIBUTION or A BELL CURVE. The curve below is for young adults in the USA. We do not know the actual number of students for each height.  

ADVANCED MATHSPIGS; You will find more data, a cute bar graph using students  and some interesting bimodal graphs (combining the Bell Curves for Female and Male heights) @#mce_temp_url#

How do Aussies compare? See the graphs below. We do not know how many students are involved. We can only say  our average Year 12 student is taller than the majority of their students!!! Ha! HA! If, that is, the data is reliable and the foot sizes suggest maybe NOT.

basket ball height Correction



height bell curve Correction


 Q 4:  How does the average height of  Aussie students for each Year level compare with celebrities? 

The pics and some stats come from The Sunday Age ( Coming Up Short 13th Sept 2009) . Here are some celebrity heights:

Lou Reed, Rock Star    1.65m

Nicolas Sarkozy  French President  1.65m

Napoleon   1.68 m

Syvester Styllone Actor 1.70 – 1.79m (No one is sure.)

Andrew Bogut, Aussie Basketball Champ (Pictured) now playing for the Milwaukee Bucks 2.13m

Tom Cruise, Actor  1.70 m

Katie Holmes, Actor  1.75 m

Nicole Kidman, Actor  1.79mmrocky

Keith Urban, Singer   1.78 m

Aaron Sanderlands and Peter Street, AFL Players    2.11 m

Gary Ablett jnr, AFL Brownlow Medal Winner 2009  1.80m

Roger Federer, Tennis Star    1.85m

Michael Phelps, Olympic Swimmer   1.95m

Grant Hacket, Olympic Swimmer  1.98 m

Liesel Jones, Swimmer  1.78 m

Tyrone Smith, Rugby Union, 1.78 m

Digby Loane, Rugby Union   1.79 m

Cate Blanchett, Actor  1.74 m

bell curve2 Correction


Sledging Ricky Can Be Tricky!!!!

July 10, 2009

Cricket fans around the world have enjoyed billionaire Richard Branson’s latest stunt.  On the 9th July 2009 according to a report on , his face covered in the St George’s Cross  was projected onto the Sydney Harbour Bridge with the words “Good luck Ricky. You’ll need it. Dicky x”  . #mce_temp_url#

According to the picture from Richard’s grinning face filled one pier of the bridge. 


You can see that it can be tricky to sledge Ricky. Firstly, according to this AAP photo published on The Chronicle website #mce_temp_url#   you can see Richard Branson looks like he has escaped from a vampire movie. Maybe he is the grandad of Cullen in Twilight.


  Lets do the Vampire maths, mathspigs.

  Each pylon is 89 m high. 

           Now this calculation is all about ratio, Horatio!!!!! By measuring this photo mathspigs,  you can now work out:

          The width of the pylon.

          From the width of the pylon you can calculate the height of his head and the “length” of Gramp Vamp Branson’s teeth!!!!!!! 




Da Vinci

 If you look at this Leonardo Da Vinci drawing to the left you may actually see a Richard Branson likeness. But Richard Branson is alleged to be too young to have posed for this Da Vinci sketch. If, however, he was really a vampire … maybe. Andit would explain his interest in Virgins!!!

 Nevertheless, the issue we are intereseted in here, mathspigs, are the  proportions. And according to Wikipedia the average height of a person is 7 ( to 7.5) times their  head height. 

  Measure the height of Gramp Vamp Branson’s head and calculate his virtual height. This should put anyone off their cornflakes.