Archive for the ‘Uncategorized’ Category


FRANTIC FRIDAY: Crazy Maths Word Maze UK edition

February 24, 2020

PDF file: 1. Crazy math maze work sheet 1 UK

PDF file: 2. Crazy math maze work sheet 2 UK


PDF file: 3. Crazy math maze work sheet ANS UK


Why do so many students HATE MATH? … um, you know, BOREDOM

September 28, 2019

According to ‘Bored Out of Their Minds’, an article by ZACHARY JASON in The Harvard Ed Magazine (2017):

Boredom accounts for nearly a third of the variation in student achievement. 

Half of high school dropouts cite boredom as their primary motivator for leaving.

Boredom begins for Math students at Grade 6 when students (Common Core Standards, USA) tackle more abstract concepts such as linear eqns, exponents, probability, geometry and so on.

Math curriculums in the USA, UK & Australia all demand students solve REAL LIFE problems. Too often these are of the type:

Q. Ronaldo has tethered his goat on a 12ft rein in the corner of a 20ft square field. What area can the goat graze?

THE ANS: Who cares?


Ask students maths questions which have answers they want to know.

Students really don’t care about Ronaldo’s goat, but here are some questions which involve intriguing answers they might want to work out. And many of these questions involve funny or age-relevant activities, which also helps engagement.

1. Mean, Median STATS: Mean, Median and Coffee: Busting an Urban Myth

2. Parabolas: Can you beat the 12-14 yo World Record for a Watermelon Pip spit?

3. Geometry: Build a Freestanding Tower

Rates (Speed) & Units:

4a. The Terrifying Math of Running from a bear

USA Units


4b. How old is your hair?

5. Decimals, %, Volume: What Volume of alcohol is lethal for teens?

6. Decimals, Algebra, Weight Units

How much blood can a kid lose and survive?


Metric Units

Graph Hunger Game Math

7. GEOMETRY. Angles

Why killer heels can kill!

Any Topic:

8. Middle School Math Photo Scavenger Hunt

9. Write Your Own Math Song

Space Math Song here

10. Make a Math Poster


The average time it takes an audience at a conference to switch off is 11 minutes. Keep in mind this audience is, at least, being paid to be bored witless.


Outdoor Math Adventures___________ Middle School

September 9, 2019

As the weather improves – Spring in Melbourne, my city & Autumn in USA & UK – it is an ideal time to take math outdoors. Here are some fab exercises for Middle School Math.

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.


Dangerous Math: Would You Survive a Shark Attack

July 5, 2019

Aussie Pro surfer, Mick Fanning, grabbed world attention when he was attacked by a shark in the Fanning J-Bay Open, South Africa on Sunday 19 July, 2015. Fanning was knocked off his board and forced to fight for his life. He survived.

1 Mick fanning shark attack

One shark expert suggested the shark was a young great white shark under 3.5 m or 12 ft.

Would you survive a shark attack?

Let’s do the maths.

How fast can a shark swim?

According to the Smithsonian National Museum of Natural History:The torpedo shape of the great white is built for speed: up to 35 miles per hour (50 kilometers per hour). And then there are the teeth — 300 total in up to seven rows.

How fast can you swim?

According to Junior Olympic Games Qualifying Times 2015

For 13-14 yo 100m or 328 ft freestyle:

t girl = 1.15 or 75sec

t boy =1.10. Or 70 sec

Let’s assume you are an average swimmer but highly motivated on seeing a shark:

t kid = 100 secs

So you can swim 100m (328 ft) in 100 sec. But will you survive??????

 Surf Lesson Bluey’s Beach NSW 2009

We’re sooo tough in Australia! Shark, Smark! Whatever.

Picture from Daily Telegraph

Also according to the Smithsonian: Sharks can detect both the direction and amount of movement made by prey, even from as far as 820 feet (250 meters) away.

But there is hope as, according to the National Geographic Channel, Most shark attacks occur less than 100 feet or 30.5 m from the shore mainly around popular beaches in North America (especially Florida and Hawaii), Australia, and South Africa. 
3 Shark attack diagram Mathspig

4 shark attack maths mathspig

If average swimmer Dav is 100 ft (30 m) offshore and starts swimming when he sees the shark 820 ft (250 m) away, he would swim 63 ft (19.2 m) before the shark attacked. He is still 37 ft offshore. He might make it to shallow water. Or not!!!!

A Shark vs the World’s Fastest Swimmer

Again we will assume that the swimmer is 30m ( 100 ft) offshore when he sees the shark fin 250m (820 ft) away. But this time we will have the world’s fastest swimmer. This time we are talking Dav Holmes vs Shark!!!!!!!!!

5 shark attack Maths mathspig

If world champion swimmer Dav starts swimming when he saw the shark 820 ft (250 m) away, he would swim 163 ft (49.6 m) before the shark attacked. He would easily make it to shore before an attack. Dav would be swimming on sand.


Don’t play it again Sam! The iPod, iPad & iPhone Shuffle

June 7, 2019

Here is an example of Gambler’s Fallacy, but for non-gamblers. 

We see – in this case – hear a pattern and then attribute meaning to this pattern  – It’s a conspiracy!!!! – when there is no pattern and no meaning!!!!! So Apple found when designing their iPod shuffle feature later on the iPad and iPhone. 

“When Apple first introduced the shuffle feature on its iPods, the shuffle was truly random; each song was equally likely to be picked than any other. However, the randomness didn’t appear random, since some songs were occasionally repeated, and customers concluded that the feature contained some secret patterns and preferences. As a result, Apple was forced to revise the algorithm. ‘We made it less random to make it feel more random,’ said Steve Jobs, the CEO of Apple’  

p68 The Decisive Moment How the Brain Makes Up Its Mind Jonah Lehrer (Text Publishing 2009)


Try it. Pick 12 songs maybe off your playlist  – Your MP3 player, perhaps or a Top 20 Chart or Top 20 Downloads Chart – assign each song a number: 1, 2, 3….up to 12. Take two dice (Diehards Note:  It’s 1 die, 2 dice) and roll.

How many throws until you get 2 songs played in a row?


The Terrifying Math of Running from a Bear … USA Units

May 14, 2019



Grizzly Bear

Weight:  550 lb        

Height:  8’ 2”   

Top Speed: 35 mph  =   51 ft/s    

Brown Bear

Weight:  1,500 lb       

Height:  8’ 2”              

Top Speed: 22 mph  =  32 ft/s     

Comparing these speeds to the fastest man on earth, Usain Bolt:

Usain Bolt:

Top speed: 27 mph  =   40 ft/s     

Bears are not dangerous:


In fact, more Americans die each year from choking on their own vomit than are killed by bears.

More death stats here

Nevertheless, bears are very fast. So you can see why Park Rangers offer the following advice:

More information at Mountain Nature.

The reason for waiting until the bear is 15 ft away is to make sure the spray doesn’t disperse in the air. If the Pepper Spray is too spread out it will not stop the bear.

Ref: Dog helps save hikers after grizzly chases them for 20 minutes.


The Terrifying Maths of Running from a Bear … Metric Units

May 14, 2019



Grizzly Bear

Weight:   250kg

Height:   250cm

Top Speed: 56kph  =   16 m/sec

More bear stats here. 

Brown Bear

Weight:  680kg

Height:   250cm

Top Speed: 35kph  = 10m/s

More bear stats here.

Comparing these speeds to the fastest man on earth, Usain Bolt:

Usain Bolt:

Top speed: 243kph =   12m/s

So Usain Bolt could out run a Brown Bear but NOT a Grizzly!

Bears are NOT as dangerous as:

In fact more Americans die choking on their own vomit each year than a re killed by bears.

More death stats here.

But bears are very fast so Park Rangers recommend the following survival tactics:

More bear survival info here.

REF: Dog helps save hikers after grizzly chases them for 20 minutes here.


Sharp Shooter Maths …. METRIC

May 10, 2019

Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Australia has a very strict gun laws today. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against our fridge. He pocketed the magazine.

A .22 means a bullet calibre of .22 inches.

My Dad the Sharp Shooter stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s  distributor cap. Phht! Car go no more. More on my childhood here.



Sharp Shooter Maths

One measure of the accuracy of rifles, riflescopes but also the sharpshooter is the MOA or Minute of Angle.  The MOA can also be used to define the target zone (circle).

I cannot show you a triangle with an angle of 1′ because it would have to be 100m long on one side and only 3cm tall.

Needless to say, drawings are NOT to scale.

A sharpshooter can put 5 out of 6 bullets in a target zone drawn at 1′ angle around centre of target at any distance.

As the distance away from the target increases the target zone circle area increases.

A sharp shooter would be considered very skilled if they can shoot within a target zone (circle) of 10.5 inch radius at 1000 yds. Hitting a bull’s eye at this distance is down to luck.


Medals, Meglomaniacs and Sharp Shooters…….. The Maths METRIC

May 10, 2019

When Mathspig recently saw images of some Russian soldiers covered in medals it prompted the question

‘Could medals protect the wearer from a sharpshooter?’ 

Mathspig was interested in this question because megalomaniac military dictators who take over countries by force tend to award themselves lots of medals. But they are also likely to be the target of sharpshooters from a liberation movement.


The target zone (circle) had a diameter of 1.9cm. This is smaller than the diameter of an American Quarter, an Australian 10c and a UK pound all of which have a diameter of appro 2.4 cm.

So the megolmaniac military dictator wins!!! He IS protected – on his chest – by his medals!!!!!! Unless the sharpshooter manages a ‘lucky’ shot.


Which sport is more DANGEROUS to play? Cricket or baseball?

April 22, 2019

Reposted due to popular demand.

Mathspigs you are about to be hit on the head with some BALL PARK figures. There is so much maths involved in comparing cricket and baseball I hardly know where to begin. So I will just set you up with comparative statistics for starters. Here they are:

cricket and baseball stats mathspig

You now have sufficient information to calculate the following:

cricket 1_tnsQ1. If a cricket player  makes 4 runs (and runs between the wickets) and a baseball player hits a home run, who runs the furtherest?

ANS: 4 runs in cricket distance = 80.48 m

Home run in baseball distance = 109.6 m

Q2. What are the delivery ball speeds of an average pitcher and a mid paced bowler in m/sec?

ANS: Average Bowler Ball Speed = 110 – 125 km/h = 30.5 – 34.7 m/sec

Average pitcher Ball Speed = 80.47 km/h = 22.4 m/sec

Q3. How far would the delivery of an average pitcher and a  medium paced bowler travel in 10 seconds?

S = d/t

t = 10 secs:

d = S x t = S x 10

ANS: In 10 sec a ball bowled by an average bowler would travel 305 – 347 M

In 10 sec a ball thrown by an average pitcher would travel 224 m

baseball_01_tns Q4. If Shoaib Akhar fielded a ball in cricket 20 m from the wicket when the batsman was still 8m from the wicket (A typical running speed for humans is 32 km/h) would he be able to run him out?

Akhar ball speed S = 45.0 m/sec

d = 20 m

S = d/t

t = d/S

t  = 20/ 45.0

t = 0.44 secs

Batsman Speed = 32 km/h = 8.9 m/sec

How far can the batsman run in 0.44 secs?

d = S x t

d = 8.9 x 0.44 = 3.9 m

So batsman would be easily run out by Akhar as he is 8 m from the crease.

 Q5. How long would it take a ball thrown by Joel Zumaya to reach the batsman if the pitchers mound was exactly in the middle of the baseball square?

ANS: Speed of ball pitched by Zumaya = 168.65 km/h = 46.8 m/sec

Zumaya speed ball

shane warne cricketline



 Q6. Which sport is more dangerous?

We will base our calculations on the speed (or velocity) and the weight (or mass) of the ball. We must use the same units in all calculations. For each sport plot x-axis: velocity of ball (v) against y-axis mass x velocity (mv) of the ball. mv is the momentum. In ballistics the change in momentum is called the IMPULSE (impact for us). If you are hit on the head with a ball it is the change in momentum of the ball that does the damage. A small ball at a high speed can do as much damage as a larger ball at a slower speed. We are not including spin, curve balls or air resistance to keep calculations straight forward … literally!!! 

Cricket baseball ball IMPACT mathspig

cricket vs baseball impact mathspig

Now that you have your graph you can answer these questions:

tim_lincecum_101mphQ6a. Which sport for professional players is the most dangerous? 

You will have to look at the graph. A cricket ball is heavier than a baseball BUT the fastest pitchers can pitch a ball slightly faster than bowlers can bowl.  IMPACT (mv) depends on multiplying mass by velocity. You will see the stats for Akhar and Zumaya marked on the graph and you can use these stats to estimate impact.

BUT then there is the impact of batting, which increases the velocity of the ball. That will have to wait for another post.

Q6b. At what speed does a cricket ball do the same damage as a baseball? Give one example.  (Hint: Draw a straight line from the Y-axis)shoaib akhtar thaindian

Once again look at the  graph above!

You will find more maths on impact on Mathspig:  for a punch here and from hailstones here.


Pics: Tim Lincecum (Left) with 101 mph pitch, Shane Warne (Upper Right) and Shoaib Akhtar (Lower Left)