## Real World Maths: Surds and all that jazz …

October 12, 2022

Eddie Woo is an Aussie Maths teacher who runs his own Youtube Channel. So popular is this channel in October 2015, Woo won the NSW Premier’s Prize for Innovation in Science and Mathematics. This youtube clip won’t tell you where you will use surds, but it does something magical.

It compares surds to different kinds of music to help students understand why mathematicians go crazy over the concept of surds. This clip tells why maths is soooooo special. There is no guesswork or fake information in this maths. Maths must be accurate. And surds demonstrate this point. (Look for the 5 min mark)

## Will you use surds in real life?

Maybe. Probably, not. But surds are used in mathematical programs that demand accuracy. eg. engineering skyscrapers, building satellite dishes, and even in video games. But you won’t see them. Like so much mathematics surds will be hidden in some algorithm.

Here are two Examples:

# 1. The Golden Ratio:

Often written a 1:1.61 the Golden Ratio or Fibonacci Sequence appears in art and nature and has an aesthetic appeal to the eye, but the accurate ratio is:

Satellite dishes, headlights, torches, and bridges all designed using the parabolic arc. The parabola is defined by the quadratic function and sometimes solving for x produces an irrational no. namely a surd. Rounding off can introduce inaccuracies that can become more dramatic when scaled up to the sie of, say, a bridge.

# 3. The Golden Ratio in Music

Mozart arranged his piano sonatas so that the number of bars in the development and recapitulation divided by the number of bars in the exposition would equal approximately 1.618, the Golden Ratio. Find more @ CLASSIC FM.

Back to Mozart.

In the above diagram, C is the sonata’s first movement as a whole, B is the development and recapitulation, and A is the exposition.

And here is Mozart’s Piano Sonata No. 1 in C Major as an example. Can you hear the Golden Ratio. Not really. But it’s there.

## Outdoor Maths Adventures: Middle School

September 16, 2022

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

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!

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

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

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

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.

## Razzle-Dazzle them with Middle School Math that is, like, WOW!

September 4, 2022

## 10 Quick & Quirky Ways to Make the Math Classroom Rock!

…………………………………………………………..

## 1. Tell a Story: Life, Death, and Geometry

This is middle school maths at its best. To understand Wild Fires you must understand the angle of a slope. REQUIREMENTS: Just this story and a white or blackboard to show how the fire speed changes with the slope angle.

### Background Story

On 5th August 1949 Wag Dodge was dropped by parachute with 14 other firefighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Firefighters who parachute in to put out small blazes started by lightning are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.

### What you have to know

Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by firefighters is:

Each 10º increase in slope, the fire front speed doubles. So a fire front traveling at 60 kph (37 mph) becomes a fire front traveling at 120kph (75 mph) moving up a slope of 10º.

### What happened to the Smoke Jumpers?

When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?

ANS: Here’s the amazing thing. Wag realised he could not outrun the fire at that point. So he stopped, took off his backpack, took out some MATCHES, and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not. You will find maths exercises here: METRIC UNITS and USA UNITS.

### Requirements: SmartBoard to Project this link.

Try it first. You might be surprised.

## 3. Urban Myth Busted

Requirements: This story.

Goldfish Memory This is what Epidemiologists do. They find out if there are statistics to support the theory. These mathematicians have been providing vital information during the COVID-19 Pandemic.

According to the ABC news, this myth was busted by a 15-year-old Adelaide schoolboy named Rory Stokes. He fed his goldfish near a Red Lego brick. The fish started anticipating food near the brick. He took it away and replaced it several weeks later. The fish remembered the red brick!!! More here.

Other maths myths to check out:

Chewing food 32 times before swallowing helps you lose weight. Here.

You must drink 8 glasses of water a day. Here.

You are 6 degrees of separation from anyone in the world. Here.

It takes 43 muscles to frown and only 17 to smile. Here.

## 4. Beat this! Drum Rates in BPM.

Requirements: A pencil and a timer on a phone.

Can students manage a drumbeat to popular songs? Here are some songs with their BPMs (Beats per minute listed).

Tones and I     Dance Monkey  98 BPM.

The Rubens  Live In Life  104 BPM.

……………….Just Dance          119   BPM

Flume   Rushing Back   176  BPM   (Try the middle of the track. It varies)

Panic! At the Disco      186 BPM   (Recommended by Jog.FM for jogging)

More DRUM BEATS and a story about Drummers’ Brains here.

## ………………………….

Requirements: Phonebook.

Read the instructions at this link. Very simple. And you can amaze the students. Or Vice Versa. A student can amaze a maths teacher.

# 6.  Can you make a Square Bubble?

Requirements: pipe cleaners or stick cube and detergent and a bucket with water.

All ages love this exercise.

# 7. Photo Scavenger Hunt

Challenge: Students use a smartphone to take 5 mathsy photos for homework. Ideas here.

However, start in the maths room. Look for parallel lines, angles, rectangles, spheres, parabolas (not in the textbooks). See parabola below.

# 8. Barcode Maths

Requirements: A product with a barcode.

# 9. Secret Code

Requirements: Box of matches, an accomplice.

## ………………………………………

Requirements: 2 large coins. 20c in Australia, Half-\$ USA or 25p UK.

February 1, 2022

# The Parabola Must Be Obeyed!!!!

Aerial skiers aim for height rather than length. Their aerial flight times are much smaller than ski jumpers so air resistance has minimal impact.

In fact, there is one law the aerial skiers cannot break. It is the law of gravity.

Here is an equation for  projectile motion from Wired magazine.

Screen grab from Wired Magazine

The equation for projectile motion also applies to Motorbike Jumps and Longbow Arrows.

Here is the x-y graph for different launch angles.

trajectory wired magazine

You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. More on centre of Gravity at The Great Back Pack Attack ie.

The centre of gravity of Aerial Skiers must follow a

# parabolic curve.

Rocky Maloney Winter X Games Aspen

## Real World Maths: Surds and all that jazz …

November 23, 2020

Eddie Woo is an Aussie Maths teacher who runs his own Youtube Channel. So popular is this channel in October 2015, Woo won the NSW Premier’s Prize for Innovation in Science and Mathematics. This youtube clip won’t tell you where you will use surds, but it does something magical.

It compares surds to different kinds of music to help students understand why mathematicians go crazy over the concept of surds. This clip tells why maths is soooooo special. There is no guesswork or fake information in this maths. Maths must be accurate. And surds demonstrate this point. (Look for the 5 min mark)

## Will you use surds in real life?

Maybe. Probably, not. But surds are used in mathematical programs that demand accuracy. eg. engineering skyscrapers, building satellite dishes, and even in video games. But you won’t see them. Like so much mathematics surds will be hidden in some algorithm.

Here are two Examples:

# 1. The Golden Ratio:

Often written a 1:1.61 the Golden Ratio or Fibonacci Sequence appears in art and nature and has an aesthetic appeal to the eye, but the accurate ratio is:

Satellite dishes, headlights, torches, and bridges all designed using the parabolic arc. The parabola is defined by the quadratic function and sometimes solving for x produces an irrational no. namely a surd. Rounding off can introduce inaccuracies that can become more dramatic when scaled up to the sie of, say, a bridge.

June 9, 2020

## 10 Quick & Quirky Ways to Make the Maths Classroom Rock!

…………………………………………………………..

## 1. Tell a Story: Life, Death, and Geometry

This is middle school maths at its best. To understand Wild Fires you must understand the angle of a slope. REQUIREMENTS: Just this story and a white or blackboard to show how the fire speed changes with the slope angle.

### Background Story

On 5th August 1949 Wag Dodge was dropped by parachute with 14 other firefighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Firefighters who parachute in to put out small blazes started by lightning are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.

### What you have to know

Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by firefighters is:

Each 10º increase in slope, the fire front speed doubles. So a fire front traveling at 60 kph (37 mph) becomes a fire front traveling at 120kph (75 mph) moving up a slope of 10º.

### What happened to the Smoke Jumpers?

When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?

ANS: Here’s the amazing thing. Wag realised he could not outrun the fire at that point. So he stopped, took off his backpack, took out some MATCHES, and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not. You will find maths exercises here: METRIC UNITS and USA UNITS.

### Requirements: SmartBoard to Project this link.

Try it first. You might be surprised.

## 3. Urban Myth Busted

Requirements: This story.

Goldfish Memory This is what Epidemiologists do. They find out if there are statistics to support the theory. These mathematicians have been providing vital information during the COVID-19 Pandemic.

According to the ABC news, this myth was busted by a 15-year-old Adelaide schoolboy named Rory Stokes. He fed his goldfish near a Red Lego brick. The fish started anticipating food near the brick. He took it away and replaced it several weeks later. The fish remembered the red brick!!! More here.

Other maths myths to check out:

Chewing food 32 times before swallowing helps you lose weight. Here.

You must drink 8 glasses of water a day. Here.

You are 6 degrees of separation from anyone in the world. Here.

It takes 43 muscles to frown and only 17 to smile. Here.

## 4. Beat this! Drum Rates in BPM.

Requirements: A pencil and a timer on a phone.

Can students manage a drumbeat to popular songs? Here are some songs with their BPMs (Beats per minute listed).

Tones and I     Dance Monkey  98 BPM.

The Rubens  Live In Life  104 BPM.

……………….Just Dance          119   BPM

Flume   Rushing Back   176  BPM   (Try the middle of the track. It varies)

Panic! At the Disco      186 BPM   (Recommended by Jog.FM for jogging)

More DRUM BEATS and a story about Drummers’ Brains here.

## ………………………….

Requirements: Phonebook.

Read the instructions at this link. Very simple. And you can amaze the students. Or Vice Versa. A student can amaze a maths teacher.

# 6.  Can you make a Square Bubble?

Requirements: pipe cleaners or stick cube and detergent and a bucket with water.

All ages love this exercise.

# 7. Photo Scavenger Hunt

Challenge: Students use a smartphone to take 5 mathsy photos for homework. Ideas here.

However, start in the maths room. Look for parallel lines, angles, rectangles, spheres, parabolas (not in the textbooks). See parabola below.

# 8. Barcode Maths

Requirements: A product with a barcode.

# 9. Secret Code

Requirements: Box of matches, an accomplice.

## ………………………………………

Requirements: 2 large coins. 20c in Australia, Half-\$ USA or 25p UK.

## COOL FOOTY MATHS: THE LONGEST KICK

May 25, 2019

………………………………………………

The following maths is suitable for Year 9+

but can be presented to lower grades just to show

maths is cool!

## 6. If the pilot dies the control tower can talk you down.

January 3, 2019

So mathpigs, here is a small taste of what you would need to do to land a small aircraft in an emergency if the pilot is unconscious/dead.

# A = Airspeed

Find airspeed indicator on instrument panel.

Instrument Panel Piper PA-28

Check speed.

Knots or mph or kph?

Avoid red zone. Too fast.

Knots outer scale. mph inner scale. Recommended velocity between blue & red.

# B = Contact nearest air traffic controllers.

1. Call MayDay MayDay MayDay

2.  Look for plane ID. It will be on instrument panel somewhere.

3. Check fuel.

On the Piper Cherokee there are 2 fuel tanks, R & L. Check both.

Check aircraft operating handbook to see fuel consumption and remaining time in air.

Quick calc.

# C = Checklist

Follow Emergency Landing Checklist in aircraft operating handbook for Power OFF or Power ON landing.

Keep in mind, if your air speed is too low you can drop from air, but the higher the landing speed the bigger crash.

Crash energy increases with the square of speed. It’s a parabola!!!!!

The likelihood of a passenger with

## very small.

The likelihood of a passenger with

## WINTER OLYMPICS: One Rule Aerial Skiers Cannot Break

February 10, 2018

Aerial skiers aim for height rather than length. Their aerial flight times are much smaller than ski jumpers so air resistance has minimal impact.

In fact, there is one law the aerial skiers cannot break. It is the law of gravity.

Here is an equation for  projectile motion from Wired magazine.

Screen grab from Wired Magazine

The equation for projectile motion also applies to Motorbike Jumps and Longbow Arrows.

Here is the x-y graph for different launch angles.

trajectory wired magazine

You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. More on centre of Gravity at The Great Back Pack Attack ie.

The centre of gravity of Aerial Skiers must follow a

# parabolic curve.

Rocky Maloney Winter X Games Aspen

## 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

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:

Fractions, % and decimalsand 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:

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!!!!!!

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