## Amazing and Terrifying Wildfire Maths . . . . . . . . . . . . . . METRIC UNITS

July 25, 2022

With wildfires  burning across the US and Europe , Mathspig had to update this firefighter maths post for middle school classrooms.

Radiant Heat Stats WA Fire Dept FACEBOOK, Australian Bushfires 14 NOV 2019 MyFireWatch WA

Wildfires USA 2022 Map: NASA

# Background Story

On 5th August 1949 Wag Dodge was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening 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.

# METRIC UNITS

## Time Trial:

Mark out a 10 m course. Make 3 time trials.

t1 =

t2 =

t3=

Average your time:

tav = (t1 + t2 + t3)/ 3 =

Your Speed S = 10/tav = ……… m/sec

## HOW FAST IS A GRASS FIRE?

This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at 20kph (up to 30 kph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 20 kph = 20 x1000/(60 x 60)

= 20 x 0.27777777 = 20 x 0.28 m/sec

= 5.6 m/sec

# CAN YOU OUT RUN A FIRE?

Average Running Speed Boy 13–14 yo = 3.0 m/sec

Average Running Speed Girl 13–14 yo = 2.4 m/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 3.0 m/sec. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

This is not looking good. See more Firefighters Need Maths here.

We can do very accurate calculations using simultaneous equations. Wildfire Algebra: Detailed Worksheet using simultaneous equations and solutions  here.

## NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?

We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.

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

Each 10º increase in slope, the fire front speed doubles.

Now you can calculate the distance travelled by the fire front up a slope at a 30º angle.

Don’t forget you can use the WEB 2.0 Calculator here.

Even at your top running speed, which is unlikely up a slope, you can run 180 m in 1 minute. In that time the forefront has moved 2688 m or 2.7 km.

It depends how far away you are from the fire front, but it seems you cannot out run this fire front.

Again we can do very accurate calculations using simultaneous equations.

See Firefighters Need Maths here.

Wildfire Algebra: Worksheet and solutions here.

# CAN YOU OUT RUN A WILD FIRE?

High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 110 kph and temperatures up to 2000 °C, which can and does melt glass and cars.

The fire front speed doubles with every 10º, so speeds for the fire front can reach 220 kph, 330kph and up to 550kph.

# 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 out run the fire at that point. So he stopped. Took off his back pack. 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.

June 19, 2022

## What’s the Maths Curriculum got to do with it? WHEN Maths is, like, soooo BORING!!!!!

February 22, 2022

Australia is reviewing its Maths Curriculum.

Sides are taken. Arguments are rife. See the excellent article by Donna LuCracking the formula: how should Australia be teaching maths under the national curriculum?, The Guardian,13 FEB, 2022)

Should teachers teach? Or students explore problems? (Called Cognitive Activation in academe!)

Why not, both? Then add outdoor maths (below) plus defronting the classroom sometimes and try some maths selfies for homework. More ideas here

It doesn’t matter what’s written in the curriculum, the biggest problem in maths for students is

# BOREDOM.

Here, to tackle boredom are:

# 41 Maths things to do before you’re 12

A growing body of research shows us that outdoor play leads to better physical and mental health, has positive effects on cognitive function and learning, and reduces the incidence of behavioural problems.” Maria Zotti, Nature Play, SA.

Peter Dunstan, Principal Kilkenny PS, SA, writes in SAPPA magazine, Primary Focus, that outdoor play fosters “wonderment, independence and freedom” as well as “social skills, imagination, creativity and problem solving”.

Inspired by SAPPA and NaturePlay,  Mathspig has produced her own outdoorsy maths list:

References:

9. You can measure the volume of your lungs by blowing one breath into a balloon and pushing it into a full bucket of water. Measure the overflow.

21. Light intensity links. Here and here.

## The Bitter Truth: How We See the Numbers

October 10, 2021

The pandemic has launched a data storm. But some numbers cut through this white out. Despite following the numbers closely I was shocked by the following headline on the front on The Washington Post a few weeks ago.

Using data from the Worldometer Website, I thought it would be interesting see how other countries compare with the USA. America has already dropped below this grim marker. And low is not the way to go!!!!

# BEST: New Zealand              1: 200,000

Here are some more stats:

August 22, 2021

## 3.2.1. Lift-off. How STEM opens new horizons for girls.

May 17, 2021

Aviation Aerospace Australia has produced an amazing Video Here to show girls what careers are available in the aviation and aerospace industries. Mathspig has met 3 female Boeing Engineers and a female engineer that worked on the Williams Formula 1 car.

An information brochure (link below) that goes with the video gives subject advice and income ranges over a lifetime career:

information_brochure

Meanwhile, this is why girls (and boys) should do STEM.

## Terrifying Tennis Maths: The Speed of Novak Djokovic’s serve. METRIC

February 7, 2021

USA units post here.

### Could you return his serve? Do the maths!!!!!!

The ball leaves Djokovic’s racket and hits the ground 0.31 secs later.

Go here to see why this simplified calculation works!

Mathspig tested her reaction time here. TRY IT!

Mathspig’s best, best, best reaction time = O.33 sec

## Terrifying Tennis Math: The Speed of Novak Djokovic’s serve. USA units

February 7, 2021

METRIC post here.

### Could you return his serve? Do the math!!!!!!

The ball leaves Djokovic’s racket and hits the ground 0.30 secs later.

Go here to see why this simplified calculation works!

Mathspig tested her reaction time here. TRY IT!

Mathspig’s best, best, best reaction time = O.33 sec

## _______ Politicians vs Reality ______ Why BACK-to-BASICS Maths FAILS

December 8, 2019

“There are many such examples of excellence across Australian schools. But there are not enough. While individual schools might shine, the results of international tests, released earlier this week, suggest our education system as a whole is stagnating. For the first time, Australia failed to exceed the OECD average in maths, and the nation’s results in reading and science have declined since Programme for International Student Assessment (PISA) testing began in the early 2000s.” More here.

# What about SINGAPORE?

Meanwhile, SINGAPORE students do well in maths because they have very ENTHUSIASTIC teachers. If you want to see how Singapore and other countries promote maths in the classroom go to Maths News: Around the World from International Congress of Mathematical Education 2016.

# Here we go again!

I wrote the following post in 2014 and here we are, 5 years later, back where we started.

# Is maths becoming a dead language?

In the 1980’s American restaurant chain A&W was going to kick Mcdonald’s marketing butt. How? Instead of a quarter pounder burger they brought out and promoted a third pounder!!!! The promo failed. Why? Americans didn’t get fractions. More frightening, in Why do Americans stink at maths?, Elizabeth Green, The New York Times ( 23 JUL 2014), was the US study that found 17 percent of medication errors were caused by maths mistakes made by doctors or pharmacists.

Meanwhile, students in Australia, the USA, and the UK are dropping out of maths like flies.

Something is seriously wrong with the way we teach maths.

…………………………………………………………………………………..

# Vote 1 Me. (Probably can’t count to 2 anyway.)

Politicians around the world use education to win votes. We will raise numeracy standards they promise. Of course, this may not help your child, just the state averages.

Nevertheless, Back to Basics concepts are constantly pushed in the UK, the USA, and Australia by politicians.

In 2009 Obama backed “common standards” and “common core” curriculum in maths supported by \$USA 4 Billion in grants. (Why do Americans stink at maths?, Elizabeth Green, The New York Times, 23 JUL 2014).

.

.

Later this year a new ‘Back to Basics’ Curriculum will be rolled out in the UK with an emphasis on times tables and mental maths. (Schools must go back to basics to raise maths standards, Graeme Paton, The Telegraph, UK, 18 FEB 2014)

.

Australia has introduced a National Curriculum and National Testing (NAPLAN) in numeracy and literacy in recent years. The current government just put up \$22 million to back Direct Instruction in Indigenous Schools across Qld, NT and WA Jamie Walker, The Australian, 5 JUL 2014) Direct Instruction is a commercial product involving very rigid and proscriptive Back to Basics curriculum and testing program from National Institute of Direct Instruction based in Eugene, Oregon.

Teachers use strict guidelines and must keep within the program. Eg:

# Do back to basics programs work?

Maybe. It depends on what you are measuring. Students can improve some maths skills. The worksheets are very clear and that is to be applauded. And so, in time, standards may rise on paper.

But there are still two huge problems.

…………………………………………………………………………….

# We have ways of teaching to make you hate maths!!!!

Firstly, there is the McMath Element. Do you want Pythagoras with that quarter pounder? Repetitive, pre-packaged, parrot-style learning is easily forgotten. According to Professor Roediger professor of psychology at Washington Uni ‘effortful, varied practice builds mastery’. New York Times, 18 Jul 2014).

Secondly, rigid drilling is boring. Students grind through the exercise after exercise being constantly reminded that maths is dry, dull and boring on a coma-inducing scale. Students will, as is the current trend, drop maths as soon as they can.

………………………………………………………………………….

# Why do some kids think maths is a cruel and unusual punishment?

According to Peter Sullivan, Professor of Mathematics Edu at Monash University students drop maths because it is:

### See STOP THE PRESS: Maths Teaching Fails

But it is not just students who find maths boring. Teachers who are forced to adopt rigid, repetitive and monotonous prepackaged courses also become disillusioned.

# One size does not fit all and local knowledge counts

I’m sitting in a Grade 3 classroom in a remote Indigenous School on Elcho Island off the coast of NT. (Last week I ran some fun/creative workshops for staff.) The young enthusiastic teacher (with the help of two indigenous interpreters) was teaching the students to count to 10 and write the numbers from 1 – 10.

Students arrive at school speaking only the local Indigenous language. They must acquire literacy skills in their own language before they are taught English in Grade 4. There is a good deal of catching up to be achieved in numeracy skills. Many Indigenous languages only name the numbers 1, 2, 3 and many. The teachers on the island are familiar with the difficulties facing their students and work hard with empathy and enthusiasm to overcome multiple disadvantages of their students.

Teachers on the island have developed extraordinary resources and create programs to engage their students in learning maths. Imposing a rigid curriculum regime like Direct Instruction on Elcho Island schools will further disadvantage the students and also demoralize the dedicated staff.

# Ways of teaching maths that work

Here are two teaching methods that are not only flexible and fun, but they have also been proven to work in the classroom.

### The Walker Learning Approach

Kathy Walker is an Australian educator, author and early years curriculum expert. Her books include What’s the Hurry? and Play Matters. The Walker Learning Approach, which is used in many schools around Australia including Elcho Island, is an evidence-based strategy that encourages play-based discovery and learning as well as explicit instruction in numeracy and literature (K – Year 8). More here.

…………………………………………………………….

### Magdelene Lampert: Learning by Communication Method

Magdalene Lampert, until recently professor of education at the University of Michigan in Ann Arbor and author of “Teaching Problems and the Problems of Teaching, has replaced ‘.(Why do Americans stink at maths?, Elizabeth Green, The New York Times, 23 JUL 2014)

She advocates incorporating communication in maths as ‘being able to explain your thinking so that someone else grasps your ideas’ improves your understanding ( as any teacher knows from their own experiences in front of the classroom.)

…………………………………………………………………………….

# LET TEACHERS TEACH

Yeah! MATHS: Guaranteed to be boring one day and scary the next but always a complete waste of time – there’s a product that’s not going to sell.

Let teachers teach. This should be a campaign slogan to put maths teaching back into the hands of the people, who know what is going on in the classroom. Imposing rigid regimes on teachers is counter productive as the teachers become as bored, as angry and as disenfranchised as their students. I mean ‘why bother?’ We need teachers with passion, enthusiasm and creativity to teach maths, not Mathsbots pre-programmed by politicans to win votes.

Politicians do not teach your children. Teachers do. If politicians and the bureaucracy make teachers lives miserable, this misery will be passed onto their students … Your children. There must be checks and balances – and cliches, I guess – but it is the teacher who passes on their love or hatred of maths to your children. If the community gives teachers the chance to teach maths creatively and with humour, they will take up the challenge and your child will benefit.

I was taught by a young and enthusiastic Maths teacher at a small rural hgh school in the sixties. That’s almost 50 years ago – OMG! Don’t do the maths. His name was Barry Underhill.

## Amazing and Terrifying Wildfire Maths . . . . . . . . . . . . . . METRIC UNITS

November 13, 2019

With the catastrophic Californian fires burning into November and wildfires currently burning in NSW and Qld, Australia, I had to repost this firefighter maths for middle school classrooms.

Radiant Heat Stats WA Fire Dept FACEBOOK, Australian Bushfires 14 NOV 2019 MyFireWatch WA

Wildfires USA 2019 Map: Ecowest,

# Background Story

On 5th August 1949 Wag Dodge was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening 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.

# METRIC UNITS

## Time Trial:

Mark out a 10 m course. Make 3 time trials.

t1 =

t2 =

t3=

Average your time:

tav = (t1 + t2 + t3)/ 3 =

Your Speed S = 10/tav = ……… m/sec

## HOW FAST IS A GRASS FIRE?

This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at 20kph (up to 30 kph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 20 kph = 20 x1000/(60 x 60)

= 20 x 0.27777777 = 20 x 0.28 m/sec

= 5.6 m/sec

# CAN YOU OUT RUN A FIRE?

Average Running Speed Boy 13–14 yo = 3.0 m/sec

Average Running Speed Girl 13–14 yo = 2.4 m/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 3.0 m/sec. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

This is not looking good. See more Firefighters Need Maths here.

We can do very accurate calculations using simultaneous equations. Wildfire Algebra: Detailed Worksheet using simultaneous equations and solutions  here.

# NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?

We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.

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

Each 10º increase in slope, the fire front speed doubles.

Now you can calculate the distance travelled by the fire front up a slope at a 30º angle.

Don’t forget you can use the WEB 2.0 Calculator here.

Even at your top running speed, which is unlikely up a slope, you can run 180 m in 1 minute. In that time the forefront has moved 2688 m or 2.7 km.

It depends how far away you are from the fire front, but it seems you cannot out run this fire front.

Again we can do very accurate calculations using simultaneous equations.

See Firefighters Need Maths here.

Wildfire Algebra: Worksheet and solutions here.

# CAN YOU OUT RUN A WILD FIRE?

High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 110 kph and temperatures up to 2000 °C, which can and does melt glass and cars.

The fire front speed doubles with every 10º, so speeds for the fire front can reach 220 kph, 330kph and up to 550kph.

# 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 out run the fire at that point. So he stopped. Took off his back pack. 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.