## 41 Maths things to do before you’re 12

March 25, 2019

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.

November 3, 2016

# Building THINKING Classrooms

Peter Liljedahl , Assoc. Professor , Faculty of Edu, Simon Fraser Uni, Canada, has developed a revolutionary way of teaching maths.

He wants students of all levels to get the Aha! Experience in maths class. I met him at the ICME 13 congress in Hamburg.

His research, which extends across 600 Year 7 – 10 maths classrooms shows that his approach is very successful.You will find many examples of his recommendations at the Vertical Non-Permanent Surfaces hashtag or VNPS Twitter feed here.

This is what he recommends:

# 1. DEFRONT THE CLASSROOM

Students stand around the walls working. Desks allow anonymity and this means students can avoid thinking. Some call this approach 360 maths, but that’s just the beginning.

In the 360 Math Classroom the desks aren’t needed.

But wait, there’s more to this.

# 2. USE WHITE BOARDS

White boards proved to be the best non-permanent surface. Students scribbled calculations on the boards and wiped them off. They worked across the surface.

Some teachers even stood tables on end to get enough white board surfaces.In the following youtube clip teacher Lindsay Chinn is piloting 360 degree maths on  whiteboards.

# 3. USE RANDOMLY SELECTED GROUPS

Frequent and visible random selection was very successful. Students accepted the fairness of this approach. And teachers devised all sorts of means of randomising groups. They gave students numbers and drew numbered marbles out of a bowl or pulled names out of a bag.

The groups should consist of 3 or 4 members to be effective.

Jacob, Morten, Philip and Shania attempt to calculate

where one of them should lie on the floor

to land an m&m from an m&m cannon in their mouth.

This is from fab Jes Jorgensen’s maths class in Denmark.

And here is the youtube clip in Danish.

# 4. PROVIDE OPEN ENDED MATHS TASKS

Here is a numeracy task recommended by Peter Liljedahl.

Here are some students from Mylene Abi-Zeid’s 1P Math Class in Ottowa, Ontario, Canada

working in a decentred classroom on Vertical Non-Permanent Surfaces. You will find Mylene’s Twitter feed here.

CELL PHONE PLANS

Students must pay for their own cell phone plans. There are three plans Pay As You Go, Basic Plan and Easy 4 U Plan. Costs are defined. Students must write an explanation that will convince their parents this is the best plan for them.

You’ll find open ended maths tasks for all levels here.

Plus some card tricks here.

And an excellent summary of Peter Liljedahl’s revolutionary ideas here.

## Fire Fighters Need Maths

October 22, 2015

Black Saturday Bush Fires Australia

The Fire Season in Australia arrives suddenly. The frightening warning (above) can be heard on the national broadcaster as fires spring up around Australia. It seems no time at all since Aussie fire fighters were helping fight fires in California. Now they’re back. Elvis, The Aircrane, returns form the US for another tour of duty in Victoria.

Aircrane, Elvis, returns to fight bush fires in Australia. Herald Sun

Here is something you may not realise:

## MIDDLE SCHOOL MATHS.

You can check out a typical Fire Fighter Maths Curriculum here. The significance of the Fire Fighter Maths is that the numbers are shocking. You can look at a wildfire on TV, but when you calculate how much time you have to escape, the answer is truly terrifying.

So here is a Fire Fighter Maths problem from one of Mathspig’s Middle School Worksheets titled:

# METRIC UNITS

On 7th February 2009 a bushfire began in Victoria Australia that killed 173 people, injured 414 people, destroyed 2,100 homes and displaced 7,562 people. Known as The Black Saturday Bushfires the fire front travelled at up to 600m per 30 seconds. The radiant heat produced was capable of killing people 400 meters away.

Are fire fighters safe in such a fire? How much time do they get to escape the fire in a fire truck even if the fire front is 5 km away? We can do the math:

Q 7: You are a fire fighter in a fire truck when the wind hits the fire front at 120 km/hr. Suddenly, the fire front starts moving at 100 kph. You are, thankfully, in a fire truck but the wind and smoke haze makes driving the truck difficult. You can only make 80 kph along a straight road away from the fire (See pic above)The fire front is 5 km away. How long have you got before the fire front hits?

1. Find S1 (Fire Front Speed) and S(Fire Truck Speed) in m/sec and kph.
2. Fill in this equation where  d  (distance of fire front from point on map) and d2 (Distance of Fire Truck from the same point on a map)

d1 =   d2   +   ………

3. Use the following equations to calculate the time t that you have before the flames hit.

# USA UNITS

On 7th February 2009 in The Black Saturday Bushfires the fire front travelled at to 656 yds per 30 seconds. The radiant heat produced was capable of killing people 437 yds away.

Are fire fighters safe in such a fire? How much time do they get to escape the fire in a fire truck even if the fire front is 3.1 miles away? We can do the math. Answers below.

Q 7: You are a fire fighter in a fire truck when the wind hits the fire front at 75 mph. Suddenly, the fire front starts moving at 62 mph. You are, thankfully, in a fire truck but the wind and smoke haze makes driving the truck difficult. You can only make 50 mph along a straight road away from the fire (See pic above). The fire front is 3 miles away. How long have you got before the fire front hits?

1. Find S1 (Fire Front Speed) and S2 (Fire Truck Speed) in ft/sec and mph
2. Fill in this equation where  d1   (distance of fire front from point on map) and d2 (Distance of Fire Truck from the same point on a map)

d1 =   d2   +   ………

3. Use the following equations to calculate the time t that you have before the flames hit.

# WORKSHEETS

Fire Fighter Math 1: Wildfire Algebra You will find the worksheets in both METRIC & USA Units Here. Yes! There is a small fee. Mathspig and Roni the Rodent (left) have this very, very slow get rich quick scheme going. Ha!

Lesson Plan:

Students discover that fire fighters need middle-school math. Students complete some warm-up exercises involving unit conversions (mph to ft/sec or kph to m/sec) without and with a calculator and then they simplify algebraic expressions and solve simultaneous equations. Students use this math to calculate real life fire front speeds that fire fighters have faced in Montana, USA and Victoria, Australia. The power of this math is that the calculations are based on the stories about and conditions faced by these real fire fighters. No lectures are needed on the danger of wildfires as the numbers speak for themselves.

## An Interview with Warwick Holmes Aero-space Engineer, Rosetta Project, ESA!

November 28, 2014

Warwick Holmes with the Rosetta lander 10 years ago!!!!

What is an aero-space engineer?

An Aero-Space engineer is responsible for turning an “idea” or a “need” into physical reality by creating an “hardware” or “Software” Engineering solution.  In the case of the ESA Rosetta and Philae mission, the “idea” was to make a spacecraft to orbit and land on a comet outside the Asteroid belt.  Aero-space engineers turned that idea into the physical reality of the Rosetta and Philae spacecraft by applying Science, Technology, Engineering and Mathematics to create the spacecraft.  Rosetta then flew for more than 10 years through the solar-system on an interplanetary trajectory, four times around the Sun, a total distance of 6.5 billion km to successfully orbit and land on Comet-67P.

What got you hooked on Aero-space engineering?

I saw Neil Armstrong stepping on the Moon when I was only 8 years old on a flickering black & white television set from my Grade-2 class in Adelaide. From that moment, I was determined to work in space engineering to build spacecraft and experience the excitement of space exploration and science.

Where did you go to school?

(2)  Red-Hill Primary and Telopea Park High school (Canberra)
(3)  The Kings school Parramatta (Sydney)

What maths did you like?

I liked everything about mathematics, I like solving functions (polynomials) and differential calculus.

What maths did you hate?
None !!!

Were you a nerd or simply a student with a passion?

Definitely not a nerd, definitely a student with a passion with a really well defined objective, to become an engineer and become involved in building and launching a spacecraft (that actually ended up becoming 10 spacecraft!)

How do you become an aero-space engineer? What maths do you need?
I completed three degrees, two at Sydney University and one at UNSW

(1)  Science (majoring in Physics and Pure Mathematics)
(2)  Electrical Engineering.
(3)  Masters of Technology Management
It depends what stream of engineering you choose, but the most common mathematics involved in Space Engineering includes:  Matrix algebra, statistics, conformal mappings and complex transformations, differential calculus, Fourier analysis, Laplace transforms and series expansions.

What was your job on the Rosetta project?

(1)  Assembly Integration and Test Engineer – working directly with the companies that built the Rosetta spacecraft
(2)  Avionics Systems Engineer with the European Space Agency – performing complete integrated system tests of the spacecraft mission operations.

I performed the initial electrical integration of several electronic units on the Rosetta spacecraft (NAVCAM, gryoscopes, reaction wheels, Antenna pointing mechanism, etc).  Then followed complex system testing where as many of the spacecraft modes and functions were tested as possible.  After several years of testing , the engineers follow the spacecraft to the launch site to launch the spaceraft for the start of its long mission.

What was the biggest challenge in the entire project?

The spacecraft has a lot of built-in software “intelligence” so the it can look after itself when very far from Earth.  This software was very complex and difficult to understand the decisions and actions it was making sometimes.  Getting all the systems working together in one spacecraft was difficult.

Rosetta Spacecraft with Thermal Blankets from the ESA webpage

Did anything go wrong?

During the testing 100’s of things were wrong, and that was our job as test engineers to find (hopefully) all the errors before launch.  The design of the spacecraft has a lot of flexibility in the software ad hardware which means even after launch many problems can still be solved.

What can we learn from this project?

This project will potentially prove two very important and currently unknown questions here on Earth.
(1) Possibly prove that the Earth’s sea water comes from Comets and
(2) The reason life started so quickly after the oceans formed was because the comets also seeded the water with exotic carbon compounds (specifically amino acids) that gave the formation of life a big kick-start.

What advice would you give to any student who wants to be an aero-space engineer?

There is only one secret, work hard and do as well as you can because there are many others people who want to do the same work. The only thing managers want to see and that is you are doing good work and working well in the team with other engineers (scientists, mathematicians, etc).

## 41 Maths things to do before you’re 12

September 1, 2014

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.

## 6. Clean Up Mega Messes

September 18, 2013

32 people died when the Costa Concordia ran aground in a protected marine park off the coast of Italy. The \$US800 million salvage operation to remove the Costa Concordia needs lots of maths.

It is the biggest salvage operation ever undertaken in seafaring history.

THIS IS THE PROBLEM. It is a one off project and the engineers have to hope they get the maths right.

Here’s the plan:

Here are the maths problems:

# Problem 1:

The ship, which is 290 meters (951 feet) long and 36 meters (118 feet) wide, is on its side and full of seawater. It has a displacement of 50,000 metric tons plus the weight of the water inside that, at a guess, could weight 30,000 metric ton. This is a BIG problem. Normal salvage methods cannot be used.To give you an idea of the scale:

50,000 metric ton = 50,000,000 kg

1 London Double Decker Bus = 8,000 kg (Empty) or 12,000 kg full

according to the BBC

The wt of a half-full London = 10,000 kg

## 1 Costa Concordia = 5,000 London Buses

Now add the water.The salvage operation must lift the equivalent, maybe, of 8,000 London Buses.

…………………………………………………………….

# Problem 2:

The ship is resting on a seabed that slopes at an angle of 200.

Simply winching the ship upright would have it roll down the slope. A horizontal platform must be built that can take the 50,000 metric ton plus load.

……………………………………………………………….

# Problem 3:

The platform has to be built underwater. This will take 111 salvage divers working around the clock to secure the platform and attach cables to the ship.This steel platform weighs three times as much as the Eiffel Tower.

The total weight of the Eiffel Tour = 8,560,000 kg

The weight of the salvage platform = 26,000,000 kg

or 2,600 London Buses.

……………………………………………………………….

Problem 4:

The Costa Concordia must be winched onto the platform slowly. Too quickly it might topple off the platform.

As the  50,000 metric ton ship (plus the weight of trapped seawater) is winched upright the load on the winches decreases (See simplified diag below.) Think of picking up a chair off the floor.  As you rotate the chair upwards the load decreases to zero …. when the CENTRE OF GRAVITY  lies directly above the PIVOT POINT then gravity works with you and the chair drops with a thud to the floor.  Engineers cannot allow 50,000 plus  metric ton to drop with a thud. Winches must be carefully controlled. The winching operation took 19 hours.

……………………………………………………………….

# Problem 5:

The Costa Concordia was winched upright on 17 Sept 2013. Floats must now be welded onto the damaged side of the ship. Once the ship is refloated it will be towed away to be broken it up for scrap metal. This will take 2 years.

# UPDATE:

The costa Concordia is floating again. On 27 July 2014 the crippled cruise ship arrived in Genoa, it’s final destination, where it will be broken up for scrap metal. The complex engineering feat to refloat the vessel proved successful.

From Newstalk 931