Archive for the ‘Junior School’ Category

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3. Middle School Madness: BIG MATHS

May 25, 2017

Mathspig loves this ‘Street Art’ time lapse clip made by projective geometry students at the Technical University, Munich. 

SO … thought Mathspig … lets do it! Two days later Mathspig’s eyes nearly crossed trying to locate the Vanishing Point (below), which helps artists draw 3D images. It didn’t work due to the angle of elevation of the camera. 

SO .. rethink needed. (See project 1 & 2 below)

Maths Meets Street Art:

Project 1

Students can draw this ‘hole in the earth’ by Circle/Line Art School on paper fairly quickly. The aim here is to practice 3D street Art.

Maths Meets Street Art:

Project 2: The BIG ONE

Students can draw this ‘concrete hole’ by MiltonCor on paper using a ruler, set square and pencils. Then they have to scale it up to a size large enough for them to sit on the steps. The class can the ‘concrete hole’  in chalk in the school yard. Basic shading only is required, not the shading detail shown in this video.

Finally, students can take a photo of themselves sitting on the ‘steps’ with maths books beside them. 

Another MATHS SELFIE!!!!

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Pi on TV

March 8, 2017

1.  The Simpsons

When Marge is accused of stealing from Apu’s Quickie Mart his memory is tested. He says his memory is very good. He can recite pi to 40,000 places!!! Also on Numberphile: A Mile of Pi.

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2.  The Late Show with David Letterman

Maths savant Daniel Tammet explains that he can recite Pi to 22,000 places. But wait until you hear how long it takes. Amaaaazing!!!!!

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3.  Star Trek

Spock sorts out a computer with the command to calculate Pi. Cool!!!!

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4.  Mathletics

Look for the second maths blooper in this clip. The folks at Mathletics get Pi wrong!!!!! Great spotting Mathologer.

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5.  MTV Kate Bush

Some may prefer to listen to Apu reciting Pi to 40,000 decimal places. Nevertheless, here is Kate Bush singing about Pi.

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The Simple Maths of a Car used as a Weapon … METRIC units

February 3, 2017
NIce Truck Attack 2016 The Independent, UK

Nice Truck Attack 2016 The Independent, UK

Berlin Christmas Maraket Attack 2016, ABC

Berlin Christmas Maraket Attack 2016, ABC

Melbourne Car Attack 2017

Melbourne Car Attack 2017.

Cars (and trucks) have been used as weapons by drivers purposefully driving into crowds including:

2014: Saint-Jean-sur-Richelieu, Quebec

2014 : Jerusalem, Israel.

2016: Nice, France

2016: Berlin, Germany

2017: Jerusalem, Israel

2017: Melbourne, Australia.

What does the maths tell us?

Melbourne is Mathspig’s home town. The car attack killed, tragically, 6 people and injured many more. The question many seem to ask is:

Why can’t people get out of the way?

Look at the video below of the Melbourne car. It doesn’t appear to be going that fast. But the maths tells a different story. You need quite a distance between you and a car travelling at approx 60 kph to have enough time to run clear. (See calculations below)

How fast do you react?

We will set your reaction time at 0.4 sec. This allows time for you to react and turn. If you want to test your reaction time go here. But remember you have to turn as well.

How fast would you run?

According to the Telegraph, UK, the average human can run at 15.9 mph (25.6 kph) and the National Council of Strength and Fitness 15 mph (24.1kph), which Mathspig has rounded off to 25 kph.

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How do you escape a car travelling at 60 kph towards you when you are less than 9 m away?

Jump upwards!

You might reduce the impact and even go over the roof.

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Smoke Jumpers and their Amazing Wildfire Maths . . . . . . . . . . . . . . USA UNITS

December 5, 2016

 

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With wildfires in Texas and now Australia is facing the fire season, it is time to think about fire fighter maths.

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USA UNITS

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.

HOW FAST CAN YOU RUN?

USA UNITS

Time Trial:

Mark out a 30ft course. Make 3 time trials.

t1 =

t2 =

t3=

Average your time:

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

Your Speed S = 30/tav   ft/sec

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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 12mph (up to 20mph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 12 mph = 12 x 5280/(60 x 60)

                           = 17.6 ft/sec

                           = 18 ft/sec

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CAN YOU OUT RUN A FIRE?

Average Running Speed Boy 13–14 yo = 10 ft/sec

Average Running Speed Girl 13–14 yo = 8 ft/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 10 ft/sec and -Wow! – this is easy math. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

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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?

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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.

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

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

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Even at your top running speed, which is unlikely up a slope, you can run 1080 ft in 1 minute. In that time the forefront has moved 8640 ft or 1.6 miles. It depends how far away you are from the fire front when you start running, but it seems likely that 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 70 mph 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 in a strong wind can reach 140 mph, 210 mph and up to 280 mph.

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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.

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How to Die from HOMEWORK!

November 29, 2016

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We are good at graphs in maths, even funny graphs, but we often forget the power of story telling. Here’s a story about HOW NOT TO DO your MATHS HOMEWORK*.

*NOTE: Homework has never been recorded as the cause of death of a 13 year old.

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Read longer version of Hugo Does His Homework here.

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1. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

November 3, 2016

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Funky, Fab and Fantastic INTRO

Building THINKING Classrooms

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peter-liljedahlPeter 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:

 

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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.

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

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More info on TEACH here. More on 360 Maths Classroom here.

But wait, there’s more to this.

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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.

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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.

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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.

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4. PROVIDE OPEN ENDED MATHS TASKS

Here is a numeracy task recommended by Peter Liljedahl.

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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.

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2. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

October 19, 2016

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Funky, Fab and Fantastic INTRO

IMAGINARY

IMAGINARY is a German website where ART and MATHS combine. It is AMAZING.

Schools, museums, students, anyone can download interactive Computer Programs like MORENAMENTS (below) to create art, maths demonstrations and public exhibitions. IMAGINARY also contains maths/art films, an art gallery, programs for printing 3D-sculptures, maths texts and exercises, and more.

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It is FREE.

It is written in ENGLISH.

Here are a few highlights picked by Mathspig, but you have to explore the website yourself.

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SURFER

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 SURFER is a program that allows you to put in any equation and test the resulting 3D image. There is a brief video explaining how it works and you can download the program here.

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WORKSHEETS

You can download worksheets for every school level, but get ready. Here is a worksheet for 5-7 year olds. But why not? Five year olds can look at sheet music without running away screaming, why not show them ALGEBRA too?

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Mathematicians Just Wanna Have Fun

The following videos show mathematicians having fun! If your middle-school students think maths is ‘boring’ show them just one of these videos.

 

Explore IMAGINARY. Enjoy.