Posts Tagged ‘geometry’

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Real World Maths: Geometry, Heavy metal + Headbangers Heads

October 4, 2020

Are Headbangers Neck Wreckers?……..

Check out the Maths!


pic 1 headbanging-AWG4JT_188x156

The NHS reports that Australian Researchers Declan Patton and Andrew McIntosh, Uni of NSW, have conducted a study into brain and neck injuries of headbangers published in the British Medical Journal.

pic 2 headbanger hair pic

Concerts included as part of the study included Motörhead, Mötley Crüe, Skid Row, The Hell City Glamours, L.A. Guns, Ozzy Osbourne, Winger, Ratt, Whitesnake, and W.A.S.P.

Here’s Motorhead with a ‘nice’ moshpit.

motorhead

140 BPM for Ace of Spades. Motorhead BPM range is 91 – 203 

The Headbanger Study Concluded:

1. Head movement of more than 75o for an average heavy metal beat will cause head and neck injuries. This movement causes headache and dizziness.

 2. Beats above 130 bpm (beats per minute) cause neck injury.

The average headbanging song has a tempo of about 146 beats per minute (bpm).

and according to Mathspig:

3. Being punched up in the mosh pit. Do you need maths for that conclusion?

Researchers recommendations:

1. Reduce range of head and neck movement

2. Headbang to a  slower tempo

3. Wear a neck brace. (Isn’t a bad hair cut enough?)

Headbanger Rates Exercise:

How many headbeats per song of 5mins would a headbanger manage for the following song tempos?

Mathspigs excited. Look there is a band called Mutemath!!!!!!!! And here they are:

mutemath

……………………………………………………………………………

Just to show that there is something spookily primitive about headbanging here is Headbanger Baby:

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Make A Maths FACE Mask

July 21, 2020

MATERIALS:  Sheet of paper (eg. A4), ruler, scissors & coloured felt pens.

I am using an Aranea Black Mask Design. We are going to design and make a MATHS MASK PATTERN. If you want to make one out of fabric you will find all the necessary instructions here.


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Post- COVID … We need Middle School Maths that is, like, WOW!

June 9, 2020

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

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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.

Lady Gaga      Bad Romance     118  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.

……………………………………………………..

5...MatHoudini

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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.

How? Read the link here.

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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.

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8. Barcode Maths

Requirements: A product with a barcode.

Read this link and check the barcode.

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9. Secret Code

Requirements: Box of matches, an accomplice.

Read this link and amaze the class.

………………………………………

10. Rolling coin Paradox & the Radius 

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

Read this link first. It’s so counterintuitive.

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It is Xmas … Ah! The Joy of Algebra!

December 5, 2019

Great Math Xmas Ornament Ideas for Middle School here @ MathEqualsLove blog.

Mathematicians can make mountains out of mince pies, but in this case Dr Eugenia Cheng, who is Professor of Pure Mathematics at the University of Sheffield, UK, makes it look fun. The video clip includes some great Middle School Maths that you can eat.

mince-pie-diag

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Amazing and Terrifying Wildfire Maths . . . . . . . . . . . . . . USA UNITS

November 13, 2019

mathspig-smoke-jumpers 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,

mathspig-usa-units-fire-math

 

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

mathspig-firefirghter-maths-1

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

mathspig-firefighter-maths-2

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.

mathspig-fire-fighter-table-4

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?

mathspig-cfa-diag-usa-units

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.

mathspig-fire-fighter-table-5

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

mathspig-fire-fighter-table-6

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.

20o-angle-mathspig-2

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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Outdoor Math Adventures: Grade 3 – 5

September 12, 2019

It’s Autumn in UK & FALL in the USA so it’s the perfect time for a little bit of outdoor math for Grade 3-5 with AUTUMN leaves. Of course, you don’t need FALL LEAVES for this exercise, but it is colorful.
Outdoor Maths 1 Mathspig 2

This fab idea comes from Juliet Robertson, an outdoor education consultant in Scotland. Her blog Creative star learning is one of the most inspiring outdoor maths blogs you will find.

Outdoor Maths 2 Mathspig

Outdoor Maths 3 mathspig

Outdoor Maths 4 Mathspig

Outdoor Maths 5 Mathspig

Outdoor Maths 6 Mathspig

Outdoor Maths 7 Mathspig

Outdoor Maths 8 Mathspig

Check out Mathpig’s protractor joke here.

Outdoor Maths 9 Mathspig

Outdoor Maths 10 Mathspig

Another fab idea from Juliet Robertson.

 

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Math Joke 4: Geometry

February 18, 2019

Protactors and dinosaurs mathspig

Protractor headed Mathspig

Protractor Tattoo Mathspig

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Why Math Teachers should, um, speak proper!

October 12, 2018

Students can misunderstand teachers.

If math teachers mumble this is the result:


So I’m helping a Year 7 student. Smart kid. This is her test paper. 

NOTE: Students must hear terms clearly pronounced to learn them.

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Mad Mince Pie Maths

December 13, 2016

Mathematicians can make mountains out of mince pies, but in this case Dr Eugenia Cheng, who is Professor of Pure Mathematics at the University of Sheffield, UK, makes it look fun. The video clip includes some great Middle School Maths that you can eat.

mince-pie-diag

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

December 5, 2016

mathspig-smoke-jumpers 

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

mathspig-metric-units-fire-math

METRIC 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?

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

mathspig-firefirghter-maths-1

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

mathspig-firefighter-maths-2

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.

mathspig-fire-fighter-table-1

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.

mathspig-cfa-diag

mathspig-fire-fighter-table-2

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.

mathspig-fire-fighter-table-3

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.

20o-angle-mathspig-2

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.