Outdoor Maths Adventures: Middle School

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!

 

McGill Uni link here.

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.

Outdoor Math Adventures: Grade 3 – 5

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.

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.

Check out Mathpig’s protractor joke here.

Another fab idea from Juliet Robertson.

 

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

 

10 Quick & Quirky Ways to Make the Math 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 5^th 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.

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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.

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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.

When Area Calcs mean Big Bucks

Bank Notes returned to RBA data.

RBA grids for damaged notes.

MIDDLE SCHOOL MATH: Mapping, Matrices and GAME DEVELOPMENT

The aim of this post is to show middle school math students that MATRICES are used in the REAL WORLD of GAME DEVELOPMENT.

They don’t have to do the math. 

To have some fun playing with a 2D to 2D transformations go to this MathIsFun post.

Crazy Guy uses Infrared Sensors on Xbox Kinect to create WoW! Synth-Pop VIDEO

The aim of this post is to show middle school math students that MAPPING is used in the REAL WORLD of Synth-Pop Music Video Production.

IT Records on Facebook

Amazing and Terrifying Wildfire Math . . . . . . . . . . . . . . USA UNITS

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

Radiant Heat Stats WA Fire Dept FACEBOOK.

 Wildfires USA 2022 Map:NASA

 

USA UNITS

Background Story

On 5^th 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:

t_av = (t₁ + t₂ + t₃₎/ 3 =

Your Speed S = 30/t_av   ft/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 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

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.

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 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 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.

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.

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

 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

METRIC UNITS

Background Story

On 5^th 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:

t_av = (t₁ + t₂ + t₃₎/ 3 =

Your Speed S = 10/t_av = ……… 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.

Stranger Things Math 2: Now You are the Galton Ball

Mathspig has become obsessed with the Galton Board since watching ELEVEN dropping discs into the peg board on STRANGER THINGS 4.

Now thanks to David Butler, University of Adelaide, you can turn your middle school class into Galton Balls. You can find 100 randomly generated instruction sheets for each human Galton Ball at David’s website. (Link above)

Ideally, you would have 3,000 students to do this activity. But the class exercise ends with something approximating a Normal Distribution or Bell Curve constructed from video tap casettes. And the NOrMal Distribution is spooky.

More on the Galton Board Math here.

Stranger Things Math: Eleven and the Galton Board

NOTE: Michael (above), who seems appropriately scary for this post, uses a commercial Galton Board.  It has one flaw. Many balls feed into the grid at once and this will change the pathways taken because the balls bump into one another. The best results come from dropping in the balls one at a time. If you had the patience to drop in 3,000 balls one at a time.