Archive for the ‘Parabolas’ Category

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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.

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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.

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COOL FOOTY MATHS: THE LONGEST KICK

May 25, 2019

Mathspig Football Maths 1

Mathspig football Maths 1a

Mathspig Football Maths 2aMathspig Football Maths 3Mathspig Football Maths 4

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The following maths is suitable for Year 9+

but can be presented to lower grades just to show

maths is cool!

Mathspig Football Maths 5Mathspig Football Maths 6bMathspig Football Maths 7

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6. If the pilot dies the control tower can talk you down.

January 3, 2019

So mathpigs, here is a small taste of what you would need to do to land a small aircraft in an emergency if the pilot is unconscious/dead.

A = Airspeed

Find airspeed indicator on instrument panel.

Instrument Panel Piper PA-28

Check speed.

Knots or mph or kph?

Avoid red zone. Too fast.

Knots outer scale. mph inner scale. Recommended velocity between blue & red.

B = Contact nearest air traffic controllers. 

1. Call MayDay MayDay MayDay

2.  Look for plane ID. It will be on instrument panel somewhere.

3. Check fuel.

On the Piper Cherokee there are 2 fuel tanks, R & L. Check both.

Check aircraft operating handbook to see fuel consumption and remaining time in air.

Quick calc.

 

C = Checklist

Follow Emergency Landing Checklist in aircraft operating handbook for Power OFF or Power ON landing.

Keep in mind, if your air speed is too low you can drop from air, but the higher the landing speed the bigger crash.

Crash energy increases with the square of speed. It’s a parabola!!!!!

The likelihood of a passenger with

NO flying experience landing a plane safely in an emergency is

very small.

The likelihood of a passenger with

NO MATHS skills landing a plane safely in an emergency is

ZERO.

 

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WINTER OLYMPICS: One Rule Aerial Skiers Cannot Break

February 10, 2018

Aerial skiers aim for height rather than length. Their aerial flight times are much smaller than ski jumpers so air resistance has minimal impact.

In fact, there is one law the aerial skiers cannot break. It is the law of gravity.

Here is an equation for  projectile motion from Wired magazine.

Screen grab from Wired Magazine

Screen grab from Wired Magazine

The equation for projectile motion also applies to Motorbike Jumps and Longbow Arrows.

Here is the x-y graph for different launch angles.

trajectory wired magazine

trajectory wired magazine

 

You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. More on centre of Gravity at The Great Back Pack Attack ie.

The centre of gravity of Aerial Skiers must follow a

parabolic curve.

Aerial Parabola final 2

Rocky Maloney Winter X Games Aspen

Rocky Maloney Winter X Games Aspen

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MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig …………………………………………………. with Kerry Cue

July 10, 2015

Mathspig m&m maths intro

Hellooooo My Little Sweeties,

There is so much maths you can do with m&ms, it’s hard to believe there is any other sort of maths.

You can study:

Countingtimes tables, set theory, Bar graphs, Fractions, % and decimalsMean, median, modeand parabolas (using a really cool peg-powered catapult).

But my favouritest ,developed by Patrick Len, is using m&ms to demonstrate half life in radioactive substances and therefore write an exponential equation.

m+m ACTIVITY:

m&ms  table

Throw a fixed no. m&ms on a table. Mathspig chose 128 m&ms for a very good reason. Eat the ones with the m showing. Count remainder. Throw again. Eat the ones with the m showing. Count remained. Keep doing this. You will end up with results like the following. (Not identical as chance is involved)

mathspig   m&m maths exponential fn  2

Wow! m&m’s and exponential equations. How yummy is that!!!!!!

More yummy maths:

m+m maths 1: find the volume using m+ms!

m+m maths 2: Guess, NO, calculate the number of m+ms in a jar!

m+m maths 3: how many m+ms will kill you?

m+m maths 4: How many m+ms will kill my dog?

m+m maths 5: how many m+ms will kill my cat?

m+m maths 6: How many m+ms will kill my pet rat?

m+ms maths 7: how many m+ms will kill my pet mouse?

Mmmmmmm! Can’t talk. Face full of chocolate.

Bye bye

Mathspig

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Outdoor Maths Adventures: Middle School

June 30, 2014

 

 

Outdoor maths middle school 1 mathspig

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!

 

Outdoor Maths Middle School 2 Mathspig

McGill Uni link here.

Outdoor Maths MIddle School 3 Mathspig

Don’t forget to throw in Mathspig’s lame protractor jokes.

Outdoor Maths Middle School 4 mathspig

You’ll find full calculations at the Maths is Fun blog.

Outdoor Maths Middle School 5 Mathspig

You’ll find more fab outdoor junior and middle school maths activities at the terrific Maths and Movement blog.

Outdoor Maths Middle school 6 Mathspig

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.

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2. One Rule Aerial Skiers Cannot Break

January 23, 2014

Aerial skiers aim for height rather than length. Their aerial flight times are much smaller than ski jumpers so air resistance has minimal impact.

In fact, there is one law the aerial skiers cannot break. It is the law of gravity.

Here is an equation for  projectile motion from Wired magazine.

Screen grab from Wired Magazine

Screen grab from Wired Magazine

Here is the x-y graph for different launch angles.

trajectory wired magazine

trajectory wired magazine

You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. MOre on centre of Gravity at The Great Back Pack Attack ie.

The centre of gravity of Aerial Skiers must follow a

parabolic curve.

Aerial Parabola final 1

 

Aerial Parabola final 2

 

Rocky Maloney Winter X Games Aspen

Rocky Maloney Winter X Games Aspen

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3 Ellipsoid Collipsoid

April 9, 2013

Maths-is-Awesome Activity

Ellipsoid Collipsoid

Skill: Geometry, scale, ratio, conic sections, ellipses, parabolas, hyperbolas and more.

Level: Senior School

102 Conic section 1901

Senior maths students are busy, mathspiggies. But insipration energises.

Mathspig was amaaaaaazed by these cardboard models were made by Martin Schilling because he made them in 1901. This was long before computers made the job easier. More info here.This is what a car looked like in 1901.

car 1901

If Martin Schilling could make these Conic Sections, so can any senior student. You will find Conic Section diagrams and equations here.

Could you do this mathspiggies?

Make a conic section in 3D?

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8 What the World Needs Now is More Parabolas

April 9, 2013

Maths-is-Awesome Activity

What the World Needs Now is More Parabolas

simpson's parabola

Skills: Graph, scale, measurement …. balancing that last cardboard section.

Level: Middle & Senior School

If you cannot make it to MOMaths Maths Museum in NY for a Mad Maths Monday, then you can run a Mad Maths Monday in your own class.

Build your own giant parabola out of cardboard.

We’re being awesome

We’re thinking big.

Make it big enough to arch over the front door of the school.

97 Mo Math Parabola

 

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Hunger Games : Survival Maths 2

April 11, 2012

Katniss’ weapon of choice is the bow and arrow.

Mathspig noticed in the film that Katniss was aiming the arrow directly at the target. This is a problem. Arrows drop under gravity. If Katniss aims directly at the target she will hit it below her aim point. To overcome this she must raise her arrow aim.

What angle should she choose?

Robin Hood used a long bow and in the film Robin Hood archers raised their bows at a very high angle to cover long distances. See the diagrams below from Robin Hood Give Us Your Best Shot

 According to The Flaming Arrow the speed of a modern arrow is 100 m/sec with a 65 lb draw weight.

Mathspig believes in using the SIMPLEST maths solution. In this case, very short arrow flight times are involved. 

So we will assume the arrow velocity (Va) equals horizontal vector speed (Vx). This is an approximation that makes the maths sweet. Such an approximation might work for the arow flight in the first diagram (above), but not in the second.

First, mathspigs, we’ll calculate the arrow flight time to a target 100m away and then we will calculate the distance the arrow would drop vertically in that time as this will tell us the point in the air where Katniss should aim.

 NB: An arrow will drop 4.9m over 100m to the target. In other words, Katniss would miss a human completely if she did not allow for gravity. Experienced archers automatically make this adjustment to their aim.

Gravity Eqn in the graph above comes from School for Champions