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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!
Archive for the ‘geometry’ Category
Toilet Paper FUN FACTS Maths
June 1, 2021
Mathspig is in Melbourne, Australia. We’re in Lockdown. AGAIN!
And toilet paper has disappeared off the supermarket shelves. AGAIN.
So today we are doing maths based entirely on toilet paper using information from the Toilet Paper Fun Facts website. Yes! It exists here.
Toilet Paper Fun Facts Website
Protractor Wind Speed Calculator
POP UP ANS Q 1 & 2 Yr 7&8 Toilet Paper fun facts
Pythagoras Equation Diagram here
Here is the Sine Rule (Watch 1.5 mins)
Check sine curve here:
Listen to sine curve here:
Real World Maths: Gotye and Some $$ that he got to know
November 12, 2020
Melbourne singer, songwriter, and geometrically inclined performer Gotye performing with Kimbra won 3 Grammy Awards for his song Somebody that I used to Know in 2013.
The Gotye youtube clip has had 1,535,344,012 or 1.5 Billion hits since it was first uploaded 5th July 2011.
Mini Rates Exercise:
In 111 months Somebody that I used to know has scored 1.5 Billion hits. How many hits a. per month, b. per day, c. per minute? (Round off numbers)
Ans: a. 13.5 Million per month
b. 450,000 per day (Assuming 30 days per month)
c. 37,500 per hour and 625 per minute (for over 9 years non stop!)
Estimate of Youtube Earnings for this Song:
The Influencer Marketing Hub puts the rates an advertiser pays between $0.10 to $0.30 per view on Youtube, but averages out at $0.18 per view. Using the lower rate, how much has this song earnt in just over 7 years?
Earnings = 0.10 x 1.5 x 109 = 1.5 x 108 = $150,000,000 = $150 million*
*This calculation is based on a click per view of the video. Gotye will not receive anything like $150M, however, because advertisers pay per click on their ad.
According to the Influencer Marketing Hub again ‘on average, the YouTube channel can receive $18 per 1,000 ad views. This equates to $3 – $5 per 1000 video views.’ Again, using the lower rate:
Video Hits =1.5 x 109
Divide by 1,000 = 1.5 x 109 ÷103 = 1.5 x 106
$3.00 per 1,000 video clicks earnings = 3.00 x 1.5 x 106 = 4.5 x 106
Realistic Earnings = 4.5 x 106 = $4,500,000 = $4.5 million
A Geometric Parody:
Here is Mathspig’s take on the song:
Somebody that I used to Know:
It’ll either help students do their exercises or work like Clockwork Orange and have them running screaming out of the room when they hear the first few notes.
Real World Maths: Geometry, Heavy metal + Headbangers Heads
October 4, 2020
Are Headbangers Neck Wreckers?……..
Check out the Maths!
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.
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.
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:
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Just to show that there is something spookily primitive about headbanging here is Headbanger Baby:
Why do so many students HATE MATH? … um, you know, BOREDOM
September 28, 2019According to ‘Bored Out of Their Minds’, an article by ZACHARY JASON in The Harvard Ed Magazine (2017):
Boredom accounts for nearly a third of the variation in student achievement.
Half of high school dropouts cite boredom as their primary motivator for leaving.
Boredom begins for Math students at Grade 6 when students (Common Core Standards, USA) tackle more abstract concepts such as linear eqns, exponents, probability, geometry and so on.
Math curriculums in the USA, UK & Australia all demand students solve REAL LIFE problems. Too often these are of the type:
Q. Ronaldo has tethered his goat on a 12ft rein in the corner of a 20ft square field. What area can the goat graze?
THE ANS: Who cares?
Simple.
Ask students maths questions which have answers they want to know.
Students really don’t care about Ronaldo’s goat, but here are some questions which involve intriguing answers they might want to work out. And many of these questions involve funny or age-relevant activities, which also helps engagement.
1. Mean, Median STATS: Mean, Median and Coffee: Busting an Urban Myth
2. Parabolas: Can you beat the 12-14 yo World Record for a Watermelon Pip spit?
3. Geometry: Build a Freestanding Tower
Rates (Speed) & Units:
4a. The Terrifying Math of Running from a bear
5. Decimals, %, Volume: What Volume of alcohol is lethal for teens?
6. Decimals, Algebra, Weight Units
How much blood can a kid lose and survive?
Graph Hunger Game Math
7. GEOMETRY. Angles
Any Topic:
8. Middle School Math Photo Scavenger Hunt
Space Math Song here
EVEN TEACHERS GET BORED!!!
The average time it takes an audience at a conference to switch off is 11 minutes. Keep in mind this audience is, at least, being paid to be bored witless.
Outdoor Math Adventures: Grade 3 – 5
September 12, 2019It’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.
1. Movie Stunt Math: Rolling a CAR
October 29, 2018“With enough stupidity you can get any car to roll over” (MSN AUTO)
What stuntmen and women need is maths!
Maths is essential to the process, from calculating speeds and braking distances to looking at the ratio of the amount of film shot to the length of time of the end sequence. The stunt and crash is outlined, and the co-ordinator explains how he must calculate speeds and stopping distances carefully.
So you want to be a stuntman?
First think of the pain.
Mark Eiden, 52, a professional stuntman (pictured) who is not only afraid of heights, but was once told he likely wouldn’t walk again. Eiden’s had surgery on both arms and shoulders, five knee surgeries, six nasal reconstructions, foot and hand surgery and a facial cast. He fell off the top of a stunt car at 40 mph when the tyre blew. He gaffer taped his ear and continued, despite severe concussion. Northern Express Michigan
If you still want to be a stuntman do the Maths:
Rolling a Car:
You can use quick handbrake turn, speed around a corner, fishtail into the curb or some other lunatic thing. The most controlled way to roll a car is to use a ramp.
These ramps often have a kicker at the end to add extra lift. Ramp calculations can be complicated, but the simplest way to look at the maths is to determine the angle a car will roll ie. When the Centre of Gravity moves over the base.
Centre of Gravity vs Base Width
The distance between the front wheels in cars is often called the track width.
Table from Accident Reconstruction Website
So the Lamobgini Diablo is very hard to roll (build a higher ramp) and it therefore beats the SUV for stability every time.
Balancing on 2 Wheels
A more skilled stunt involves driving a car on two wheels. A very skilled stunt driver can lift the car onto wheels by snaking the car back and forth across the road until it balances on 2 wheels.
From the Centre of Gravity vs Base angles above you can see that the SUV is the easiest car to balance of 2 wheels.
But there is nothing quite as crazy as this SUV stunt:
Saudis changing car tyres, just insane.
View full video here.
Safe Driving Info here
3. Movie Stunt MATH: The Motorbike Jump
October 23, 2018Star Stuntman
Star Stuntman Monte Perin (pictured) has involved many films, including “Spider-Man,” “Star Trek, “Indiana Jones and the Kingdom of the Crystal Skull” and portraying Arnold Schwarzenegger’s stunt double in “Terminator 3: Rise of the Machines.”
Perhaps his most difficult stunt was landing his Harley in an open boxcar of a moving train for Disney’s 2008 Adam Sandler movie “Bedtime Stories”. In a career of over 25 years Perin has broken “almost everything” including both his arms, legs, knees, feet, ankles, several ribs, his back and his pelvis. See Confessions of a stuntman
Veteran stuntman Evel Knievel (1938 – 2007) was the pioneer of many stunt jumps. Here he is jumping 10 cars and 3 vans in 1973.
His injuries are legendary:
More Evel Knievel
Ramp Design
The angle of the kicker in ramp design can vary from 100 – 700 (See below)
Moto-X Ramp Jump Maths
The Problem?
If the ramp angle is too high, the stunt jumper also goes high, but doesn’t travel very far.
If the ramp angle is too low, the stunt jumper doesn’t stay in the air for very long and therefore doesn’t travel far. (see below0
The stunt jumper wants the OPTIMUM RAMP ANGLE.
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METHOD 1: TRIGONOMETRY (cos we can)
As any bike nut knows increasing speed at ake off will increase jump distance.
Here is a graph from final gear for speed vs angle to jump 90m.
OPTIMISING RAMP ANGLE
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METHOD 2: MORE TRIGONOMETRY
METHOD 1 is approximate (See STEP 1 & STEP 2 above), but as METHOD 2 produces the same ans (See above), it is very useful.
You will find a thoroughly detailed calc for STUNT JUMP MATHS here:
And everything you ever wanted to know about PHYSICS OF STUNT JUMPS here.
2. Middle School Madness: BIG MATHS
June 1, 2017
Mathspig just loves this Fluid Geometry Mural by artist Clint Fulkerson. Here is a Speed Clip of Flulkerson at the University of Maine Art Gallery 2012.
Mathspig went crazy trying to produce her own Fluid Geometry Mural. These guys are artists. But your middle school maths class can use a simple method (See GIF below) and make a fab mural on a white/black board or down a school hallway. This is a great end of year/semester/pre-holidays project.
The reason for tackling such a project is to engage students, who are otherwise not interested in maths as well as do some whole school PR for maths. The mural WILL be noticed. And it makes maths look COOL.
You will find more interesting Fluid Geometry works by Clint Fulkerson here.
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