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.
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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.
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.
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.
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.
Try it first. You might be surprised.
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.
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.
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.
Requirements: pipe cleaners or stick cube and detergent and a bucket with water.
All ages love this exercise.
How? Read the link here.
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.
Requirements: A product with a barcode.
Read this link and check the barcode.
Requirements: Box of matches, an accomplice.
Read this link and amaze the class.
Requirements: 2 large coins. 20c in Australia, Half-$ USA or 25p UK.
Read this link first. It’s so counterintuitive.
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.
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.
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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!
Mona Chalabi is a British-Iraqi data journalist and illustrator based in London. She specialises in all things data.
An outstanding communicator her work proves that MATH can be artistic and ART can be data-based. She is an honorary fellow of the British Science Association.
Mona Chalabi Self Portrait on INSTAGRAM
WARNING: Mona Chalabi INSTAGRAM account is politically graphic and contains sexually explicit graphs. Yeah! Dick graphs etc. The Instagram links in this post connect with individual illustrations.
I found Mona Chalabi through her illustrated New York Times article (7 April, 2022) 9 WAYS TO IMAGINE JEFF BEZOS’ WEALTH.
So Jeff Bezos personal wealth is $172 Billion (US$) Her Toblerone Block vs Mt Everest comparison was in this article.
NOTE: Median wealth is the mid-point wealth ie. 50% of Americans have more wealth. 50% of Americans have less wealth.
Mona also includes relevant the data in her posts. eg.
This idea comes from Burkard and Giuseppe @ the fabulous MATHOLOGER channel. Students can make a pattern called a cardioid that pops up all over math according to Burkard.
Follow these steps. There is a pdf file below the first diagram for printing exercise sheets.
And then watch the MATHOLOGER video for a really interesting explanation.
x2 Tables on a Circle pdf file for printing
This circle graph blank could also be used for x3 and x4 tables, which produce totally different yet equally amazing patterns.
Halfway there, now it gets tricky. +52 to each point on the circle and keep multiplying by 2.
ie. 27 x 2 = 54, 28 x 2 = 56 and so on.
so 0 = 52, 1 = 53, 2 = 54, 3 = 55, 4 = 56 etc
This shape is called a CARTIOID.
Nathan Chen, 22, USA, wins GOLD in the Men’s Figure skating with 5 brilliant, soaring quadruple jumps executed to perfection to Elton John’s “Goodbye Yellow Brick Road” and “Rocket Man.”
According to the fab NBC video, Mathletes, nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.
Kailani Craine, Australia
This is a typical figure skating score card for one competitor.
The final score, however, is based on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.
Screen grab NBC Mathletes
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.
The average:
Same score cards but Skater B gets a higher average score than Skater A.
Skater A is, in fact, beaten by a random number selector!!!!
Here is the sensational pairs team from the 2018 Winter Olympics.
But why do ice skaters spin so fast?
Here is the math!
Well, mathspiggies, the girl in this video is right. Angular momentum remains constant unless external forces are applied.
L = angular momentum
v = linear velocity
r = separation of object
Louisa Barama, USA
Let’s have a look at this equation:
The fastest spin on ice skates was achieved by Natalia Kanounnikova (Russia) with a maximum rotational velocity of 308 RPM (rotations per minute) at Rockefeller Centre Ice Rink, New York, USA on 27 March 2006. See Guinness Book of Records.
Other spins include:
Mao Asada, Japan, triple Axel
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Skaters can spin faster during a triple axel jump because there is no friction from the ice slowing their spin.
To complete a quad axel, it’s estimated that the skater would have to rotate in the air at:
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More info here.
Kim Yuna, South Korea
Now, mathspiggies, you must separate Linear Velocity (v1 ) from Angular Velocity (vr ). Linear Velocity is measured in m/sec ie. it is the speed of, say, a skaters foot around the circle. Angular Velocity is measured in either RPM (Revolutions Per Minute) or degrees or Radians per minute. Ie. It is the rate of spin. We can’t judge how many m/sec a skaters foot is moving in a circle. We can only see how fast they spin. In other words, we see their Angular Velocity. When a skaters foot is in the Camel position that foot travels in a very big circle.
But when that same foot is in a Triple Axel postion it moves in a very, very small circle.
Patrick Chan, Canada, Camel Spin
Patrick Chan, Canada, Triple Axel
By halving the radius, firstly, a skater’s Linear Velocity doubles due to the conservation of angular momentum.
Then, secondly, by halving the radius the circumference of the circle moved by , say, the skaters foot is halved.
Overall, by doubling the velocity around the circle and halving the circumference a skater increases their rotational velocity by a factor of 4.
Look at the numbers:
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That’s about right.
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