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.
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.
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.”
Nathan Chen’s Winning Performance on You tube HERE.
According to the fabNBC 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.
Tessa Virtue and Scott Moir(Above) GOLD Medal performance at Pyeongchang 2018 here.
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
……………………………………………………
Now consider the IDENTICAL SCORE CARDS
of Skater A & B:
Skater A:
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)
7.00 + 7.00 + 7.00 + 6.75 + 7.00
……………………………………..
= 34.75/ 5 = 6.95
Skater B:
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:
7.00 + 7.25 + 7.00 + 7.00 + 7.00
……………………………………..
= 35.25/ 5 = 7.05
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!!!!
“Eating even the moderate amounts of red and processed meat sanctioned by government guidelines increases the likelihood of developing bowel cancer” according to the above article in The Guardian, UK.
The sample size was 500,000. That’s good. It is a self-selecting sample. That’s not good. They could all be health fanatics. But here is the kicker:
“The researchers found those who ate the most and least red and processed meat tended to exaggerate their consumption or lack thereof.”
That’s a shock. People lie or exaggerate. Even the researchers then suggest – despite the screaming headline – that you don’t change your diet.
Although, looking at the plate above … I would!
Real Men Eat Red Meat and Die … Sometime!
According to this headline in THE AUSTRALIAN 25th, March 2009 meat eaters are at risk of dying of cancer. The study published in Archives of Internal Medicine involved half a million people over 10 years. So far so good. That is a good sample size. The sample consisted of people aged 50 to 71 years at baseline or, obviously, after 10 years 60 to 81years!!!! So some deaths would be expected. Nevertheless, the article states:
“Men whose red meat intake put them in the top 20 percent consumption band were 22 percent more likely to die of cancer in the 10 years of the study, compared to men whose intake was in the lowest 20 percent. For women, there was a 20 percent increase in risk.”
Here is the problem. Firstly and I quote from the original study: “Meat intake was estimatedfrom a food frequency questionnaire administered at baseline.’ So they asked people once what their eating habits were then assumed they continued for the next 10 YEARS??? How likely are your eating habits to change in 10 years???
Secondly, and this was mentioned in the article without explaining the maths, big meat eaters tend also to be big drinkers, smokers, obese and the rest. This study has tried to separate out meat eating from other unhealthy lifestyle choices using the Cox Regression. Mathematical wizardry has produced these numbers but they don’t mean much.
If the study used a control group of drinking, smoking, obese vegans then compared mortality rates over 10 years that would be interesting. But where do you find half a million of them????????
Finally, the study concluded ‘Red and processed meat intakes were associatedwith modest increases in total mortality, cancer mortality,and cardiovascular disease mortality.’ Not the stuff of headlines at all!!!!!!!
Requirements: A coin for each student & smart board or data projector.
First ask your students to toss a coin 10 times each.
Ask each student how many heads in a row they threw.
Now ask students ‘Do you think it is possible to throw 10 heads in a row?
It can be done. Here is how you do it.
Derren Brown is a UK mentalist, magician, hypnotist and maths guru. He’s awesome. He shows audiences how a lack of understanding maths, especially probability, leads to misinterpreting the facts.
This exercise works best if for homework the middle school students count the digits in their own cell phone, passport, bill code or some other number. They don’t have to show the passport or bill. They just have to count the digits.
According to the fabNBC 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.
Tessa Virtue and Scott Moir win GOLD at Pyeong Chang 2018
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
……………………………………………………
Now consider the IDENTICAL SCORE CARDS
of Skater A & B:
Skater A:
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)
7.00 + 7.00 + 7.00 + 6.75 + 7.00
……………………………………..
= 34.75/ 5 = 6.95
Skater B:
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:
7.00 + 7.25 + 7.00 + 7.00 + 7.00
……………………………………..
= 35.25/ 5 = 7.05
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!!!!
You can find the free pdf worksheet (included below) here.
Other fun middle school math(s) worksheets in the Hot Heels series at TpT include
Unit Rates, Angles, Ratios and Algebra.
There is a lot of maths and science behind coffee sloshing in a coffee mug. ‘The human stride has almost exactly the right frequency to drive the natural oscillations of coffee’ explains fluid physicists at the University of California at Santa Barbara. You will find their full explanation here.
Derren Brown is a UK mentalist, magician, hypnotist and maths guru. He’s awesome. He shows audiences how a lack of understanding maths, especially probability, leads to misinterpreting the facts.
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