Archive for the ‘Middle School’ Category

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No Frills MATHs Skills for Parents 4: FRACTIONS for Beginners

June 6, 2022

Here is a post on Lego Fractions by New York Grade 3 teacher Alycia Zimmerman. Surprisingly I found this on an art website.

teaching-children-math-lego-blocks-alycia-zimmerman-thumb640

teaching-children-math-lego-blocks-alycia-zimmerman-8

Just play with the Lego blocks. Add and subtract … you can even multiply and divide.

Next time.

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No Frills MATHs SKILLS for Parents 3: Pre-Algebra

May 23, 2022

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FOR THE LONGEST KICK or THROW in Football you need this MATHS

April 19, 2022

Mathspig Football Maths 1

Mathspig football Maths 1a

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

………………………………………………

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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Killer Easter Egg Math

March 30, 2022

According to The Guinness Book of Records the largest chocolate Easter Egg went on display at Le Acciaierie Shopping Centre, in Cortenuova, Italy, on 2011.

 Egg Weight   = 7,200 kg  = 15,873 lbs

Height = 10 m =  34 ft

Circumference = 19.6 m = 64 ft

The sugar content for easter eggs is: 55-65% by weight

So we will assume the sugar content of the giant egg was in the middle:

60%

The weight of sugar in the giant egg equals:

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Draw a Cool Pattern with x2, x 3 & x4 Tables… but it is trickier than you think.

March 18, 2022

A COOL MIDDLE SCHOOL MATH EXERCISE

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.

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Dave Grohl and The Curious Nature of Drummers’ Brains

March 4, 2022

Live music is back.

The Foo Fighters play a stadium concert in Geelong TONIGHT. This is the first stadium concert in Australia in 2 years!!!!! Dave Grohl, the FF’s guitarist,  is a legend. He played drums for Nirvana and is considered by many to be the best drummer in the world. Meanwhile, Taylor Hawkins, the drummer for the Foo Fighters, is also considered one of the best rock drummers ever. 

In honour of this auspicious occasion and to work out what might be going on inside these rock legends’ heads, I’m reposting (below) the math article about drummers’ brains.

 

 

In a 2011 article in the New Yorker Burkhard Bilger wrote about neuroscientist David Eagleman and his research into time and the brain especially drummers’ brains.

Eagleman New Yorker

Some of the drummers he has interviewed and/or tested include William Champion of Cold Play, Brian Eno of Roxy Music and Larry Mullen, Jnr of U2.Roxy Music with Brian Eno

Eno, on keyboards (above) who was working on a U2 album,  talks about Mullen’s amazing timing.  They were using a click-track (computer generated beat) when mMullen complained he couldn’t drum to it. ENO adjusted the beat. Mullen was happy.

larry Mullen

ENO adjusted the beat by 6 milliseconds!!!!!!!!!

6 thousandths of a second or 0.006sec.

Cool Larry Mullen Jnr Drum solo

Tempo is measured in beats per minute or bpm. 

Drum Beats for different tracks:

Drum Beats

Here are some drum beats provided by Justin Alan Cox so you can get your timing right:

60 bpm

80 bpm

100 bpm

120 bpm

Drummer Maths:

How Cool a Drummer are you?

Pick a beat and see how accurate you can beat tempo. Time how long it takes you to beat out 60, 80, 100 or 120 drum beats using a pencil.  It should, obviously, take one minute if you are an ENO or a Mullens.

What was the difference in time in seconds?

But drummers like Eno, Grohl and Hawkins have other problems!!!!!

Bilger’s conclusion:

‘Like perfect pitch, which dooms the possessor to hear every false note and flat car horn, perfect timing may just makes a drummer more sensitive to the world’s arrhythmias and repeated patterns, Eagleman said—to the flicker of computer screens and fluorescent lights. Reality, stripped of an extra beat in which the brain orchestrates its signals, isn’t necessarily a livelier place. It’s just filled with badly dubbed television shows.’

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What’s the Maths Curriculum got to do with it? WHEN Maths is, like, soooo BORING!!!!!

February 22, 2022

Australia is reviewing its Maths Curriculum.

Sides are taken. Arguments are rife. See the excellent article by Donna LuCracking the formula: how should Australia be teaching maths under the national curriculum?, The Guardian,13 FEB, 2022)

Should teachers teach? Or students explore problems? (Called Cognitive Activation in academe!)

Why not, both? Then add outdoor maths (below) plus defronting the classroom sometimes and try some maths selfies for homework. More ideas here

It doesn’t matter what’s written in the curriculum, the biggest problem in maths for students is

BOREDOM.

Here, to tackle boredom are:

41 Maths things to do before you’re 12


Mathspig outdoor play quote

mathspig outdoor-play-app

A growing body of research shows us that outdoor play leads to better physical and mental health, has positive effects on cognitive function and learning, and reduces the incidence of behavioural problems.” Maria Zotti, Nature Play, SA.

Peter Dunstan, Principal Kilkenny PS, SA, writes in SAPPA magazine, Primary Focus, that outdoor play fosters “wonderment, independence and freedom” as well as “social skills, imagination, creativity and problem solving”.

Inspired by SAPPA and NaturePlay,  Mathspig has produced her own outdoorsy maths list:

 Mathspig 41 maths things 1Mathspig 41 maths things 2mathspig 41 maths things 3

Mathspig 41 maths things 4mathspig 41 maths things 5

References:

7. Robin Hood Give us your best shot.

9. You can measure the volume of your lungs by blowing one breath into a balloon and pushing it into a full bucket of water. Measure the overflow.

15: Outdoor Maths: Times Tables

21. Light intensity links. Here and here.

25.  Sound Volume Measurement

36. Killer heels that really kill.

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NATHAN CHEN wins Gold but Figure Skating Scores can be BAD MATH

February 10, 2022

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 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.

Tessa Virtue and Scott Moir(Above) GOLD Medal performance at Pyeongchang 2018 here.

Kailani Craine, Australia

figure skating score 9 judges nbclearn

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

Screen grab NBC Mathletes

……………………………………………………

Now consider the IDENTICAL SCORE CARDS

of Skater A & B:

figure skating score A

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

figure skating score B

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!!!!

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Winter Olympics 2022: Why do figure skaters spin so fast?

February 3, 2022

Here is the sensational pairs team from the 2018 Winter Olympics.

But why do ice skaters spin so fast?

Here is the math!

REASON  1:

Well, mathspiggies, the girl in this video is right. Angular momentum remains constant unless external forces are applied.

L = mvr

L = angular momentum

v = linear velocity

r = separation of object

Louisa Barama, USA

Louisa Barama, USA

Let’s have a look at this equation:

Figure skate maths1

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.

 Record spin :  vr = 308 RPM

Other spins include:

Mao Asada, Japan, triple Axel

Mao Asada, Japan, triple Axel

Triple Axel spin vr = 220 – 280 RPM

……………………………………………………………………………………………..

 Maximum Triple Axel spin vr = 402 RPM

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:

540 rpm.

…………………………………………………………………………………

Camel spin vr = 90 RPM

More info here.

Kim Yuna, South Korea

Kim Yuna, South Korea

…………………………………………….

REASON 2:

How can a figure skater move from

a camel spin into a very fast standing spin?

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, Camel Spin

Patrick Chan, Canada, Triple Axel

Patrick Chan, Canada, Triple Axel

figure skate maths 2

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:

Camel spin vr = 90 RPM

…………………………………………………………………………………

Triple Axel spin vr = 4 x 90 RPM = 360 RPM

That’s about right.

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WINTER OLYMPICS 2022: One Rule Aerial Skiers Cannot Break

February 1, 2022


The Parabola Must Be Obeyed!!!!

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