Archive for the ‘Year 7 mathspig’ Category

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Razzle-Dazzle them with Middle School Math that is, like, WOW!

September 4, 2022

 

10 Quick & Quirky Ways to Make the Math 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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When Area Calcs mean Big Bucks

August 25, 2022

Bank Notes returned to RBA data.

RBA grids for damaged notes.

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Stranger Things Math: Eleven and the Galton Board

July 3, 2022

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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How BIG is Australia?

June 19, 2022

There are 26 million people in Australia.

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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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Mona Chalabi’s Data Art: Maths never looked so good even the dick graphs

April 10, 2022

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.

1. Mona Chalabi on Jeff Bezos’ Wealth. 

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.

2. Mona Chalabi CAFFEINE DATA ON INSTAGRAM

Mona also includes relevant the data in her posts. eg.

 

3.  Mona Chalabi on OUR MOST COMMON FEARS on INSTAGRAM

4. Mona Chalabi on Earth’s Orbit on INSTAGRAM

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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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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

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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

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=  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

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=  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

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 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.

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Camel spin vr = 90 RPM

More info here.

Kim Yuna, South Korea

Kim Yuna, South Korea

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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

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

That’s about right.

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WINTER OLYMPICS: How ski Jumpers Use Math to Increase their Jump Length

February 3, 2022


While air resistance has little impact on aerial skiers it is a significant factor used by ski jumpers to increase their jump distance.

The significant maths for ski jumpers is therefore X-section area.

Here is the jump at Pyeong Chang, 2018. Just imagine going down that at top speed!!!

              A ski jumper is set to jump in Pyeongchang.

                   Casey Larson USA Pyeong chang 2018

Ski jumpers increase their speed going down the ramp by reducing their X-section area:

Lindsey Van, USA, practicing in a wind tunnel

           Lindsey Van, USA, practicing in a wind tunnel

Once they leave the ramp, ski jumpers try to increase their X-section area like Ski Divers to slow their vertical fall. But they have to land safely so they keep their skis at a minimum  angle.

Abby Hughes, USA, practicing in a wind tunnel.

Abby Hughes, USA, practicing in a wind tunnel.

Abby Hughes, USA, in the air

          Abby Hughes, USA, in the air

Here are the X-section areas for Abby Hughes*:

Abby Hughes X-section

Here is the formula for Air Resistance of Drag:

D = ½CApv2

Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.

A is the X-section Area,

p is the density of the air and

v the velocity of the object.

More here.

As Abby Hughes has tripled her X-section area in the air, she will have tripled the vertical drag during her jump. This will slow here decent.

*Mathspig calculated the X-section area by the old fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Huges so that her head was the same size in both pictures.