Archive for the ‘decimals’ Category

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ZOOM Math: 3D Animation …. USA units

July 4, 2020

Middle school students around the world have been learning maths via Zoom. ZOOM needs computers & WIFI. There are so many resources online but I cannot over-emphasise the amazing 3D skills developed just by playing with objects in TINKERCAD(See logo above. More info below) Anyone who wants to work developing video games or animated films has to understand the logic and maths of 3D. Read on. And it is more challenging than you might think.

1. Storyboard Sketches

The Pixar film, Finding Dory, began as storyboard sketches. There were 103,000 drawn for the film. The sketches are placed side-by-side in sequence in order to convey scenes and deliver a rough sense of how the story unfolds.

How many 64-page Exercise books would the storyboard take?

Only one side of the page of the 64-page exercise book would be used for storyboarding.

No. exercise books = 102,000/32  =  3,187.5

If put into flip Book form the storyboard sketches would produce a ‘rough’ version of the film.

Superman Vs Goku

………………………………………..

2. Ratio

If you are making a film about, say, Godzilla, you want him to be big. VERY BIG. But he has to share a screen with human characters.

If Godzilla is too big all the humans look like ants.

If he is too small … he looks like a toy TRex.

The Monster Maths:

Height: 355ft  Godzilla’s towering height in the 2014 film—the tallest onscreen incarnation ever

Tail: 550ft 4in Total length of Godzilla’s spiked tail.

Volume: 90,000 tons Godzilla’s volume if filled with water

Teeth: 3.51 ft Length from the root to the tips of Godzilla’s canine teeth

Teeth: 60 Teeth in Godzilla’s mouth

Roar: 3 miles. Approximate distance Godzilla’s roar reverberates. (100,000W Power of the 12-foot-high, 18-foot-wide speaker array from which the sound designers blasted Godzilla’s roar to record the sound in a “real world” context)

Feet: 58ft  Total width of Godzilla’s feet across the widest point

Feet: 60ft  Length of Godzilla’s footprint from toe to heel

You vs Godzilla

The average height for 14-year-old boys in the U.S. is 64.5 inches or 5 feet 4½ inches.

For 14-year-old girls in the U.S. the average height is 62.5 inches or 5 feet 2½ inches.

Godzilla = 355ft

14 yo =  5’ 3”

Height:

355/5.25= 67.6 = 68

To make a 3D graph like this see below.

Footprint

You vs Godzilla’s Footprint

60/5.25 =  11.4

Teeth

You vs Godzilla’s Tooth

 3.5/5.25 = 0.7

………………………………………………

3. 3D Modeling: Polygon Count

3D modeling can be approached in several ways. There is a good explanation here.

One method is to use a 3D scanner to produce a 3D mesh.

Godzilla model under construction

Digital Godzilla as 3D mesh

The mesh consists of polygons. You’ll find everything you want to know about polygons here.

The greater the no. of polygons the better the resolution in a 3D mesh, the better the resolution of the character or object as more shading and texture variation can be added.

So the POLYGON COUNT or POLY COUNT is a measure of the quality of an image.

Here are some POLY COUNTS:

Godzilla

500,000 polygons.

It took the 4 CGI artists 6 months to fully nail the texture of Godzilla’s scales. (See above)

Elysium

Just the space station ran close to 3 trillion polygons.

Transformers 2

Devastator had 13 million polygons

Clash of the Titans

The Kraken had 7 million Polygons.

Avatar

Apart from some bluescreen shots of live-action actors in cockpits, it’s all CG: gunships, missiles, smoke trails, water, fire, an army of photorealistic virtual characters, and a giant tree made of 20 million polygons with 1.2 million leaves.

More here.

Lord of the Rings – The Two Towers (2002)

(See below)

The Gollum head model consisted of just over 2,600 polygons, which were mostly quads.

More here.

Film Animation vs Game Animation

The POLY COUNT is always greater in animated movies than in video games mainly because a higher poly count takes longer and costs more. A higher resolution is needed in a movie as it is shown on a much bigger screen.

Gollum: Game vs Film 3D model

Here are some POLY COUNTS for some popular games:

The Amazing Spiderman

Spiderman – 11,652

Assassin’s Creed 3

Benjamin Franklin – 17,744

Charles Lee – 25,994

Connor Kenway – 28,501

Desmond – 14,934

Haytham Kenya – 19,985

Batman: Arkham City

Batman: Film Version

Batman: Game Model

Batman Beyond suit – 13,050

Harley Quinn – 17,731

Harley Quinn (DLC) – 19,110

Poison Ivy – 15,977

Call of Duty: Black Ops

Frank Woods (full gear) – 19,777

Crysis 2 (console)

Nano suit – 19,073

Multiplayer suit – 27,414

………………….

FREE 3D MODELING FOR MIDDLE SCHOOL STUDENTS

TINKERCAD is the free online resource that allows students to create their own 3D graphs – like Godzilla vs You (above) or 3D images that can be used for 3D printing. Play with the program. Mathspig had a little play and produced the genetically challenged chicken (below).

Tinkercad Dashboard

Find here.

Drag and drop shapes.

More here.

Play with shape dimensions.

More here.

Create figures for 3D printer.

MATHSPIG REPORT CARD: More playing with program needed!!!

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Why do so many students HATE MATH? … um, you know, BOREDOM

September 28, 2019

According 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

USA Units

METRIC UNITS

4b. How old is your hair?

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?

USA UNITS

Metric Units

Graph Hunger Game Math

7. GEOMETRY. Angles

Why killer heels can kill!

Any Topic:

8. Middle School Math Photo Scavenger Hunt

9. Write Your Own Math Song

Space Math Song here

10. Make a Math Poster

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.

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Math Joke 3:How long will it take you to grow a really bad 70s-styles haircut?

February 18, 2019

1 Mathspig 1980s hair

2 Hair follicle

The follicle diagram (above) came from bgoffforensics blog. More on hair growth rates here.

QUESTION 1:

3 Mathspig how old is your hair!!!!

How long to grow that really bad 70s style hair cut?

The length of Fabio’s hair (below) is approx 50cm.

t = 50/1.25 months

t=40 months          

t = 3 Years 4 months!!!!

Is it worth the effort? Ha!

4 Mathspig 1970s celebrity hair

QUESTION 2: 5 MAthspig world's Longest Dreads

The growth rates of 1.25 cm/month or 0.5 inches/month are rounded off. Calculations using these growth rates will produce different answers for very large numbers (as above). Read more about the above story in the Daily Mail, UK here. By the way, Asha has been growing her hair for 25 years. Her hair weighs 3 stone or 19 kg. You can find more hair records including the World’s longest ear hair here.

QUESTION 3:

6 Mathspig Natasha's hair

Natasha lives in Rio de Janeiro, Brazil. Read more about Natasha in the Daily Mail here. Once again Mathspig has rounded off the length of hair for easy calculation. The Daily Mail puts Natasha’s ‘mane’ at 5 feet 2 inches or 157 cm. This is the length of hair to be cut off. So Mathspig adjusted the length to 180cm or the approx length of her longest hair.

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1. You can duck a bullet

January 15, 2019

You will find all the ballistics stats you need here:

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Winter Olympics: Bad Math of Figure Skating Scores

February 22, 2018

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 win GOLD at Pyeong Chang 2018

                                   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: Beaten by 0.001 seconds

February 14, 2018

 

In 2014 Winter Olympics Annette Gerristen (below) lost the Gold Medal in the 1000 m Women’s speed skate competition by 0.02 seconds.

Annette Gerritsen fromthe Netherlands

Annette Gerritsen fromthe Netherlands

What are the speed skating times for women?

Women’s Speed Skating Calulations:

Here are the speed calcs for Yara Van Kerkhof of the Netherlands in the 2018 Winter Olympics:

If Yara lost the Gold Medal by 0.02 secs (2 hundredths of a second) what would the distance be between the Gold and Silver place getters?

When 1st and 2nd place are separated by 0.02 seconds, they are travelling at almost the same speed. So the second place contestant is:

23.8 cm behind the Gold Medalist

The 2018 Olympic Gold Medalist in the 500m Women’s Speed Skating was Arianna Fontana.

Italy’s Arianna Fontana wins the 500 m Speed Skating 2018 Olympic Gold Medal in 42.569 seconds ahead of Yara van Kerkhof of the Netherlands and Kim Boutin of Canada. 

Men’s Speed Skating:

At longer distances the men’s speed skating speed is similar to the women’s speed above.

If you lose by  0.001 secs…………

Apollo Ono (below) competed in the 1500m men’s speed skating. He has won 8 Olympic Medals.

If a speed skater lost the Gold Medal by 0.001 seconds, the smallest measured time segment at the Olympics, they would be:

1.19 cm

behind the winner. That is less than the length of a small fingernail.

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Cars in the USA are how old? Really? No way! Look at the World and Do the Math

February 3, 2018

 

The average age of the 60 years of FORD vehicles here is 30 years. MODEL NAMES at end of post.

I did this to show that averages can tell us a lot or, in this case, not very much.

Here are some averages that tell us a lot about different countries and their love of cars!

The average age of vehicles in USA is a record-high of 11.6 years. More here.

Car ownership rates data here.

This is the average vehicle age, which includes vans and utes. Almost 1,000,00 vehicles were scrapped in 2015-16. More than 30% of vehicles are less than five years old. Data here.

In 2016, the average age of vehicles on Canadian roads was 9.66 years. Data here.

The average age of cars in UK is 7.7 yrs. some interesting stats here.

The average age of vehicles in New Zealand is 14.3 years. The average age of trucks and buses is over 17 years. Data here.

Cars in the European Union are on average 10.7 years old. Data here.

The average age of vehicles in Poland is 17.2 years. Daata here.

The average age of vehicles in Romania is 15.3 years. Data here.

The average age of vehicles in Greece is 13.5 years. Data here.

Ethiopia has the lowest car ownership in the world with 2 per 1,000 inhabitants in 2014.

The average age of Ethiopia’s fleet is 15-20 years. Best guess! Data here.

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1. Maths is BORING!

December 9, 2017

Middle School Maths that is AMAZING

psst! That means it’s not boooorrrrinng!

NEW POSTS!

1a. The WORLD POPULATION as ONE BIG CROWD … METRIC

1b. The WORLD POPULATION as ONE BIG CROWD … USA Units

2a. If all the cars in the world were parked together what area would they cover? Metric Units

2b. If all the cars in the world were parked together what area would they cover? USA UNITS

3. If you put the population of the world into AUSTRALIA what area in m2 would we get each?

Meanwhile this Mathspig blog is full of AMAZING middle school maths such as:

KARATE MATHS

HOW MUCH BLOOD CAN YOU LOSE AND SURVIVE?

WHAT VOL OF ALCOHOL IS LETHAL FOR TEENS?

THE TERRIFYING MATH OF RUNNING FROM A BEAR USA UNITS

THE TERRIFYING MATHS OF RUNNING FROM A BEAR METRIC UNITS

PARABOLAS AND THE ART OF SPIITING WATERMELON PIPS

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Why maths is NOT boring!!!!

November 28, 2017

 

Middle School Maths that is AMAZING

psst! That means it’s not boooorrrrinng!

NEW POSTS!

1a. The WORLD POPULATION as ONE BIG CROWD … METRIC

1b. The WORLD POPULATION as ONE BIG CROWD … USA Units

2a. If all the cars in the world were parked together what area would they cover? Metric Units

2b. If all the cars in the world were parked together what area would they cover? USA UNITS

3. If you put the population of the world into AUSTRALIA what area in m2 would we get each?

Meanwhile this Mathspig blog is full of AMAZING middle school maths such as:

KARATE MATHS

HOW MUCH BLOOD CAN YOU LOSE AND SURVIVE?

WHAT VOL OF ALCOHOL IS LETHAL FOR TEENS?

THE TERRIFYING MATH OF RUNNING FROM A BEAR USA UNITS

THE TERRIFYING MATHS OF RUNNING FROM A BEAR METRIC UNITS

PARABOLAS AND THE ART OF SPITING WATERMELON PIPS

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Why Maths is NOT BORING!

November 13, 2017

The Amazing Answer is here.

Mathspig is full of AMAZING middle school maths such as:

KARATE MATHS

HOW MUCH BLOOD CAN YOU LOSE AND SURVIVE?

WHAT VOL OF ALCOHOL IS LETHAL FOR TEENS?

THE TERRIFYING MATH OF RUNNING FROM A BEAR USA UNITS

THE TERRIFYING MATHS OF RUNNING FROM A BEAR METRIC UNITS

PARABOLAS AND THE ART OF SPITTING WATERMELON PIPS