Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology

Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.

Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology

Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.

This is the best Middle School Probability outdoor exercise EVER!

Equipment:

1 coin per student.

Instructions:

In the schoolyard, students move back and forward with the flip of a coin. Must be a good flip. This exercise works best with a grid drawn on the schoolyard in chalk, perhaps. (See pic below) If possible film the exercise from above.

Now here are lots of people doing this 2D random Walk on Wall St. The results are totally amazing.

…………………………………………………………

Watch for the Bell Curve. It’s AWESOME.

This video was made by The National Museum of Mathematics NY.

The random walk is a way to create a path based on random decisions at junctions. If you’ve played a procedurally generated video game, including major examples like Minecraft and Stardew Valley as well as cult favorites like Spelunky and Dwarf Fortress, you’ve encountered a random walk in the form of a dungeon or terrain made this way in the programming. More @ Popular Mechanics

2D Random Walk math helps game programmers to plot interesting pathways in games like Minecraft Dungeons. (above)

Plot a 2D Random Walk

There are 4 choices:

UP, DOWN, LEFT, RIGHT

Note: This 2D random walk is limited to a 1-unit step length and right angles turns.

Set the Random Number Spinnerhereto 4 and generate 8 random moves of 1 unit and plot the moves on the worksheet(below).

These 2D Random Walks do not look like the path taken by a drunk mathematician.

Drunken Mathematician

This looks like a drunken mathematician and the 2D Random Walk for a drunk mathematician would look like pathways shown below with variable step lengths and turns from 0-360°.

All Random Walks can be mathematically modeled. eg. Go to MIT here. This math can be quite complicated (See here.) But all we want to do is plot the 2D Random Walk to see random numbers in action.

Choco Yum Yum! Mathspig lervs chocolate. But did you know chocolate can kill you?

Chocolate contains a chemical called Theobromine. This alkaloid ( other alkaloids include cocaine, nicotine, caffeine, and strychnine) can kill humans. More infoWired Magazine.

How much chocolate is too much?

Firstly, the darker the chocolate the more Theobromine it contains.

According toAbout Chemistrybased on the highest possible toxicity:

* Vetmedicine: Cooking chocolate contains 8-10 times the Theobromine in Milk Chocolate.

According toWiredlarge doses of theobromine may cause “nausea and anorexia ….. sweating, trembling and severe headache.”

The Royal Society of Chemistrynotes that chocolate does not contain caffeine, but theobromine induces similar symptoms.

LD50 for the lethal dose for 50% of the population for Theobromine is:

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 inTINKERCAD. (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.

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).

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 inTINKERCAD. (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: 108.2m Godzilla’s towering height in the 2014 film—the tallest onscreen incarnation ever

Tail: 167.74m Total length of Godzilla’s spiked tail

Volume: 89,724 m^{3} Godzilla’s total volume in the 2014 film.

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

Teeth: 1.07mLength from the root to the tips of Godzilla’s canine teeth

Teeth: 60 Teeth in Godzilla’s mouth

Roar: 4.83km Approximate distance Godzilla’s roar reverberates. (100,000W Power of the 3.7m-high, 5.5m-wide speaker array from which the sound designers blasted Godzilla’s roar to record the sound in a “real world” context)

Feet: 17.66mTotal width of Godzilla’s feet across the widest point

Feet: 18.18m 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 164 cm.

For 14-year-old girls in the U.S. the average height is 158.75 cm.

Godzilla = 108.2 m

We’ll assume an average height of, say, 1.6m for a 14 yo.

14 yo =1.6 m

Height:

108.2/1.6 = 67.6 = 68

Footprint

You vs Godzilla’s Footprint

18.18/160 =11.4

Teeth

You vs Godzilla’s Tooth

1.07/1.60 = 0.7

Here is Superman vs Godzilla

A very funny Aussie commentary.

………………………………………………

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 theresolution 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.

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).