Great white sharks



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GREAT WHITE SHARKS

&

MATHEMATICS

Stephen Ralph


Great White Sharks (Carcharodon carcharias) are the apex predators of much of the world’s oceans. This massive fish can reach sizes of approximately 6m and can weigh more than 2 tonnes. They are the largest predatory fish on the Earth and feed on things such as seals, whales, fish, turtles and every now and then humans.
They are amazing creatures that have evolved over millions of years into the ultimate killing machine. They are streamlined and torpedo shaped and have powerful tails that can propel the sharks along at speeds of up to 50 km/h.
Their mouths are filled with around 230 teeth at any one time, all arranged in rows and each tooth is replaced with another when it falls out.
They are generally found in cool, coastal waters around the globe. As you can see in the diagram below, Great White sharks can be found all over the planet. They generally favour colder, shallower water near coastlines. Experts are pretty certain that this is due to the nature of their prey.

In this first week we are going to be using mathematics to work out some interesting facts about Great White sharks. We will be analysing their sizes, ages, teeth, bite strength, attack statistics and we will be using tagging statistics to measure how far and how fast these amazing animals can travel.


If you would like to find out more information about Great White sharks have a look at this website
http://www.environment.gov.au/cgibin/sprat/public/publicspecies.pl?taxon_id=64470


SIZE: Great Whites can grow to massive sizes. They however are not the largest shark on the Earth today. There are tiny sharks like the smallest, the Dwarf Lantern shark (Etmopterus perryi) through to the massive but harmless Whale shark (Rhincodon typus).
Activity 1: Create a PowerPoint presentation with the sharks below on an individual slide. Find a picture of each shark and their scientific name for each slide. Leave enough room on each slide so that you can add extra information.
Activity 2: Use the internet to find maximum sizes in metres for the following sharks:

  1. Whale Shark

  2. Great White Shark

  3. Tiger Shark

  4. Bull Shark

  5. Greenland Shark

  6. Thresher Shark

  7. Mako Shark

  8. Hammerhead Shark

  9. Angel Shark

  10. Blue Shark

  11. Dwarf Lantern Shark

  12. Port Jackson Shark

  13. Cookiecutter Shark

  14. Basking Shark

  15. Goblin Shark


Activity 3: Convert the sizes in metres of each shark to centimetres


  1. Whale Shark

b) Great White Shark

c) Tiger Shark

d) Bull Shark

e) Greenland Shark

f) Thresher Shark

g) Mako Shark

h) Hammerhead Shark

i) Angel Shark

j) Blue Shark

k) Dwarf Lantern Shark

l) Port Jackson Shark

m) Cookiecutter Shark

n) Basking Shark

o) Goblin Shark



Activity 4: In a lot of places around the world they measure fish lengths in feet and inches. You need to convert the measurements of the sharks from cm to feet and inches.


  1. Whale Shark

b) Great White Shark

c) Tiger Shark

d) Bull Shark

e) Greenland Shark

f) Thresher Shark

g) Mako Shark

h) Hammerhead Shark

i) Angel Shark

j) Blue Shark

k) Dwarf Lantern Shark

l) Port Jackson Shark

m) Cookiecutter Shark

n) Basking Shark

o) Goblin Shark


Activity 5: Use the internet to find out the maximum weight in kilograms that these sharks grow to.
a) Whale Shark

b) Great White Shark

c) Tiger Shark

d) Bull Shark

e) Greenland Shark

f) Thresher Shark

g) Mako Shark

h) Hammerhead Shark

i) Angel Shark

j) Blue Shark

k) Dwarf Lantern Shark

l) Port Jackson Shark

m) Cookiecutter Shark

n) Basking Shark

o) Goblin Shark
Activity 6: Some of these sharks get really big. If their maximum weight is over 500kg convert their weight to tonnes.
Activity 7: Create a bar graph showing the lengths in metres that all of these sharks can grow to. Use graph paper. Once completed on paper complete one in Excel and paste to your PowerPoint presentation.

Activity 8: Create a bar graph showing the weight in kilograms that all of these sharks can grow to. Use graph paper. Once completed on paper complete one in Excel and paste to your PowerPoint presentation.
Activity 9: Great White sharks are slow growing animals. A male shark was tagged off the Eastern Seaboard of America two years ago. At that stage it was 3.2m long. The shark was recently caught again in the same place. It had grown to 3.9m long. Using this information, calculate the rate of growth in m/year for this male shark. Show all working.


Activity 10: Using the growth rate you have worked out, please work out the size that the following tagged sharks will be in metres in a) 2 years time, b) 4 years time.
a) Albert 9ft 8in

b) Courage 12ft 6in

c) Edna 14ft 2in

d) Sofia 8ft 6in

e) Jill 9ft 7in

Activity 11: The sharks above are actual real-life sharks that have been tagged around the world. Have a look at the following website for up to date and live information about tagged Great White sharks.

http://sharks-ocearch.verite.com/

Check out the sharks above and see where they were tagged and where they have been travelling.

Using the website, choose four different sharks. Write their names below


a)______________________
b)______________________
c)______________________
d)______________________
You are now going to draw on a map the paths that each shark has taken.

Activity 12: Using the paths you have drawn on the maps and the scale of the maps, you need to calculate the distance in km each shark has swam since they were tagged.

Activity 13: Using the website, find out how long each shark has been tagged for. Calculate the average distance each shark covered per day.

Activity 14: Using the distance covered by each shark and the time they have been tagged for, calculate the average speed each shark has been swimming at per day.

Activity 15: Some sharks have been known to swim great distances. Using the average speed of your fastest shark calculate how long it would take a Great White tagged off Esperance to reach Cape Town, South Africa.


Activity 16: Great White sharks have approximately 230 teeth at any one time. These teeth are arranged in 5 rows. If a tooth falls out a new one automatically replaces it. Some sharks can go through around 50,000 teeth in a lifetime.

a) If on average, a tooth falls out every day how long would it take in hours and days for all 230 teeth to be replaced?


Hours:


Days:

b) If a tooth falls out everyday, how old would a shark be if it had used up all 50,000 teeth?


c) On average a shark loses 10 teeth every time it eats something. If a Great White shark eats every 3 days, how old would the shark be in days and years when it goes through its 50,000 tooth?


Days:


Years:
Activity 17: The bite of a 3m Great White shark has been measured at 1.1 tonnes of pressure. Calculate how much pressure that is in kg.


Activity 18: The bite of a 3.6m Great White shark has been measured at 1.4 tonnes of pressure. Calculate how much pressure that is in kg.


Activity 19: Using the information above, predict how much pressure a shark of the following sizes could generate.

a) 4.2m
b) 4.8m


c) 5.2m
d) 6m

Activity 20: We know that Great Whites have approximately 230 teeth in their mouth at any one time. Using this information calculate how much pressure one individual tooth will exert in kg during one bite from a 3.6m shark.

Activity 21: It has been proven that 800kg of pressure can puncture through skin, fat, muscle and fracture the femur bone of a human. Using this information, how many teeth would a 3.6m Great White shark have to bite a surfer with to break the surfers femur?


Activity 22: A shark would need to generate at least 1.8 tonnes of pressure to bite a humans leg clean off. Using this information, calculate the minimum size of shark that would be able to do this to a surfer.

Activity 23: The ancient Megalodon shark that grew to a length of 20 metres could bite down with a force of approximately 15 tonnes of pressure. It has been proven that approximately 3 tonnes of pressure will break a fibreglass sheet of 3cm thick. Many boat hulls are made out of fibreglass. Calculate the maximum thickness of a boat hull that could be destroyed by the bite of a Megalodon shark (if it were still alive).


Activity 24: As you have seen, sharks have a very strong bite force. Check out the bite force of the animals below

a) Salt Water Crocodile: 1.5 T

b) Lion: 0.8 T

c) Grizzly Bear: 1 T

d) Hippopotamus: 1.2 T

e) Gorilla: 1.1 T



f) Hyena: 1.05 T
Using the internet find the maximum size these animals grow too. Make a graph showing bite strength v length/size/weight

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