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What in the world is this creature?!

See what you can discover using evidence and math! Let's get started!

1 Challenge

The Egg Is Discovered!

Here’s what we know: a very large egg – possibly a dragon egg – was discovered near Walt Disney World in 1971. The egg was approximately 3.5 feet tall.

What we’d like to know: how tall is the creature that could lay an egg that size?!

Since the egg could belong to a dragon, let’s look at the mother-to-egg ratio of the largest flying creature to have ever existed: the pterosaur. Pterosaurs were prehistoric flying reptiles, and some of them were larger than any flying animals on earth today. A recently excavated pterosaur fossil shows that the height of the mother was roughly 8 times the height of the egg, or 8:1.

Assuming the mother-to-egg ratio of the dragon egg is the same as that of the pterosaur, how tall is our (possible) dragon mother? Note: the height will not include her tail length!

Known Variables:

Egg Height (3.5 feet)

Pterosaur Mother-to-Egg Ratio (8:1)

Assumed Dragon Mother-to-Egg Ratio (8:1)

see solution download pdf

2 Challenge

New Clue – A Footprint!

A footprint was just discovered not too far from the nest – it looks like the clues could be leading us to a dragon after all!

Here’s what we know: the footprint measures 2 feet long and 1.8 feet wide.

What we’d like to know: how big is this particular dragon? Based on the mother’s estimated height from Challenge 1 (28 feet), is the dragon fully grown?

Once again, we’ll need to base our estimate on other information we know. Let’s start with a large reptile whose footprint is a similar size – the Tyrannosaurus Rex. An Adult T-Rex has a foot length of approximately 3 feet (although its footprint was much smaller because it walked on tip-toe). Its total height was five times its foot length, or 5:1. Its total body length, including its tail, was 13 times its foot length, or 13:1.

Assuming the dragon’s body ratios are the same as the T-Rex’s body ratios, see if you can estimate the following:

  • the dragon’s height
  • the dragon’s total length, including tail
  • the length of the tail only

Known Variables:

Length of Dragon Footprint (2 feet)

T-Rex Foot Length (3 feet)

T-Rex Height to Foot Length Ratio (5:1)

T-Rex Body Length to Foot Length Ratio (13:1)

Assumed Dragon Height to Foot Length Ratio (5:1)

Assumed Dragon Body Length to Foot Length Ratio (13:1)

Mother Dragon’s Height (28 feet)

see solution download pdf

3 Challenge

How Much Time to Reach Full Size?

Wow! The creature we are tracking is pretty big – it is looking more and more like a dragon! But since we figured out that the dragon is probably still growing, is there any way to determine when it will finish growing?

Here's what we know: based on our earlier calculations, the dragon's mother (who we are assuming is fully-grown), is 28 feet tall; the dragon we are tracking is 10 feet tall. We also know the dragon hatched in 1971, which means the dragon is about 41 years old.

What we'd like to know: when will the dragon reach its full size (assuming it grows at a constant rate)?

All right, we know the dragon egg was 3.5 feet tall, which means the dragon, like all creatures that hatch from eggs, was slightly smaller than the egg. Based on this information, it is safe to assume that the baby dragon was approximately 3 feet tall when it hatched. This assumption means that between 1971 and 2012, the dragon has grown 7 feet in height (for a total of 10 feet as of today). Unfortunately, we don't know if the dragon will exceed its mother's size, but we can assume that it will be at least the same size. See if you have enough information to answer the following questions:

  • What percentage of the dragon’s growth has already been completed?
  • What percentage of the dragon’s growth remains?
  • Can you estimate how long it will take for the dragon to reach its full size?

Known Variables:

Mother Dragon’s Height (28 feet)

Dragon’s Hatchling Height (3 feet)

Dragon’s Current Height (10 feet)

Dragon’s Age (41 years)

Dragon’s Growth Over 41 Years (7 feet)

Assumed Dragon Height at Full Size (28 feet)

see solution download pdf

4 Challenge

New Clue – Poop Discovered!

We might not know exactly what this creature is, but you would be amazed at the things you can learn from poop! A very large poop was recently discovered, and it does not belong to any of the creatures native to Florida.

Here's what we know: the creature, which we still think is a dragon, loves Florida's oranges and orange tree leaves.

What we'd like to know: how much does a creature of this size need to eat every day in order to survive?

It looks like the dragon only eats fruit and leaves, so it is an herbivore. Keeping in mind that the dragon is currently 10 feet tall, it would make sense to find an herbivorous creature that is about the same size as our estimates for the dragon. An elephant is probably too big – an elephant is so heavy that it would be really hard for it to fly (except for Dumbo!). And a deer is probably too small. So how about something in-between, like a giraffe? An adult giraffe eats about 75 pounds of foliage per day. If we assume the dragon eats approximately the same amount of food as the giraffe, and the dragon is only eating oranges (which, on average, weigh about 7 oz. each), how many oranges a day is the dragon eating?

Hint: 16 ounces equals 1 pound.

Known Variables:

Amount of Food a Giraffe Eats Daily (75 pounds)

Assumed Amount of Food a Dragon Eats Daily (75 pounds)

Average Weight of an Orange (7 ounces)

Number of Ounces in 1 Pound (16)

see solution download pdf

5 Challenge

A Real Wing-Dinger!

The more we discover, the more this creature appears to be a dragon! So aside from breathing fire, what else makes dragons awesome? Their massive wings!

Here’s what we know: our dragon is pretty large, and it is only going to get bigger. This means that its wings need to be large enough to hold it up when it is flying, but not so large that the dragon can’t flap them to get off of the ground.

What we’d like to know: how wide is the dragon’s wingspan?

It's time to go back to our favorite prehistoric flying creature, the pterosaur. Pterosaurs actually came in all different sizes – some of them were the size of small birds and others were apparently the size of F-16 jets. One average-sized pterosaur's fossil showed that its wingspan was approximately 3 times its height plus 2 feet.

Assuming our dragon’s wingspan follows this same formula, what is the dragon’s wingspan in feet?

Known Variables:

Pterosaur’s Wingspan Ratio (3:1 + 2)

Assumed Dragon’s Wingspan Ratio (3:1 + 2)

see solution download pdf

6 Challenge

Hear the Dragon Roar!

Yesterday, one of the Disney Imagineers heard what sounded like a dragon roar. The roar seemed to be coming from the direction of a wooded area located about 5 miles away from where the Imagineer was working.

Here's what we know: although the speed of sound varies depending on location, sound travels at an approximate speed of 1,116 feet per second. We also know that there are 5,280 feet in a mile.

What we'd like to know: assuming the dragon roar was coming from the nearby wooded area, how long did it take for the sound to reach the ears of the Imagineer?

Keep in mind that you will need to use the Distance Formula to solve this challenge!

Distance Traveled = Rate x Time


Known Variables:

Distance Between Dragon and Imagineer (5 miles)

Speed of Sound (1,116 feet/second)

Number of Feet in a Mile (5,280)

Distance Formula (Distance Traveled = Rate x Time)

see solution download pdf

7 Challenge

Speed Dragon!

There have been two recent dragon sightings! An Imagineer reported seeing a dragon take flight at 6pm from the east side of New Fantasyland; a local man reported seeing a dragon land around 9pm in a wooded area about 65 miles away from New Fantasyland.

Here's what we know: if both sightings were of the same dragon, then the dragon was flying for 3 hours and traveled a distance of 65 miles.

What we'd like to know: how fast was the dragon flying?

In order to solve this problem, we have to assume that the dragon was flying in a straight line and at a constant speed for the duration of its trip.

Known Variables:

Number of Hours the Dragon Was Flying (3 hours)

Distance the Dragon Traveled (65 miles)

Distance Formula (Distance Traveled = Rate x Time)

see solution download pdf

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SOLUTION: CHALLENGE 1

ANSWER: The mother dragon’s height is 28 feet.

How to solve Challenge 1:

We do not know the dragon mother’s height, so we need to assign an unknown variable to represent her height. Let’s use “X”.

We know the pterosaur’s mother-to-egg ratio is 8:1, which we can rewrite as a fraction:

The ratio of the dragon mother to her egg is X:3.5, which we can also rewrite as a fraction:

Because the mother-to-egg ratio of the dragon is the same as the pterosaur's mother-to-egg ratio, we can set both of the ratios equal to one another:

Now we need to isolate the variable "X" so we can solve for it. Because we are dividing "X" by 3.5, we need to use the inverse operation on the right side of the equation to isolate "X" (the inverse of dividing by 3.5 is multiplying by 3.5). So we multiply the right side of the equation by 3.5. And if we multiply one side by 3.5, we have to multiply the other side by 3.5 – this action keeps both sides equal to one another.

Since 3.5 divided by 3.5 equals 1, the 3.5's drop out of the right side of the equation:

In order to keep both sides equal, we have to repeat this entire process for the 1 on the left side of the equation:

Since 1 divided by 1 equals 1, the 1's drop out of the left side of the equation:

Now divide each side by 1 to get “X” alone:

Once you have solved for “X,” don’t forget to include the units of measurement! If the height of the dragon egg is 3.5 feet, then at a ratio of 8:1, the mother’s height is 28 feet.

COME BACK TOMORROW FOR ANOTHER CHALLENGE!

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SOLUTION: CHALLENGE 2

ANSWERS: The dragon’s height is 10 feet; the dragon’s body length is 26 feet; the dragon’s tail length is 16 feet; the dragon is not fully grown.

How to solve Challenge 2:

Let’s solve for the dragon’s height first. Because we do not know the height, we need to assign an unknown variable to represent this height. Let’s use “H”.

We know the T-Rex’s height to foot length ratio is 5:1, which we can rewrite as a fraction:

The ratio of the dragon’s height to its foot length is H:2, which we can also rewrite as a fraction:

Because the height to foot length ratio of the dragon is the same as that of the T-Rex, we can set both of the ratios equal to one another:

Now we need to isolate the variable "H" so we can solve for it. Because we are dividing "H" by 2, we need to use the inverse operation on the right side of the equation to isolate "H" (the inverse of dividing by 2 is multiplying by 2). So we multiply the right side of the equation by 2. And if we multiply one side by 2, we have to multiply the other side by 2 – this action keeps both sides equal to one another.

Since 2 divided by 2 equals 1, the 2's drop out of the right side of the equation:

In order to keep both sides equal, we have to repeat this entire process for the 1 on the left side of the equation:

Since 1 divided by 1 equals 1, the 1's drop out of the left side of the equation:

Now divide each side by 1 to get "X" alone:

Once you have solved for "H," don't forget to include the units of measurement! If the dragon's foot length is 2 feet, then at a ratio of 5:1, the dragon's height is 10 feet (minus tail length).

Now let's solve for the dragon's total body length, including its tail. Because we do not know the total body length, we need to assign an unknown variable to represent this length. Let's use "L".

We know the T-Rex's body length to foot length ratio is 13:1, which we can rewrite as a fraction:

The ratio of the dragon's body length to its foot length is L:2, which we can also rewrite as a fraction:

Because the body length to foot length ratio of the dragon is the same as that of the T-Rex, we can set both of the ratios equal to one another:

Remember how we used the inverse operation to find the dragon's height? Use the same process to solve for "L":

Now divide each side by 1 to get "L" alone:

Once you have solved for “L,” don’t forget to include the units of measurement! If the dragon’s foot length is 2 feet, then at a ratio of 13:1, the dragon’s total body length (including its tail) is 26 feet.

*TEACHERS: Another approach might be to have students place the known variables into a table or chart, and then look for patterns in order to solve for the unknown variables.

Now that we know the dragon’s height (10 feet) and its total body length from head to tail (26 feet), we can do simple subtraction to figure out the length of its tail:

26 feet – 10 feet = 16 feet

The dragon’s tail is approximately 16 feet long!

So is the dragon fully-grown? Well, because we estimated the mother’s height (not including her tail) to be 28 feet, and we estimated our dragon’s height to be 10 feet, we can assume that our dragon has a lot more growing to do before it reaches its full size!

COME BACK TOMORROW FOR ANOTHER CHALLENGE!

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SOLUTION: CHALLENGE 3

ANSWERS: The dragon has completed 35.7% of its total growth; the dragon has to grow another 64.3% to reach its full size; it will take at least another 105 years for the dragon to reach its full size.

How to solve Challenge 3:

Let's start by figuring out what percentage of the dragon's growth is already complete. If the mother is 28 feet tall and the dragon is 10 feet tall, we can figure out the percentage of completed growth by translating the following question into a math formula:

10 feet is what percent of 28 feet?

"Percent" means "for each one hundred," so we are going to create a proportion where one ratio will be an unknown amount divided by 100 (e.g., ). For the other ratio, we want to compare the "part" – the dragon's current height of 10 feet – to the "whole" or total – the dragon's eventual height of 28 feet. We can write this ratio as 10:28. Now we can set both ratios equal to one another:

Now use the inverse operation we learned in Challenges 1 and 2 to solve for "N":

So if 100% represents the dragon's full size, then the dragon has completed 35.7% of its growth over the course of 41 years.

Now we need to figure out what percentage the dragon has left to grow. Well, if 100% is its total growth, then we can subtract 35.7% from 100%:

100%-35.7% = 64.3%

The dragon still has to grow another 64.3% to reach its full size.

If the dragon is currently 10 feet tall, it needs to grow another 18 feet to be the same size as its mother. Since we are assuming the dragon grows at a constant rate of 7 feet every 41 years, we can figure out how many years it will take for the dragon to reach its full size.

Just so we can practice converting units of measurement, let's try to solve for how many inches per year the dragon is growing (instead of solving for the number of feet per year the dragon is growing). Since there are 12 inches in 1 foot, we can figure out how many inches are in 7 feet by doing simple multiplication:

12 inches x 7 = 84 inches

Every 41 years, the dragon grows 84 inches. To figure out how many inches the dragon grows every year, we have to divide the inches by the years:

Now we know that the dragon grows 2.05 inches per year.

Next we need to find out how many inches the dragon has left to grow in order to reach its mother's height of 28 feet. Since we know the dragon has to grow another 18 feet to reach its mother's size, we need to figure out how many inches are in 18 feet:

12 inches x 18 = 216 inches

Now we need to figure out how many times 2.05 inches goes into 216 inches, and then we will know how many years it will take the dragon to reach its full size:

It is going to take about another 105 years for the dragon to reach its mother's height of 28 feet – that's a long time!

*TEACHERS: Another approach might be to have students create a simple line graph with a trend line to track the dragon's constant rate of growth over time (e.g., by age or by calendar year).

COME BACK TOMORROW FOR ANOTHER CHALLENGE!

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SOLUTION: CHALLENGE 4

ANSWER: The dragon has to eat at least 171 oranges every day to get its necessary 75 pounds of food.

How to solve Challenge 4:

First we need to know how many ounces are in a pound:

16 oz. = 1 pound

Next we need to figure out how many ounces are in 75 pounds. If there are 16 ounces in 1 pound, then we need to multiply 16 ounces by 75:

16 oz. x 75 = 1,200 oz.

If we know that the average orange weighs 7 ounces, then we have to see how many times 7 ounces goes into 1,200 ounces:

Now we know that our dragon would have to eat about 171 oranges every day to get its necessary 75 pounds of food. That's a lot of oranges!

COME BACK TOMORROW FOR ANOTHER CHALLENGE!

X

SOLUTION: CHALLENGE 5

ANSWER: The dragon’s wingspan is approximately 32 feet.

How to solve Challenge 5:

First we need to take the phrase “3 times its height plus 2 feet” and translate it into an equation, using “W” as the unknown variable for the wingspan and “H” as the height:

W = 3(H) + 2

Next we need to substitute our dragon’s height for “H” (remember, our dragon is 10 feet tall):

W = 3(10) + 2

Because we only have one variable, and it is already isolated on one side of our equation, we can solve for "W":

W = 30 + 2

W = 32

Once we have solved for "W," don't forget to include the unit of measurement! If the dragon's height is 10 feet, at a ratio of 3:1 + 2, our dragon's wingspan is 32 feet. That's almost as long as a school bus!

COME BACK TOMORROW FOR ANOTHER CHALLENGE!

X

SOLUTION: CHALLENGE 6

ANSWER: It took the sound of the dragon's roar 23.66 seconds to reach the Imagineer.

How to solve Challenge 6:

Let's start by figuring out how many feet are in 5 miles. If there are 5,280 feet in 1 mile, then we need to multiply 5,280 by 5:

5,280 feet x 5 = 26,400 feet

Now we know that the sound had to travel a distance of 26,400 feet.

Next we will use the Distance Formula to help us finish solving the challenge. We are solving for time, and we already know the distance the sound traveled and the rate at which it traveled:

Distance Traveled = Rate x Time

26,400 = 1,116 x Time

Now we divide both sides by 1,116 in order to get Time by itself:

Once you have solved for the Time, make sure you include the units of measurement! Since sound travels at 1,116 feet per second, it took the dragon roar 23.66 seconds to travel 5 miles.

COME BACK TOMORROW FOR ANOTHER CHALLENGE!

X

SOLUTION: CHALLENGE 7

ANSWERS: The dragon was flying at a speed of 21.67 miles per hour.

How to solve Challenge 7:

Once again, we will need to rely on the Distance Formula to help us solve this challenge:

Distance Traveled = Rate x Time

We know that the dragon traveled 65 miles in 3 hours:

65 = Rate x 3

Now we need to divide both sides by 3 in order to get the Rate by itself:

Once you have solved for the rate, don't forget to include the units of measurement! Because the dragon was flying 65 miles over the course of 3 hours, we know that its rate was 21.67 miles per hour. Our dragon may be big, but he is NOT fast!

Congratulations on helping us solve all of these challenges! It looks like we were correct – there is a very big dragon living near Walt Disney World!

If you have any other math challenges about the dragon, feel free to send them to us, we would love to hear from you!

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FOR TEACHERS:

This dragon-themed "math journey" was designed to encourage students to experiment with some dynamic applications of math in engaging and playful ways.

The following narrative challenges link to curriculum in grades 5-8, and cover these specific concepts: performing operations with ratios and percentages; converting units of measurement within a given measurement system; calculating rates of speed and distances traveled; analyzing proportional relationships; and writing and interpreting numerical expressions.

We hope you and your students enjoy using math as a tool for sleuthing, estimating and predicting – now let’s get to work!