Giant Panda Problem We start out with four pregnant Pandas. They have one cub every second year. Some have twins, but the second rarely survives. We want you to know how many pandas there will be in fifteen years if we follow four pregnant Pandas. Panda's normally have one baby though... One way of figuring it out 1 yr. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 baby baby baby baby baby baby baby baby 1 baby 2 3 4 5 6 7 8 Explanation for First Solution We thought, if first we made a timeline that showed fifteen years, because we are tracking the pandas for that period of time, we could find our first answer. Then we have to take our answer and multiply it by four because there are four female pandas. Then we took it farther. Since pandas start having cubs at the age of five, we subtracted five years for those pandas cubs. Then we made a timeline for ten years. After we got an answer on how many cubs those pandas would have, you add the products. Once that is finished, you subtract five years from the ten for the five years the panda cubs don't have cubs. We added that answer to our other answer. Then we divided our solution by two, because they're not all female. 8 cubs

x 4 pregnant females

-----------------

32 cubs + 4 females=36 Pandas First Solution continued... 1 yr. 2 3 4 5 6 7 8 9 10 baby baby baby baby baby 1 baby 2 3 4 5 5 babies

x 4 pregnant females

---------------

20 Pandas 36 Pandas

+ 20 Pandas

------------------

56 Pandas First Solution Continued... 1 yr. 2 3 4 5 baby baby baby 1 baby 2 3 3 cubs

x 4 pregnant female

------------------

12 Pandas 56 Pandas

+ 12 Pandas

----------------

68 Pandas

----------------

Since there not all girls... 68 Pandas / 2=

34 Pandas

So, about 35 Pandas Explanation for Second Solution Another way works well to check your answer if you did it like our first solution. All you need to do is divide the first product we got in two. Do the same with the second product and add those together. Next divide the third product by two and add that to your new found solution. After that add four and you'll have the answer again. 32 cubs/2

------------

16 cubs 20 cubs/2

--------------

10 cubs 16

+ 10

-------------

26 cubs 12 cubs/2

-----------

6 cubs 26 cubs

+ 6 cubs

--------------

32 cubs 32 cubs

+ 4 female

---------------

36 Pandas

---------------

So, about 35 Pandas Explanation Number Three... Year 0 Year 1 Y. 2 Y. 3 Y. 4 Y.5 Y.6 Y.7 Y.8 Y.9 Y.10 Y.11 Y.12 Y.13 Y.14 Y15 The Original four Pandas After about five months (which I rounded to six months [half a year {short lines}]) they had four babies. I represented this as the first yellow star... Then so on. The pandas give birth to one cub every two and a half years (one cub for every two years and a five month gestation period rounded to six months [half a year]). Then it gets even more difficult, the cubs that the original pandas had first after 5 1/2 years (five years until they can have cubs plus the five [rounded to six] months gestation period) and then they start having cubs every two and a half years. I marked this with a blue star. Then every two and a half years I put a blue star. The pandas that were born second from the original four pandas had cubs after about five and a half years. Two and a half years later they have another cub. I marked this with green stars. That continues until they have total of four cubs. Then the pandas that were born third from the original four pandas have cubs after they are five and after the gestation period of five months (rounded to six). They have two cubs. This is represented by a dark red star. Then the pandas that were born fourth from the original four pandas have cubs 12 and a half years into the time the scientists are tracking these giant pandas. They each have two cubs. This is represented by the pink star. Then the pandas first born from the original four pandas' cubs have cubs. These pandas have two cubs. This is represented by the light blue outlined circle. Then the four original pandas' second cubs' cubs have cubs 13 years into the period of time. They only have one cub in the time remaining in the 15 years the scientists are tracking the pandas. This is represented by the light blue circle. Then the first cub from the original pandas' second cub has one cub in the time period remaining. They only have one cub 13 and a half years into the time period remaining. This is represented by the gray outlined circle. Then the second cub of the original four pandas' second cub has a cub. They have one cub in the 15th year. This is represented by the dark blue outlined circle. Final Step... There are 26 stars and circles, each one is a symbol for four pandas. So to find out how many pandas there are you would need to multiply the number of symbols times four because each one represents four pandas. Do the problem in your math notebook... What do you get? 2

26

X 4

104 But wait, how do we know how many pandas will be male and how many will be females? Since it's next to impossible to find the ratio of how many giant pandas are males to females on the internet, we're going to have to guess. Our group decided to divide our answer in two. Now how many pandas are there? Find out the answer in your math notebook... 52

2 104

-10

04

-4

0 No one knows how many pandas there will be--it's a estimate. Many things could affect the outcome: one of the pandas could die; more of them are male or female; a panda could be born stillborn; one of the twins could survive; the cub is slow to develop so maybe unable to have babies as quickly; or a panda cannot have babies. No one knows with all these possibilities, so there is no exact or right answer. A hard part about this problem is keeping track of all of the pandas and all the possibilities. As part of this group I really enjoyed this problem because it made me think and there is no definite answer (Everen). We had results from 34 pandas to more than a hundred pandas. Thanks for watching our presentation!

-Everen, Ellie, Logan and Andrew

The Giant Panda Problem

Solvers (TGPPS©) Conclusion... Using my way, there are 52 pandas, but it is not exactly right because I rounded the gestation period and many other things could happen. Explanation Four... Explanation Five... By: Logan Freischmidt By: Andrew Nelson By: Everen Wegner By: Ellie Allen By: Ellie Allen The four pregnant pandas. The pandas' that were born fourth from the original pandas' have cubs They have one cub 14 1/2 year that the scientists are tracking the giant pandas'.

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# Giant Panda Problem

Logan, Ellie, Andrew and Everen