## Fibonacci Fun

Logan Strople

9/20/14

Math Fibonacci Fun

Problem Solving:

In mathematics, the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence. (wikipedia)

The way i saw this interesting problem to be is a triangle thats not really changing the area of itself but more or less folding in on itself and keeping the same area and or shape. The problem was basically asking our group of four to find the sequence and or pattern in which the triangle changed. Though it still asked us what the area was, it was not relevant to our answer.

Process Description:

As a group the first thing we did is go over the problem and making sure that all group members understood what the problem was asking. We then dove in individually for about three to five minutes and come up with our own conclusions and ideas on how to solve the problem. We then shared one by one. At this point i started taking notes on others ideas and or thoughts. We collaborated and bounced of one another's ideas till we came up with a rock solid plan on how to solve the problem. In the mean time i looked up the equation to help find the area with the two upper sides of the triangle. We then started brainstorming and found that we were not so much concerned with area but more or less the pattern that was correlated between the triangles.

We found that there was a weird pattern between the different triangles and that if we could visualise what was going on we could make a simple formula. It was at this moment when i took a closer look at the paper and recognized that there was a weird label on each version of the triangle. This was basically what we based our formula off of. It was easy enough to make a formula on how these triangles correlate off of this.

Solution:

Our solution that we got is...

Y=N/2

-When N= the number of triangles you divide

Basically my answer consisted of dividing the triangles largest pieces in halfs. I believe that is continually divides this way. Basically you have to look at the triangles corresponding “N” above it . This is almost a key on a way. This is how i came to the conclusion that...

N=/

N=1 divide 1

N=2 divide 2

N=3 divide 3

The answer we got is based off of this simple rule that you always divide the biggest piece.

We decided as a group that this problem didn't make much sense in terms of finding the area. We were more concerned with figuring out the pattern and finding a formula to do so. Our solution is based off of the patterns that we saw on the paper. We could not make a 100% guarantee on what the next triangle would look like. I know that Preston got an idea of what it could look like but we could not be sure.

Self-assessment and reflection: mathematical practices and expectations:

During the whole free think friday problem i saw my group work together and collaborate as best as they could to figure out what the answer to the problem was. I was basically the designated note taker and tried as best as i could to get all the info down. At the same time i was trying to contribute to the group discussion and ideas. At the same time i did some research on google for similar problems and formulas to help guide our group to a reachable answer. I think participation and collaboration i deserve just as good as afraid as the rest as my group. We worked great together and i believe that it was at least a 9.99 and the last .1 is because we were not completely serious the whole time we were working. But this does not mean that we were not off task.

As an individual going into this i found that i didn't know really what to do. I don't see myself as a big mathematician but i rather see myself as a problem solver and a group collaborator. However i don't think that i fully understand some of the topics and answers we came to i tried my hardest and used as much as i knew to help come to an conclusion on the problem. I think that i deserve a 10 for effort but i can't grade myself for how much i know.

I developed a successful mathematical habit of work during this group assignment because i learned its not always about how much i know but more about how i can collaborate with other and i get to see how they visualize and interpret things and can base my understandings on this. I have the willpower and drive to learn math. Its always been a struggle for me but i can only get better. This group activity was just another way of improving my mathematical skills and knowledge.

9/20/14

Math Fibonacci Fun

Problem Solving:

In mathematics, the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence. (wikipedia)

The way i saw this interesting problem to be is a triangle thats not really changing the area of itself but more or less folding in on itself and keeping the same area and or shape. The problem was basically asking our group of four to find the sequence and or pattern in which the triangle changed. Though it still asked us what the area was, it was not relevant to our answer.

Process Description:

As a group the first thing we did is go over the problem and making sure that all group members understood what the problem was asking. We then dove in individually for about three to five minutes and come up with our own conclusions and ideas on how to solve the problem. We then shared one by one. At this point i started taking notes on others ideas and or thoughts. We collaborated and bounced of one another's ideas till we came up with a rock solid plan on how to solve the problem. In the mean time i looked up the equation to help find the area with the two upper sides of the triangle. We then started brainstorming and found that we were not so much concerned with area but more or less the pattern that was correlated between the triangles.

We found that there was a weird pattern between the different triangles and that if we could visualise what was going on we could make a simple formula. It was at this moment when i took a closer look at the paper and recognized that there was a weird label on each version of the triangle. This was basically what we based our formula off of. It was easy enough to make a formula on how these triangles correlate off of this.

Solution:

Our solution that we got is...

Y=N/2

-When N= the number of triangles you divide

Basically my answer consisted of dividing the triangles largest pieces in halfs. I believe that is continually divides this way. Basically you have to look at the triangles corresponding “N” above it . This is almost a key on a way. This is how i came to the conclusion that...

N=/

N=1 divide 1

N=2 divide 2

N=3 divide 3

The answer we got is based off of this simple rule that you always divide the biggest piece.

We decided as a group that this problem didn't make much sense in terms of finding the area. We were more concerned with figuring out the pattern and finding a formula to do so. Our solution is based off of the patterns that we saw on the paper. We could not make a 100% guarantee on what the next triangle would look like. I know that Preston got an idea of what it could look like but we could not be sure.

Self-assessment and reflection: mathematical practices and expectations:

During the whole free think friday problem i saw my group work together and collaborate as best as they could to figure out what the answer to the problem was. I was basically the designated note taker and tried as best as i could to get all the info down. At the same time i was trying to contribute to the group discussion and ideas. At the same time i did some research on google for similar problems and formulas to help guide our group to a reachable answer. I think participation and collaboration i deserve just as good as afraid as the rest as my group. We worked great together and i believe that it was at least a 9.99 and the last .1 is because we were not completely serious the whole time we were working. But this does not mean that we were not off task.

As an individual going into this i found that i didn't know really what to do. I don't see myself as a big mathematician but i rather see myself as a problem solver and a group collaborator. However i don't think that i fully understand some of the topics and answers we came to i tried my hardest and used as much as i knew to help come to an conclusion on the problem. I think that i deserve a 10 for effort but i can't grade myself for how much i know.

I developed a successful mathematical habit of work during this group assignment because i learned its not always about how much i know but more about how i can collaborate with other and i get to see how they visualize and interpret things and can base my understandings on this. I have the willpower and drive to learn math. Its always been a struggle for me but i can only get better. This group activity was just another way of improving my mathematical skills and knowledge.