## Semester #1

Growth of rat population

Problem statement

For this pow we had to figure out how many rats would be on rat island after 365 days. it all starts off with 2 rats, the mama and the papa. They begin the process on day one by giving birth to 6 rats, 3 females and 3 males and she can keep giving birth every 40 days until she dies.

Her offspring can give birth after 120 days and then can give birth every forty days after the 120 days. Our goal is to find out how many rats will be on the island after 365 days.

Visual representation

Breading

rounds

Newborns

40 days old

80 days old

Breeders

1

6

0

0

2

2

6

6

0

2

3

6

6

6

2

4

24

6

6

8

5

42

24

6

14

6

60

42

24

20

7

132

60

42

44

8

258

132

60

86

9

438

258

132

146

10

843

438

258

278

Process

For this pow I drew out a little table that would help me figure this problem out in a more simple way. I was never able to come up with a set answer because guaranteed I did a couple things differently in each one. But the way that I tried to figure it out was to start with the first two rats and map out their offspring and how many they would have during the whole time period and then after 120 days map out how many offspring that offspring they would have and then take into mind that after 120 days they can start giving birth every 40 until day 360.

Solution

For my final answer which I had many but the one that seemed to pop up the most between my peers and me was 9+834+438+258+278=1808. I just added my final answers up from the graph and came up with that.

Self evaluation

This pow is probably the pow that I am most proud of because I had fun figuring it out and was the pow that I figured out the most on my own. Although I did not find my final answer all the way though I am still proud of this pow and like it a lot!

Problem statement

For this pow we had to figure out how many rats would be on rat island after 365 days. it all starts off with 2 rats, the mama and the papa. They begin the process on day one by giving birth to 6 rats, 3 females and 3 males and she can keep giving birth every 40 days until she dies.

Her offspring can give birth after 120 days and then can give birth every forty days after the 120 days. Our goal is to find out how many rats will be on the island after 365 days.

Visual representation

Breading

rounds

Newborns

40 days old

80 days old

Breeders

1

6

0

0

2

2

6

6

0

2

3

6

6

6

2

4

24

6

6

8

5

42

24

6

14

6

60

42

24

20

7

132

60

42

44

8

258

132

60

86

9

438

258

132

146

10

843

438

258

278

Process

For this pow I drew out a little table that would help me figure this problem out in a more simple way. I was never able to come up with a set answer because guaranteed I did a couple things differently in each one. But the way that I tried to figure it out was to start with the first two rats and map out their offspring and how many they would have during the whole time period and then after 120 days map out how many offspring that offspring they would have and then take into mind that after 120 days they can start giving birth every 40 until day 360.

Solution

For my final answer which I had many but the one that seemed to pop up the most between my peers and me was 9+834+438+258+278=1808. I just added my final answers up from the graph and came up with that.

Self evaluation

This pow is probably the pow that I am most proud of because I had fun figuring it out and was the pow that I figured out the most on my own. Although I did not find my final answer all the way though I am still proud of this pow and like it a lot!

## King Arthur's table

Problem statement

King arthur would always play this game with his knight. This is how the game was played, all of the knights pick a chair around the round table and the king stays standing, he starts off with chair # 1 and say you are in and moves on the the next chair and says you are out the king keeps doing the same thing until there is only one knight left.

Visual representation

number of knights

winners of different rounds

1

1

2

1

3

3

4

1

5

5

6

5

7

7

8

1

9

3

10

5

11

7

12

9

13

11

14

15

Process

The first thing that i started to do to try and figure this problem out was drawing out a circle and replicating the problem for myself so that i could try to see if there was any patterns or something in common that was going on. What we first figured out was that no matter what all of the even numbers got out on the first round so if you wanted to win you would have to be an odd number. After that we started to make the table that is shown above and we started to write down different scenarios with different amount or knights. We started to notice that there was a pattern in the winning number, the pattern that we noticed was that was that the number 1 was being repeated a lot and it would always repeat itself on duplicates. The first group was # 1 then it was # 2 then it was # 4 then it was # 8 then it was # 16 then # 32 ETC.

Solution

If you where to play this game in real life you would first need to figure out how many people are going to be playing then you would need to find the grouping of chairs that are the powers of two or the duplicates as I said before. Once you find the grouping of chairs that is where you should start counting starting will #1 bc that is where it always repeats itself, after that you will need to count each chair with is odd neighbor. Once you have found the odd chair that corresponds to the number of chairs sit in that one.

Evaluation

I thought this problem was very fun and exciting, definitely hard at first but once we started to figure out the patterns and the powers of two it made it so much easier and very fun. And i really like how hannah lets us work with groups or friends, or at least I hope she does.

Self Evaluation

I think I did pretty well on this POW and especially with the help of my friends harley tanner and ava but I do think that if I were to do this in real life I would have to think about the problem fr a sec but overall I liked this POW, I found it very fun and exciting.

King arthur would always play this game with his knight. This is how the game was played, all of the knights pick a chair around the round table and the king stays standing, he starts off with chair # 1 and say you are in and moves on the the next chair and says you are out the king keeps doing the same thing until there is only one knight left.

Visual representation

number of knights

winners of different rounds

1

1

2

1

3

3

4

1

5

5

6

5

7

7

8

1

9

3

10

5

11

7

12

9

13

11

14

15

Process

The first thing that i started to do to try and figure this problem out was drawing out a circle and replicating the problem for myself so that i could try to see if there was any patterns or something in common that was going on. What we first figured out was that no matter what all of the even numbers got out on the first round so if you wanted to win you would have to be an odd number. After that we started to make the table that is shown above and we started to write down different scenarios with different amount or knights. We started to notice that there was a pattern in the winning number, the pattern that we noticed was that was that the number 1 was being repeated a lot and it would always repeat itself on duplicates. The first group was # 1 then it was # 2 then it was # 4 then it was # 8 then it was # 16 then # 32 ETC.

Solution

If you where to play this game in real life you would first need to figure out how many people are going to be playing then you would need to find the grouping of chairs that are the powers of two or the duplicates as I said before. Once you find the grouping of chairs that is where you should start counting starting will #1 bc that is where it always repeats itself, after that you will need to count each chair with is odd neighbor. Once you have found the odd chair that corresponds to the number of chairs sit in that one.

Evaluation

I thought this problem was very fun and exciting, definitely hard at first but once we started to figure out the patterns and the powers of two it made it so much easier and very fun. And i really like how hannah lets us work with groups or friends, or at least I hope she does.

Self Evaluation

I think I did pretty well on this POW and especially with the help of my friends harley tanner and ava but I do think that if I were to do this in real life I would have to think about the problem fr a sec but overall I liked this POW, I found it very fun and exciting.

Pow #1-2 reflection.

I chose these pows because of my understanding on them. they are the pows that I understand the best and feel the most confident about. the reason why I liked these pows was because I was able to figure them out before the ending date. overall I like these pows the most because I am able to understand what is going o and am able to explain it with confidence.

I chose these pows because of my understanding on them. they are the pows that I understand the best and feel the most confident about. the reason why I liked these pows was because I was able to figure them out before the ending date. overall I like these pows the most because I am able to understand what is going o and am able to explain it with confidence.

## silverton write up

Problem Statement

On October 12, 2017 the Animas High School Junior class took a field trip to Silverton, Colorado to test water quality on a variety of streams running through the town. All streams flow into our river(Animas River) and effect the water quality based on many factors. The Junior class was split into 3 groups, one for each different stream. My group was assigned to the Upper Animas creek and we had to figure out the pH, Turbidity, Conductivity, Streamflow, and Temperature.

On October 12, 2017 the Animas High School Junior class took a field trip to Silverton, Colorado to test water quality on a variety of streams running through the town. All streams flow into our river(Animas River) and effect the water quality based on many factors. The Junior class was split into 3 groups, one for each different stream. My group was assigned to the Upper Animas creek and we had to figure out the pH, Turbidity, Conductivity, Streamflow, and Temperature.

- Josie, Gage, Lucius
- October 12, 2017
- Upper Animas
- In this project we were asked to start a project based on the water quality of three creeks in silverton, Cement Creek, Mineral Creek, and Upper Animas. After this we learned about what causes the pollution, other than just the mine spill, and how it affects the environment around us.
- Introduction
- This project allowed us to find out how to use certain tools to figure out the pH, Streamflow, Turbidity, temperature, and the conductivity of the river that we used for are experiment. The main goals from this project was to teach us how to use Statistics and Data tables to find the correct information without all the test results.
- Definitions of Chemistry terms: turbidity, temperature, pH, conductivity. Streamflow is how fast the stream/river is flowing. Turbidity is the cloudiness or haziness of a fluid caused by large numbers of individual particles that are generally invisible to the naked eye, similar to smoke in air. Temperature is the degree of heat present in a substance or object. pH is a numeric scale used to specify the acidity or basicity of an aqueous solution. Conductivity is the degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field that causes the flow of current.
- Definitions of Mathematical terms: Weighted Average, Measures of Central Tendency (mean, median), Measures of Variability (maximum/minimum, range, Standard Deviation)
- Maximum: The data point with the greatest value
- Minimum: the data point with the lowest value
- Median: the center or the half of the value you have
- Mean: the average of numbers added up and divided by the same amount of numbers to find the average.

- This project allowed us to find out how to use certain tools to figure out the pH, Streamflow, Turbidity, temperature, and the conductivity of the river that we used for are experiment. The main goals from this project was to teach us how to use Statistics and Data tables to find the correct information without all the test results.
- Visual Representations (tables, graphs, charts, sketches, if applicable)
- Visual representations are appropriately labeled and briefly described
- Link to Piviot Tables https://docs.google.com/spreadsheets/d/1PfSWQwE0unnKQsgLgYeABCV-UPZrIJAe2K3C01zBX1w/edit#gid=1140795570
- Brief explanations as to why these visuals are important

- Visual representations are appropriately labeled and briefly described

- Spreadsheets/Pivot Tables are printed and labeled, including units

- Spreadsheets/Pivot Tables are printed and labeled, including units
- Explanation of Calculations
- Clarifying whether they are correct or incorrect, and why
- Include units

- Clarifying whether they are correct or incorrect, and why
- Explanation of any kind of assistance you received from Steve or myself and how it helped/didn’t help you

- Description of equipment used and various concentrations, if applicable

- Summarize trends in 5 categories of pH, turbidity, conductivity, temperature and streamflow

- Discussion of measures of central tendency, why they do/don’t make sense
- For all of our data point they average all matched up except for the turbidity and the reason i think that is because for all of the other test we tested it more than one time and for turbidity we only tested it once.
- Explain what your predicted values are below the confluence, why and why they do/don’t make sense
- For my predictions all i did was take the average of all the values that we found for each creek after it junction, what I figured out the next day was that you have to add the streamflow up and then divide that by the ph of the other confluences I think
- Discuss which types of data were reliable and why. Discuss which types of data weren’t reliable and why. Pretty much all of our data was really solid and pretty similar but the one data point that didn't match up with the rest of the averages of turbidity. The reason I think our data wasn't that precise was because for all of the other tests we tested it twice and for the turbidity we tested it only once
- Discuss what data you threw out and why
- For the turbidity it was really off so all I did was take out the min of the data so it would make it more balanced because the other data was more or less close to each other
- Compare historical USGS data to your data at the confluence and compare current USGS data to your own data at the confluence.
- Was your data in a reasonable and realistic range of USGS data?
- If your data wasn’t in a reasonable range, explain why.
- What do you model or predict for expected values?
- How confident are you in your values based off your calculations, the historical data from the USGS and the current data? Explain.

- Was your data in a reasonable and realistic range of USGS data?
- Attempt to generalize the problem based on the data you gathered
- Discussion of personal and group reaction to this investigation
- Did you consider it educationally worthwhile?

- Did you consider it educationally worthwhile?

- How would you change the problems/experiment to make the investigation better?

- Did you enjoy working on this project?

- Was it too hard/too easy and why?

- Include anything else you feel is relevant.

- Discussion of the importance of an investigation of this caliber. Why it is/is not important.

- Group Assessment: assign your group a grade for the following report and explain why you think you deserve that grade.

overall I am pretty proud with this semester because I feel that I have learned a lot more in my math three class than in any other math class that I have had. I like most of the work, I usually find it interesting or fun. the one other thing that I would like to say, is that I think me being paired with my friends help me because i feel comfortable to ask questions or make sure that im doing the right thing.