"Unit 4 - Desmos Drawing and Function Families"
Reflection:
When drawing this drawing I did not plan the drawing that I would complete I just went through and constructed two quadratic line that were reflecting the other and decided that I would make a flying saucer. As I went along I followed certain equations on the board but had to experiment with points in order to adjust them perfectly. While trying to cut lines I consulted with peers at first to fully understand how to use this function, I did not need to ask my teacher most of the time.
Using desmos to create this drawing was easier for me to learn function families because of the fun and creative way that we applied this to make a drawing. When starting my drawing I still didn’t fully understand quadratic functions and how we would use them but when I had finished my drawing I had learned so much about how I can apply that to something other than worksheets and in class assignments. I feel like when learning how to apply certain functions like cubic or just linear functions when making these I had the same amount of challenge as the other. I now understand these functions better than I would while just learning about it only in class, I was able to enjoy what I was making with complicated functions by applying them to desmos.
When drawing this drawing I did not plan the drawing that I would complete I just went through and constructed two quadratic line that were reflecting the other and decided that I would make a flying saucer. As I went along I followed certain equations on the board but had to experiment with points in order to adjust them perfectly. While trying to cut lines I consulted with peers at first to fully understand how to use this function, I did not need to ask my teacher most of the time.
Using desmos to create this drawing was easier for me to learn function families because of the fun and creative way that we applied this to make a drawing. When starting my drawing I still didn’t fully understand quadratic functions and how we would use them but when I had finished my drawing I had learned so much about how I can apply that to something other than worksheets and in class assignments. I feel like when learning how to apply certain functions like cubic or just linear functions when making these I had the same amount of challenge as the other. I now understand these functions better than I would while just learning about it only in class, I was able to enjoy what I was making with complicated functions by applying them to desmos.
Unit Reflection 2
The work I am most proudest of is the way that I have grown so much with the subject of trigonometry and how I can apply this to not only find a certain side length of a triangle in class, but to find the slope the roof of a house when constructing a building. I feel this work that had done during the unit was my proudest because of the way I really felt engaged with the subject along with my interest.
I feel like I am developing more of growth to my graphing skills which enables me to use graphs to model figures and translate them across a coordinate plane mathematically.The reason for this growth in graphing is because of the way I find it easier for me to apply in geometry class.
Trigonometry is used to in most cases find a certain side length/angle with given side lengths and angles. we had used this type of geometry in class to find out certain heights of trees or angles of which the height slopes upward. A certain appliance that trigonometry can be used in the adult world is to find the precise height of a building or to find the slope of the roof or house that is being built.
I feel like I am developing more of growth to my graphing skills which enables me to use graphs to model figures and translate them across a coordinate plane mathematically.The reason for this growth in graphing is because of the way I find it easier for me to apply in geometry class.
Trigonometry is used to in most cases find a certain side length/angle with given side lengths and angles. we had used this type of geometry in class to find out certain heights of trees or angles of which the height slopes upward. A certain appliance that trigonometry can be used in the adult world is to find the precise height of a building or to find the slope of the roof or house that is being built.
Unit Reflection 3
The work that I have been most proudest of in this unit has been the subject of area and using this with different shapes. The reason I am most proud of this is because I felt that I had known how to do this before and it was very easy to use my knowledge of this and apply it to what we learned new in this subject. I felt that I had shown this in the two homework worksheets that we have done recently which I had gotten an A on both of them. Overall this subject was very easy to understand and apply to new ways of using it during class.
I feel like I am developing ways of approaching problems better and using this in other classes. This is helping me in geometry by trying to solve a problem that I may not get right I will try and use different methods of solving it or checking over what I have already done. I feel like I have been developing this strategy throughout the year by at least trying to use other methods and figuring it out by myself but I have been really developing the last part in the last few weeks.
Area, Volume, Optimization. This is the process of using base times height in some shapes which help find the area or volume of somthing. In class we learned how to find the area of a parallelogram. to find this we used a form of trig to figure out the end side which are triangles. These types of processes can be used a bunch in the modern world ranging from how much water flows through a water pipe judging by the area of the circle to how much soda is in a soda can.
I feel like I am developing ways of approaching problems better and using this in other classes. This is helping me in geometry by trying to solve a problem that I may not get right I will try and use different methods of solving it or checking over what I have already done. I feel like I have been developing this strategy throughout the year by at least trying to use other methods and figuring it out by myself but I have been really developing the last part in the last few weeks.
Area, Volume, Optimization. This is the process of using base times height in some shapes which help find the area or volume of somthing. In class we learned how to find the area of a parallelogram. to find this we used a form of trig to figure out the end side which are triangles. These types of processes can be used a bunch in the modern world ranging from how much water flows through a water pipe judging by the area of the circle to how much soda is in a soda can.
POWS
POWs have helped me a lot by helping understand or apply my knowledge that I have learned in class. Pows let me stretch and use what I have been taught in class which helps me understand the content and help it stay with me further on in the school year.
Reed Frey
2/3/15
Pow #2 Pick up Triangles
Problem:
I have four sticks at different lengths 2,3,4,6 inches I have to use these four sticks in every pair of similar triangles. To make a complete pair of similar triangles I have an unlimited pile ranging of lengths from 1-20 inches, for each similar pair of triangles I have to choose any two sticks from the unlimited pile. I have to find out how many pairs of triangle I can make.
Process:
While I was creating I had noticed that for every original triangle I had to have the sticks of 2 and inches on at least two sides of my triangle to form a correct similar triangle.
Starting out it took me about two or three times to really find out that by using those two lengths I was able to create similar triangles without repeating or using more than two of the same lengths from the unlimited pile on one triangle. I organized my results after I would find a correct similar pair that doesn’t create a copy of another pair by creating a “bank” of different pairs of similar triangles.
Solution:
After finishing my “bank” of similar triangles I ended up not knowing the amount of similar triangles because of all the possibilities of dividing some 2 etc or multiplying them by many different options.
A new problem:
I am obviously going say that you could try and find as many similar pairs with an unlimited pile ranging from 1-10 or 1-30. you could also try and how many similar triangles in groups of 3 like we practiced a little in class.
Evaluation:
First reading the problem I had a fear of not understanding the problem and doing it the wrong way since we hadn’t gone over this type of problem in class much at that point. As we went into it more in class I began to understand what ways I could create similar triangles and how I could approach the problem in a more informed way. I felt like it was academically worthwhile because as we learned it in class and I put it towards the POW I felt like I really understood the topic in a way that I can remember in further on. I felt like it was overall pretty easy as we learned more about it in class, I would score myself at a 22 because although I understood the process and topic I still couldn’t solve it completely.
Pow #1
Problem:
During this weeks POW we were given a problem that consisted of a three by three squared chess table. Inside the chess table two black nights are at the top and two white nights are at the bottom. Our problem is to find a way to switch these nights completely in the least amount of moves possible.
Process:
The first thing I did for this problem was I started to try and found out the starting coordinates on a sheet of paper. This felt like a waste of time to me because I had to erase everything if it didn’t work. I ended up using a whiteboard and by the time I got the correct start coordinates I would write them on a piece of paper. This was a great process for me because all I did was write the white and black nights on pieces of sticky notes. This helped me switch around the nights when I was wrong. Whenever I would find a correct coordinate I would write what the chess table looked like when it was a correct step on a separate piece of paper to show the correct step steps I took to solve the problem.
Solution:
My solution for this problem is that the least amount of steps I found was 16. I found this by how many steps it took for them to switch. I feel this answer is correct because my process was clear and I have gone over it several times and could not find any other step or process that can completely switch the pieces. Overall I feel my answer is correct because I could not find another possible process’s without messing up what I had already solved.
Extensions:
A good extension would be to try and find maybe a possibly smaller amount of steps to switch the chess pieces. Another good extension may be to be given a larger chess board and add more pieces and find the least amount of steps taken.
Self assessment:
During this assignment I learned that when given a very complicated problem there is a way to solve it. I think this because when I was given this problem I knew there was a way to solve it but I also thought it may be impossible because the small chess board. I also learned with a limited amount procedure and guidance you can figure it out if you take your time and use trial and error until you find the correct way to solve the problem. I feel like I had a hard time with this problem because I didn't budget my time well. I also felt this way because I was frustrated because of the amount of errors I had made during this problem. In the end I believe I did pretty well because I stuck with it until I found the solution. I believe I should receive a 30 out of 30 because I feel like I did a great job of making it clear of what steps I made in my diagrams to solve the problem and how I kept with this until I figured out the correct amount of steps taken.
POWs have helped me a lot by helping understand or apply my knowledge that I have learned in class. Pows let me stretch and use what I have been taught in class which helps me understand the content and help it stay with me further on in the school year.
Reed Frey
2/3/15
Pow #2 Pick up Triangles
Problem:
I have four sticks at different lengths 2,3,4,6 inches I have to use these four sticks in every pair of similar triangles. To make a complete pair of similar triangles I have an unlimited pile ranging of lengths from 1-20 inches, for each similar pair of triangles I have to choose any two sticks from the unlimited pile. I have to find out how many pairs of triangle I can make.
Process:
While I was creating I had noticed that for every original triangle I had to have the sticks of 2 and inches on at least two sides of my triangle to form a correct similar triangle.
Starting out it took me about two or three times to really find out that by using those two lengths I was able to create similar triangles without repeating or using more than two of the same lengths from the unlimited pile on one triangle. I organized my results after I would find a correct similar pair that doesn’t create a copy of another pair by creating a “bank” of different pairs of similar triangles.
Solution:
After finishing my “bank” of similar triangles I ended up not knowing the amount of similar triangles because of all the possibilities of dividing some 2 etc or multiplying them by many different options.
A new problem:
I am obviously going say that you could try and find as many similar pairs with an unlimited pile ranging from 1-10 or 1-30. you could also try and how many similar triangles in groups of 3 like we practiced a little in class.
Evaluation:
First reading the problem I had a fear of not understanding the problem and doing it the wrong way since we hadn’t gone over this type of problem in class much at that point. As we went into it more in class I began to understand what ways I could create similar triangles and how I could approach the problem in a more informed way. I felt like it was academically worthwhile because as we learned it in class and I put it towards the POW I felt like I really understood the topic in a way that I can remember in further on. I felt like it was overall pretty easy as we learned more about it in class, I would score myself at a 22 because although I understood the process and topic I still couldn’t solve it completely.
Pow #1
Problem:
During this weeks POW we were given a problem that consisted of a three by three squared chess table. Inside the chess table two black nights are at the top and two white nights are at the bottom. Our problem is to find a way to switch these nights completely in the least amount of moves possible.
Process:
The first thing I did for this problem was I started to try and found out the starting coordinates on a sheet of paper. This felt like a waste of time to me because I had to erase everything if it didn’t work. I ended up using a whiteboard and by the time I got the correct start coordinates I would write them on a piece of paper. This was a great process for me because all I did was write the white and black nights on pieces of sticky notes. This helped me switch around the nights when I was wrong. Whenever I would find a correct coordinate I would write what the chess table looked like when it was a correct step on a separate piece of paper to show the correct step steps I took to solve the problem.
Solution:
My solution for this problem is that the least amount of steps I found was 16. I found this by how many steps it took for them to switch. I feel this answer is correct because my process was clear and I have gone over it several times and could not find any other step or process that can completely switch the pieces. Overall I feel my answer is correct because I could not find another possible process’s without messing up what I had already solved.
Extensions:
A good extension would be to try and find maybe a possibly smaller amount of steps to switch the chess pieces. Another good extension may be to be given a larger chess board and add more pieces and find the least amount of steps taken.
Self assessment:
During this assignment I learned that when given a very complicated problem there is a way to solve it. I think this because when I was given this problem I knew there was a way to solve it but I also thought it may be impossible because the small chess board. I also learned with a limited amount procedure and guidance you can figure it out if you take your time and use trial and error until you find the correct way to solve the problem. I feel like I had a hard time with this problem because I didn't budget my time well. I also felt this way because I was frustrated because of the amount of errors I had made during this problem. In the end I believe I did pretty well because I stuck with it until I found the solution. I believe I should receive a 30 out of 30 because I feel like I did a great job of making it clear of what steps I made in my diagrams to solve the problem and how I kept with this until I figured out the correct amount of steps taken.
Tessellation Written Response
My idea behind my tessellation was that I just cut a shape out of construction paper and once I did that I just formed a person out of what I had. When I was cutting my shape out I didn’t really think about what I wanted to cut out I just thought of trying to make a cool shape. Then once it was cut out I didn’t have a shape that I could create into a figure so I just formed it into a person. During the construction of my tessellation I started with a square and then I cut it into random designs that I thought of right as I was creating them. But I cut my design on one side and it kind of looked like a mountain range, and on the other side it was just and triangle and then a flat surface. I then used the mountain range side and on the upper mountain I made an arm and on the lower one it was a foot, I did the same with the other side. On the head it was a half oval kind of shape and I created that to be a hat for the person on my tessellation. I think that tessellations are more art than math. I think because when you create a tessellation you are create a piece of art that you create out of your imagination. You create this with some guidelines of math to ensure that your shape fits together. When you create your own tessellation you have the choice to make it whatever you want and you can color whatever you want. When I was creating my tessellation I didn’t know what I was going to create and I just cut out a random design. When I cut it out I had no idea of what I was going to put in my shape and so I just created a person out of what I had. I think that when you are making art you have a piece of you that just can create stuff out of random things. As I was coloring I just added what I thought looked best and I don’t think that I needed math to do that. Even though are tessellations are more art than math we still need math to make sure our tessellation fits together correctly and that all corresponding angles add up to 360 degrees.
My idea behind my tessellation was that I just cut a shape out of construction paper and once I did that I just formed a person out of what I had. When I was cutting my shape out I didn’t really think about what I wanted to cut out I just thought of trying to make a cool shape. Then once it was cut out I didn’t have a shape that I could create into a figure so I just formed it into a person. During the construction of my tessellation I started with a square and then I cut it into random designs that I thought of right as I was creating them. But I cut my design on one side and it kind of looked like a mountain range, and on the other side it was just and triangle and then a flat surface. I then used the mountain range side and on the upper mountain I made an arm and on the lower one it was a foot, I did the same with the other side. On the head it was a half oval kind of shape and I created that to be a hat for the person on my tessellation. I think that tessellations are more art than math. I think because when you create a tessellation you are create a piece of art that you create out of your imagination. You create this with some guidelines of math to ensure that your shape fits together. When you create your own tessellation you have the choice to make it whatever you want and you can color whatever you want. When I was creating my tessellation I didn’t know what I was going to create and I just cut out a random design. When I cut it out I had no idea of what I was going to put in my shape and so I just created a person out of what I had. I think that when you are making art you have a piece of you that just can create stuff out of random things. As I was coloring I just added what I thought looked best and I don’t think that I needed math to do that. Even though are tessellations are more art than math we still need math to make sure our tessellation fits together correctly and that all corresponding angles add up to 360 degrees.
Tessellation project
How I Made My Tessellation
Tent Fire Lab
Tent Lab Questions
- The incoming and outgoing angle both are very very similar to each other.
- These two points are the shortest path because the camper does not have to run to the river on his way to the tent.
- The point river should be located in the middle or if not close to the middle of points Camper and Tent. The river should be located here to create equal paths from camper to the tent.
Snail Trail Lab
Snail Trail Reflection
This lab was a geogebra lab which used reflection of the points to create a connected grid of points on which they made corresponding trails. Each point moves with another. I noticed that all points move together to form a reflection of the other point. This project taught me how to use reflection to make a similar trail with another point.
This lab was a geogebra lab which used reflection of the points to create a connected grid of points on which they made corresponding trails. Each point moves with another. I noticed that all points move together to form a reflection of the other point. This project taught me how to use reflection to make a similar trail with another point.