Mathematics 3
So here's what we will be learning this year in Mathematics 3:
Here's some project we will be doing:
“Water is Life": In this interdisciplinary project, students will explore water issues and learn basic bioinformatics concepts and Python programming skills in order to identify the organisms present in a water sample. Students will also conduct an original research related to a water issue and summarize their findings in meaningful info-graphics.
“EcononME”: In this financial literacy project, students will plan for their financial future, and investigating how interest rates and compounding can affect personal finances, for better or worse.
Personally, I am really looking forward to learning concepts around finances- paying bills, taxes, loans.. etc. These skills we benefit us throughout the rest of our lives. For me, it can be frustrating and hard to learn something if I don't see the practicality or application of what we're learning. I am so much more motivated when I get why we're learning something. I feel that the topics I mentioned above are extremely practical and we will use those in our lives, there is no doubt.
An assignment we had at the beginning of the year was to say "I am a mathematician because...". Here is mine:
Emily is a mathematician because… Having an analytical mind will guide her the rest of her life. Emily feels that how one approaches math problems is how one approaches many problems in life and vice versa. When one faces a challenge, it is very helpful and beneficial to look at all the different layers and aspects of the problem. People may approach a problem in their life a certain way and realize that it wasn’t the best way. Then they go back and reexamine their approach of the situation. Many times one will need the support of friends, family members, or coworkers to guide them through the situation. Math parallels very well to this. One must obverse the problem from several perspectives to find the best way to solve the problem. People also benefit tremendously from others’ help, input and perspective, especially when going about an unfamiliar problem. Another parallel is that, both in math and life, one must persist through whatever obstacles come. It is easy to get stuck, but it’s what one does when they get stuck. Do they evaluate the problem from another angle or ask for help? Emily finds that what we learn in our classroom today can benefit us in many ways in several aspects of our lives.
- make sense of problems and persevere in solving them
- reason abstractly and quantitatively
- construct arguments and critique the reasoning of others
- model with mathematics;
- use appropriate tools strategically
- attend to precision
- make use of structure
- express regularity in repeated reasoning
Here's some project we will be doing:
“Water is Life": In this interdisciplinary project, students will explore water issues and learn basic bioinformatics concepts and Python programming skills in order to identify the organisms present in a water sample. Students will also conduct an original research related to a water issue and summarize their findings in meaningful info-graphics.
“EcononME”: In this financial literacy project, students will plan for their financial future, and investigating how interest rates and compounding can affect personal finances, for better or worse.
Personally, I am really looking forward to learning concepts around finances- paying bills, taxes, loans.. etc. These skills we benefit us throughout the rest of our lives. For me, it can be frustrating and hard to learn something if I don't see the practicality or application of what we're learning. I am so much more motivated when I get why we're learning something. I feel that the topics I mentioned above are extremely practical and we will use those in our lives, there is no doubt.
An assignment we had at the beginning of the year was to say "I am a mathematician because...". Here is mine:
Emily is a mathematician because… Having an analytical mind will guide her the rest of her life. Emily feels that how one approaches math problems is how one approaches many problems in life and vice versa. When one faces a challenge, it is very helpful and beneficial to look at all the different layers and aspects of the problem. People may approach a problem in their life a certain way and realize that it wasn’t the best way. Then they go back and reexamine their approach of the situation. Many times one will need the support of friends, family members, or coworkers to guide them through the situation. Math parallels very well to this. One must obverse the problem from several perspectives to find the best way to solve the problem. People also benefit tremendously from others’ help, input and perspective, especially when going about an unfamiliar problem. Another parallel is that, both in math and life, one must persist through whatever obstacles come. It is easy to get stuck, but it’s what one does when they get stuck. Do they evaluate the problem from another angle or ask for help? Emily finds that what we learn in our classroom today can benefit us in many ways in several aspects of our lives.
Mathematics 3 Projects
I think that projects in math really help solidify want we learn and why/how its important to us. It's simply another way for us to learn information and concepts. You're not just at a desk any more or being lectured to. You are actively going out and taking the concepts in, making them your own. It makes it real and applicable. It helps you understand why you are doing and how its important to you.
MatheMusic Video
- Description: For this project, we created music videos to teach math concepts. Music is a powerful and helpful way to teach concepts. Its a really good way to memorize information. In this project we were also grouped according to our gifts. This creates a balance of strengths that we have. If someone is lacking in one place, another person steps in and fulfills that role. If everyone were to have the same talents, then the project or production wouldn't be balanced. There would be one part that would be done really well, but there'd be a lot of holes and gaps, too.
- Process: First, everyone wrote down what strengths they had, what they were capable of and how they comfortable they felt with different math concepts listed. Then we were grouped according to that so our group would be balanced. Then, we were assigned the math concept our video would be about. Our group was assigned laws of exponents. We created a parody of "Girls Just Wanna Have Fun" to "Exponents Just Wanna Have Fun." Next, we collaborated to create a story board of how each scene and shot would play out. Then we went to start shooting and recording the song. Lastly, we edited the footage to create our final piece.
- Final Product: We are still in the process of putting this together. It will be completed by Monday.
- Reflections:
What accomplishments would you like to celebrate? (i.e., what you produced, what you learned and how you worked together as a group.) I know that I put in a lot of work in writing the lyrics and I helped with the general idea of the video. Like each of us, I had a part in the music video. I would say that I wrote a good chunk of the lyrics. I helped figure out all the laws of exponents that we needed to incorporate and helped put them into lyric form. I also helped with coming up with ideas or the music video. We very quickly came up with what the theme of the video would be. But we each had says to what shots we should do and what scenes specifically we’d do. I helped with getting the props we needed as well. I also did some of the editing which I am proud of. That’s not really my gifting. I can know exactly how I want it to look is one thing but actually making it happen is another thing entirely. I’m proud that I got to figure out how to work with iMovie and figure those things out. I do enjoy editing, it can just take a lot of time and patience. I’m proud of how we all worked together. I feel that in my group, we are all very dedicated and high achieving students and I;m not usually in groups like that. We all had a lot of ideas and each shared. We didn’t hog the air or slack off, though we encountered some difficulties. Over all I feel like we collaborated well. Each had a part and it couldn’t have been done without each other.
2) Did you contribute your fair share into the group? Was the work equitably distributed in your group? Explain. Yes, I definitely did, as I mentioned before. I feel that the project couldn’t be done with one of us gone. We all got along really well. We each had what we are gifted in and used that. No one hogged the spotlight or ideas. There was no one director, we each shared ideas and went with it. No one pushed and made people do anything or were bossy. It all worked out really well. There were times where someone maybe lead a little more that someone else but that went fine. We didn’t step on each others toes. We were open to ideas and weren’t hung up on our own. Everything seemed to work out well. We didn’t have to push someone to do their job, we all took initiative and did our part.
3) What could you have done better as an individual contributor to the group? What could your group have done better? I think as a group we could have planned it out better or more that we would go along with our script better. At one point we kinda lost our story board so that made it a little tricker. If we went stronger along with the storyboard that would have reduced stress and we could have managed our time better. We would have more details for the video and we would have come up with less last minute or on the stop. It would have been great if we didn’t run into any technical issues, but that happens and it all worked out. I think I can just trust the situation and people better. I stress and get overwhelmed easily and think the worst. I need to trust that things will work out and turn out well, even though it may not be exactly how I want or planned. I need to trust people too for the same reasons. I can take control easily, I didn’t in this project though. I need to trust that people will come through and I didn’t need to do their jobs. I need to let things ok and it may not happen how I want and that’s ok.
4) What lessons did you learn about group work that you would like to take to your next project group? Just because we’re not going with my idea(s) doesn’t mean will turn out badly. Other people have great ideas, maybe even better than mine. I can be prideful and think I have the answers and best ideas. I don’t and other also have great ideas. I learned to continually step back and let others push for their ideas and make things happen. I learned that its ok to be in the background for somethings.
5) If you had more time to work on this project, what would you do to improve your product so that it is representative of your best work? Some of the shots we did were blurry or shot on an iPhone and are not the greatest quality. I would go back and redo them with a better camera. Originally, we had ideas of doing more dance scenes and doing them with others- students, teachers, Mr. Isaac and Mr. Gooch. We didn’t do much of that because of time. I think that we’d say that we’d want to shoot more of those scenes. I think those are the main things. Also, if we wanted to have someone else sing the song, that may be good. We all recognize that the song doesn’t sound the greatest, which is fun and just part of the video. But it could be nice for it to sound good.
Art of Functions "Math-terpiece"
A mini project we have just recently wrapped up in Math has been one combing art, functions and graphing. For this project we took an image, any image, and recreated it on a website called "Desmos." This is a really helpful website/tool for graphing anything at all. We had just recently learned about many different types of functions and how to get them to look or shape the specific way we desired. We were using the knowledge and all that we have learned in the past few weeks of functions and graphing and incorporating it into a work of art, a visual masterpiece. The concept of this project was very interesting and I liked it, however I had previously completed a project very similar to this in 9th grade.
For my image, I chose a dragon, a simple black and one silhouette. The final products would be given to our second grade buddies that we have, as coloring pages. My second grade buddy loves drawing, especially dragons. I wanted to add that personal touch to this project. I also decided to work with a friend of mine, which meant that we would have to create this image on a canvas, as a physical art piece. This was no problem because we are both very skilled and gifted artists.
I found this project unique and interesting and enjoyed the process. It wasn't a stressful project and I didn't do all the work, as I was in a partnership. However, I think I would have liked the work to have been distributed differently. I focused all my efforts on creating the dragon digitally on "Desmos." My partner created the physical art piece. As much as I enjoyed creating the image through functions and found it beneficial to my learning, I wish that we had each put effort into both parts of the project. I personally feel that I put more effort on my part and spent more time on it. I think that I had the much more challenging part of creating the image on the graph. I am very pleased, though, with both final products. They underline our skills and are a good display of thorough and detailed effort. I am proud of what we created.
For my image, I chose a dragon, a simple black and one silhouette. The final products would be given to our second grade buddies that we have, as coloring pages. My second grade buddy loves drawing, especially dragons. I wanted to add that personal touch to this project. I also decided to work with a friend of mine, which meant that we would have to create this image on a canvas, as a physical art piece. This was no problem because we are both very skilled and gifted artists.
I found this project unique and interesting and enjoyed the process. It wasn't a stressful project and I didn't do all the work, as I was in a partnership. However, I think I would have liked the work to have been distributed differently. I focused all my efforts on creating the dragon digitally on "Desmos." My partner created the physical art piece. As much as I enjoyed creating the image through functions and found it beneficial to my learning, I wish that we had each put effort into both parts of the project. I personally feel that I put more effort on my part and spent more time on it. I think that I had the much more challenging part of creating the image on the graph. I am very pleased, though, with both final products. They underline our skills and are a good display of thorough and detailed effort. I am proud of what we created.
Slide Surveying- Write-Up
Slide Survey Write-Up
Problem
We had to focus on a slide from the elementary playground. Our goal was to calculate the height of that slide structure without physically measuring it. We used our knowledge of right triangles to solve for this problem.
Process
On the worksheet given to us, there was an illustration of a human a certain distance away from the slide structure. There were certain distances labeled, such as the length from the base of the human to the base of the slide. We could use this diagram to solve for the problem. The way I first approached this problem was to use the height of the human, which was known, to solve for the length from the base of the human to the base of the slide. We could use sine, cosine and tangent to solve for this length, by going and finding the angle of depression. We had different tools such as a measuring tape and an inclinometer. Our teacher came around to check on the ideas we had for figuring out the problem. She thought we had a unique idea, but it wasn’t quite what she was looking for. There was a way in our worksheet that she wanted us to use. I wasn’t entirely sure about my way to begin with, so I tried the way the worksheet guided us. There was another diagram on the worksheet. This diagram was a triangle. One point of the triangle was the slide, the other two points would be range locations that we would choose. This diagram was from a bird’s eye view.
We headed over to the playground, staying on the outside of the fence. After some struggles in our group of what exactly to do and for people to understand what and why we were doing it this way, we got started on our method. We chose two points on the ground, marking them with flags to stick in the ground. We measured the length between those two points. We also measured as best we could the degrees of the angles, from the ends of that length to the slide. We applied all this data to the diagram. I wrestled a lot with trying to find the unknown length we were trying to solve for. Part of me was still trying to wrap my head around the concept. I tried using sine, cosine, and tangent, as well as Pythagorean theorem, but I quickly realized that the triangle I was working with was not a right triangle. That really threw me off and I felt pretty stuck.
Our teacher suggested that we try to create a right triangle in the triangle. I tried this, but I didn’t get very far with it. The next day, after we had all wrestled with it, our teacher went over it with us.
Solution
Reflection
This problem was definitely a struggle, for everyone. I think that that was partly the point. Sometimes, we aren’t always supposed to have the correct answer or an answer at all. Sometimes, we can’t have the answer because we aren’t able to solve it with what we know. Sometimes we need to wrestle and get stuck and realize that there is something we still need to know. I think that that was the case for this problem.
I think that this mindset of not always being able to solve the problem right off the bat even with the tools you do have is a good one to have. This problem really got me thinking and stretched me.
Problem
- Describe the task and problem.
We had to focus on a slide from the elementary playground. Our goal was to calculate the height of that slide structure without physically measuring it. We used our knowledge of right triangles to solve for this problem.
Process
- Describe how you developed the plan to solve the problem
- Describe the procedures that you did to execute the plan.
- Describe the tools (physical and mathematical) that you used and how you used them.
On the worksheet given to us, there was an illustration of a human a certain distance away from the slide structure. There were certain distances labeled, such as the length from the base of the human to the base of the slide. We could use this diagram to solve for the problem. The way I first approached this problem was to use the height of the human, which was known, to solve for the length from the base of the human to the base of the slide. We could use sine, cosine and tangent to solve for this length, by going and finding the angle of depression. We had different tools such as a measuring tape and an inclinometer. Our teacher came around to check on the ideas we had for figuring out the problem. She thought we had a unique idea, but it wasn’t quite what she was looking for. There was a way in our worksheet that she wanted us to use. I wasn’t entirely sure about my way to begin with, so I tried the way the worksheet guided us. There was another diagram on the worksheet. This diagram was a triangle. One point of the triangle was the slide, the other two points would be range locations that we would choose. This diagram was from a bird’s eye view.
We headed over to the playground, staying on the outside of the fence. After some struggles in our group of what exactly to do and for people to understand what and why we were doing it this way, we got started on our method. We chose two points on the ground, marking them with flags to stick in the ground. We measured the length between those two points. We also measured as best we could the degrees of the angles, from the ends of that length to the slide. We applied all this data to the diagram. I wrestled a lot with trying to find the unknown length we were trying to solve for. Part of me was still trying to wrap my head around the concept. I tried using sine, cosine, and tangent, as well as Pythagorean theorem, but I quickly realized that the triangle I was working with was not a right triangle. That really threw me off and I felt pretty stuck.
Our teacher suggested that we try to create a right triangle in the triangle. I tried this, but I didn’t get very far with it. The next day, after we had all wrestled with it, our teacher went over it with us.
Solution
- Describe how you analyzed the data to solve the problem.
- Draw diagrams that clearly shows the information that you gathered and the information that you solved for.
- How close were you to the actual measurement of the slide structure? If you were off, explain what could have caused the difference between your calculation and the actual measurements?
Reflection
- What did you learn from this task?
- What did you like/dislike about it?
- Why is it relevant/useful to you?
- What questions do you still have about surveying and other applications of Trigonometry?
This problem was definitely a struggle, for everyone. I think that that was partly the point. Sometimes, we aren’t always supposed to have the correct answer or an answer at all. Sometimes, we can’t have the answer because we aren’t able to solve it with what we know. Sometimes we need to wrestle and get stuck and realize that there is something we still need to know. I think that that was the case for this problem.
I think that this mindset of not always being able to solve the problem right off the bat even with the tools you do have is a good one to have. This problem really got me thinking and stretched me.