## Geometry Skills

A topic that I feel that I mastered this semester is Triangles, especially in the Pythagorean Theorem. Why I believe that I have mastered this is because I feel confident in doing any problem that involves the Pythagorean Theorem. Some activities that helped me master the Pythagorean Theorem is practice on the explorations and the POWs

How the explorations have change my experience as a math student this year was by making me think on a deeper by expelling all the possibilities, reading and rereading them, and if all else fails asking for help. Explorations have made math class harder because they forced you to actually look at the problem and read it, as well as explore the exploration at home. How the Explorations and discussions have helped me learn was by making me more independent because i actually had to explore further at home and then be able to talk about how i went about solving the problem during discussions

I do not remember what exactly I've had a breakthrough on yet I do know that when you do, everything after it just fall into place and you suddenly realize that you do know how to do this. With math, when you know how to do it, it actually becomes fun and you look forward to solve it and then you crave a similar problem to solve that as well. Its the puzzle thats truly fun. How to have a breakthrough is to just keep on pushing through that problem, asking for help from multiple people and just reading it and rereading it (reading it out loud can help immeasurably) and when your teacher is explaining the problem, to just listen attentively because sometimes she can just say something and it clicks and you have that "OHHHHHHH" moment. What I learned from this was to just keep on pulling through a hard problem, because eventually it'll suddenly click and you'll get it.

**Describe one topic you feel you have mastered this semester. Describe the activities that helped you learn this activity (show 1-2 pieces of evidence). How do you know you have mastered this skill (show 1-2 pieces of evidence)? You should reference 3-4 pieces of evidence for this answer. Your evidence should be annotated and described, not just pasted on your DP.**How the explorations have change my experience as a math student this year was by making me think on a deeper by expelling all the possibilities, reading and rereading them, and if all else fails asking for help. Explorations have made math class harder because they forced you to actually look at the problem and read it, as well as explore the exploration at home. How the Explorations and discussions have helped me learn was by making me more independent because i actually had to explore further at home and then be able to talk about how i went about solving the problem during discussions

**How have the Explorations (and group discussions of Explorations) changed your experience as a math student this year? In what ways have they made math class more challenging, and in what ways have the Explorations and discussions helped you learn?**I do not remember what exactly I've had a breakthrough on yet I do know that when you do, everything after it just fall into place and you suddenly realize that you do know how to do this. With math, when you know how to do it, it actually becomes fun and you look forward to solve it and then you crave a similar problem to solve that as well. Its the puzzle thats truly fun. How to have a breakthrough is to just keep on pushing through that problem, asking for help from multiple people and just reading it and rereading it (reading it out loud can help immeasurably) and when your teacher is explaining the problem, to just listen attentively because sometimes she can just say something and it clicks and you have that "OHHHHHHH" moment. What I learned from this was to just keep on pulling through a hard problem, because eventually it'll suddenly click and you'll get it.

**Describe a moment when you had a breakthrough in understanding a challenging concept. What nurtured your breakthrough? How did this empower you in moving forward? What did you learn from that experience?**## Problem Solving Skills

Formulate a plan - anticipate major intermediate steps

Out of all the Habits of a Mathematician I feel I have the most mastery over formulating a plan. What this skill means is going over all the steps to reach an answer. To me it means finding a precise answer without making error, and if I do happen to make an error its really easy to find where I went wrong. I have demonstrated this skill most of my work. For example in POW 4 & 3 you can clearly see all the word that I did as well as my thought process. There weren't really activities that made me develop this skill, it was more of the teachers recommending that I should do it, me following through, and seeing that it really works for me. For example when learning the Pythagorean Theorem, we practiced doing the Pythagorean Theorem on many different triangles , doing the process over and over again to the pony where it was etched into our brains. How I have grown in this skill this semester was by writing out all of my work on all of my work until I was completely confident that I had mastered that skill.

- I always write every single step in my thought process
- some of my explorations or POWs

Out of all the Habits of a Mathematician I feel I have the most mastery over formulating a plan. What this skill means is going over all the steps to reach an answer. To me it means finding a precise answer without making error, and if I do happen to make an error its really easy to find where I went wrong. I have demonstrated this skill most of my work. For example in POW 4 & 3 you can clearly see all the word that I did as well as my thought process. There weren't really activities that made me develop this skill, it was more of the teachers recommending that I should do it, me following through, and seeing that it really works for me. For example when learning the Pythagorean Theorem, we practiced doing the Pythagorean Theorem on many different triangles , doing the process over and over again to the pony where it was etched into our brains. How I have grown in this skill this semester was by writing out all of my work on all of my work until I was completely confident that I had mastered that skill.

**Which Habit of a Mathematician do you feel you have the most mastery over? Explain what this skill is and what it means to you. Explain how you have demonstrated this skill, the activities that helped you develop this skill, and how you have grown in that problem-solving skill this semester.****You should reference 2-3 pieces of evidence for this answer. Your evidence should be annotated and described, not just pasted on your DP.**