Category Archives: Math 11

Pre-Calculus 11 Core Competency Self-Assessment

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Core Competency Reflection

Working collaboratively with others. This semester in pre-calculus, we did a lot of group work. I really enjoyed working with my group and I felt it helped me understand the math better. I thought it helped me because we all had different levels of understanding for each chapter. For example, a member of the group would have a good understanding of graphing linear equalities and explain it to the group members who didn’t understand the concept. This was helpful to me because when I didn’t understand something I could get it explained to me and different way then the teacher explained it. It was also helpful to explain the concepts to other group members. Explaining how to do the math helped me further my understanding. I think I did well communicating with my group when I didn’t understand or when I needed to help them understand. I also did well catching my group member’s mistakes and explaining what they did wrong. Overall, being in a group was very helpful to further my understanding of pre-calculus.

Managing time effectively. I felt that in the class, I kept focus on my work. I limited myself to distractions and really focused on finishing my work. This helped me finished all my work during class, so I didn’t have to do it after school. When I did get homework, I would try to do it right away in flex or CENT time. This helped me to not procrastinate and finish the work. When we had tests I would put aside time to study depending on my understanding of the chapter. I could also study in my first block after I finished my work, which I would do often. This was helpful because it kept my memory fresh as pre-calculus is my second block. I think time management helped me succeed in this course.

Committing to Individual practice. When I finished my workbook questions that were assigned I would often do extra questions to get extra understanding of the concept. I think this really helped push me over the edge of proficient to extending on most of my tests and quizzes. I would do this in class after I finished my work or in flex/CENT time when I had nothing to do. I think having extra time to do my work like flex or CENT time helped me in all my classes.

Advice for Future Students

My biggest piece of advice for students next year is to keep up with the workbook questions. Either if you missed a day or you didn’t finished in class it is important to not fall behind because this class goes fast. The chapters also build on each other, so keeping up is very important to understanding other chapters. I would also recommend doing the workbook questions as soon as they’re assigned to not procrastinate your work and fall behind. The work piles up and you will fall behind if you don’t do it right away. Learning the math vocabulary is also important. It may seem like you don’t need to know it, but it comes up on the test. It is an easy question if you take the time to know the vocabulary.

Transforming Parabolas

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My parabola:

Parent parabola:

Both Parabolas

The green line is the parent parabola and the blue line is the transformed parabola

My parabola:

Parent parabola:

The significance of a, h and k in my equation

Changing the a, h, or k in an equation will change the parabola. Changing the ‘a’ will either compress or stretch the parabola. The ‘a’ value being positive or negative will also change the parabola to either reflect the parent or point upwards like the parent. In my equation, the parabola became compressed and opens upward like the parent parabola. Since my parabola has a number farther away from 0 (4), the parabola becomes compressed smaller. The ‘a’ in my equation is also positive so it opens upwards just like the parent parabola. The ‘h’ in equations makes the parabola shift horizontally (across the x-axis). This makes the ‘x’ part of the vertex positive or negative. In my equation, ‘h’ made the parabola shift horizontally 3 to the right. This made the ‘h’ +3. The ‘k’ in equations makes the parabola shift vertically (across the y-axis). This makes the ‘y’ part of the vertex positive or negative. In my equation, ‘k’ made the parabola shift vertically 6 down. This made the ‘k’ -6. Overall my parabola changed from the parent parabola because it compressed, horizontally shifted to the right, and vertically shifted down.

Self-Reflection

Give an example from this assignment where you represented the same mathematical idea in multiple ways?

I represented how parabolas would change in different ways by using my parabola as an example as wells as explaining how other parabolas would change. I explained that parabolas could change positively or negatively and shift horizontally and vertically. I also used graphs to explain how my parabola changed from the parent parabola. This can help visually explain what is happening to the parabola.

Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding

I used words like compress, horizontal shift, vertical shift, and opens upwards to describe how my parabola changed from the parent parabola. This showed my understanding by showing that I knew what the vocabulary meant and how it looks in a mathematical equation.

Give an example from this assignment where you used formatting to share the information in a clear and organized way.

I used formatting like headers and bold words to share the information in an organized way. The headers made the information clearer to read and organized the questions into different sections. The bold words showed my understanding of math vocabulary and also allows the reader to pay attention to certain words. The bold words can make it easier to read the paragraph because it makes the important information clearer.

Facing a Challenge

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Correct solution
First attempt

The first time I tried this problem I found it challenging because there were a lot of steps needed to solve the equation. When doing this problem I had trouble knowing when to FOIL the equation. The mistake I made on my first attempt to solve the problem was that I FOILED when I didn’t need to. I thought that there was more than one term. I realized that I had made a mistake when it looked too complicated for me to solve. I checked the answer key and discover that I did not need to FOIL. I did not need to FOIL because there was only one term. After I identified my mistake using the answer key, I was able to correctly solve the equation. To solve this equation I needed the skills to FOIL, combine like radicals and cancel out the radical. Next time I encounter a difficult problem I will try to read the question carefully and try to identify the difference between multiple terms vs a single term.