Pre-Calculus 11 Core Competency Self-Assessment

Core Competency Reflection

Working collaboratively with others  

This semester, I enjoyed and greatly benefited from group work. After each lesson, our class would split into groups to do “group work” questions together. I found that this practice enhanced my understanding of the topics covered in the lesson, as I was able to fill in the gaps in my comprehension of the lesson by asking my classmates who understood the lesson quite well. My group members explained concepts that I didn’t understand in a way that was helpful, kind, and constructive. I also explained concepts that I had grasped to classmates that needed help. Overall, group work was helpful to myself and my group in improving our understanding of the topics covered in class. 

Strategically preparing for assessments

This semester, I used studying practices that helped me to successfully prepare for assessments that I completed in this class. These practices included reading over the lesson notes published on OneNote, completing all assigned workbook questions, going to Flex or CENT time when I required help with a concept, and highlighting any mathematical vocabulary that I might need to know for the test. I also created a study plan a few days before the assessment day so that I wouldn’t be left cramming the night before the test. These studying practices helped me to retain the information taught in the course so that I could perform to the best of my ability on the day of the assessment. 

Managing time effectively

This semester, I managed my time effectively both in class and outside of class. In class, I was attentive during the lessons and group work. My goal for each class was to complete all or most of my workbook questions in class so that I could fully understand the concept. Most days, I was able to meet this goal. Outside of class, I booked flex and Cent blocks in Pre-Calculus so that I could receive help with workbook questions that I was struggling with or have extra time to work on a unit that I was moving slower than normal through. After school, I set aside time for studying, and completing workbook questions. Overall, my time management this semester allowed me to complete all assigned work to the best of my ability while leaving time after school for additional study time or other homework. 

Advice for Future Students

I have two pieces of advice for future students taking this course. The first piece of advice is to do all assigned workbook questions! They are very good indicators of what might be on the test, and they allow you to practice the concept over and over again until you get it. Also, don’t skip questions. Every single question has a small chance of being on the test. 

My second piece of advice is to ask questions. If you don’t understand a concept or even just don’t know why you’re getting a question wrong, it never hurts to ask the teacher or another classmate. Getting help shows that you’re not afraid to advocate for yourself. 

Transforming Parabolas

The equation of the Parent Function

The equation of My Function

DESMOS Graph

A graph of the parent function and my function

In my quadratic function, ‘a’, ‘h’, and ‘k’ all played different roles in creating the parabola.  

‘a’ determined the width of the parabola, as well as if it would open up or down. ‘a’ was positive in my parabola which caused it to open up. ‘a’ was also over the value of 1, so the parabola is more compressed than the parent function.  

‘h’ determined which way the parabola shifted horizontally. When ‘h’ is positive it shifts left and when it is negative the parabola shifts right. ‘h’ was positive in my function, so my parabola shifted to the left. ‘h’ determines the ‘x’ value in the vertex. It also determines the axis of symmetry for the parabola. In my function, ‘h’ was 1, so the axis of symmetry was –1.  

‘k’ determined whether the parabola would shift up or down vertically. When ‘k’ is positive, the parabola will shift up and when it is negative the parabola will shift down. ‘k’ was negative in my function, so the parabola shifted down. ‘k’ determines the value of the ‘y’ part of the vertex, as well as the minimum or maximum value of the parabola. In my function, the minimum value was 0. 

To conclude, ‘a’, ‘h’ and ‘k’ made my function different to the parent function by shifting it horizontally, vertically, and causing it to compress. 

Self-Assessment 

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

I used the graphing calculator to visually represent my quadratic function. I used this as a visual aid for the reader to refer to when reading my explanations of ‘a’, ‘h’, and ‘k’ and how they affected my parabola. These concepts were represented visually on the graph, and then explained in writing in paragraph form. 

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

In this assignment, I used mathematical vocabulary such as ‘positive’, ‘negative’, ‘shift’, ‘horizontally’, ‘vertically’, ‘quadratic’, ‘function’, ‘vertex’, ‘axis of symmetry’, and ‘minimum value’. These terms helped me to demonstrate my understanding of the vocabulary used in this unit. 

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

I used the colors red and green to emphasize the effects that positive and negative numbers would have on the parabola. This helps to establish clarity and enhance the meaning of the message that I am trying to convey. 

Facing a Challenge

A photo of the problem that was a challenge for me to solve. On the left side is the way that I solved the problem initially, and on the right is the correct way to solve the problem that I figured out.

The first time I tried this problem I found it challenging because I wasn’t sure how to factor the 9 out of the first square root. I was also intimidated by the combination of x with the negative sign and the two 9s in the problem, and I thought that factoring wouldn’t be simple in this case.  

Describe the mistake/problem that happened the first time you tried it. 

The mistake that I made was that I didn’t factor out the GCF properly and skipped a step. I ended up factoring the GCF out of both sides of the negative sign and transferring them out of the square root in one step, which led to an incorrect answer. 

What strategies did you use to figure it out?

When figuring this problem out, I initially tried the problem again, thinking I had made a small error. When I got the same answer, I asked Ms. Lam for help during my Flex block and she helped me to recognize my mistake. I took this new information and used it when I encountered similar problems in the workbook. 

Which concepts and/or skills did you need to be able to solve this problem?

The concepts and skills that I needed to solve this problem were factoring out a GCF, simplifying radicals, and adding and subtracting radical expressions. 

Next time I encounter a difficult problem, I might try watching a video on YouTube that goes over the concept so that I might identify the mistake I made by myself. I might also work backwards after looking at the answer key in the workbook.