Category Archives: Math 11

Pre-Calculus 11 Core Competency Self-Assessment

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Core Competency Reflection

This semester, I have focused on learning and using mathematical vocabulary, as well as working collaboratively with others. I demonstrated progress within these two topics when I reviewed the class notes multiple times in order to learn new proper math vocabulary. This occurred whenever I found myself stuck on a math question, so as a result, I would seek help through the notes and lessons. In order to comprehend the notes, I needed to make sure that I understood what words were being used in the lessons. After learning what specific words meant and what to use them for, I incorporated them into my personal vocabulary when figuring out or teaching others math concepts. Fully understanding these concepts and the vocabulary used in them helped me expand my ability to answer questions correctly, as well as teach peers how to solve them. The other topic that showed progress this semester is being able to work collaboratively with others. At first, I had to adjust to working with new people, and from time to time, I found it a challenge to communicate with peers I didn’t know very well. However, as I learned more about the math concepts and got more comfortable with my group members, I was able to have more efficient communication with them. In addition, as the semester went on, my teacher allowed us to pick our group members for group work. This allowed me to take a step further in communicating with my peers as I had picked to work with people I was previously comfortable with outside of math class. Even though at times it could be a bit distracting, I do believe this helped me expand my learning. While working in a group I was able to discuss the process of solving math problems through different perspectives. Some people would have strengths in specific topics while others struggled, so group work was a great opportunity for everyone to help each other better understand math. Throughout this semester, I have demonstrated growth in learning and using math vocabulary, as well as working collaboratively with others.

Advice for Future Students

My advice for future students is to not let workbook questions build up. This means, from the very beginning of chapter 1, you should try to finish all workbook questions in class before you go home. From my personal experience, I tried keeping up with the workbook homework pretty well in the earlier chapters but began to lose motivation and didn’t use my class time as wisely as I could’ve. This doesn’t mean that I just sat around doing absolutely nothing, but I would end up leaving most of my workbook questions to do at home. However, I’ve realized that this was not a sufficient way to prioritize my homework as outside of school, I have a very busy life. For instance, I have two jobs that I attend to after school and on the weekends. To add on, this semester, I have had all academic courses, meaning that I have no electives to give me a chance to catch up or take a break from the academic courses I find more challenging. Knowing this, I advise that you evaluate your priorities both in and outside of school, and figure out a stable way to manage your time to complete work. This means you should try your best to sign up for FLEX, CENT Time, or even come in before school starts so that you never fall behind in workbook questions. Falling behind in workbook questions causes you to fall behind in understanding each lesson. Workbook questions allow you to better understand a chapter and practice solving problems. Without doing workbook questions, you will fall behind drastically in the course, and find yourself lost, unable to answer questions. However, if you do complete all of the workbook questions in a considerable amount of time, you will most likely do significantly better on assessments.

Transforming Parabolas

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Parent Parabola Equation
My Given Parabola Equation
My given parabola and parent parabola graphed on DESMOS

The Significance of a, h, and k in My Equation:

Significance of “a”:

In my equation, “a” is represented as -1/2. Since the number is between 0 and -1, the parabola became wider than the parent equation. I know this value is between 0 and -1 because it is a fraction of “negative one half.” When “a” is in between the values of 0 and -1 or 0 and 1, the parabola curve expands wider. In addition, “a” is also a negative (-) number, causing the parabola to open downward on the graph. This is because whenever the “a” is a negative value, the parabola will open downwards and when it is a positive value the parabola will open upwards.

In this case, my given parabola equation consisted of “a” being in between 0 and -1 (also a negative number), causing the parabola to extend wider and open downwards.

Significance of “h”:

In my equation, “h” is + 7. It may be confusing when looking at the equation itself as it reads as +7, however, the “h” determines the x-value in the vertex which is actually -7. The vertex is (-7, -4). The +/- signs change when you plug -7 into the standard equation of y = a(x – h)^2 + k :

Plugging in -7 into standard formula: y = a(x – – 7)^2 + k –> y = a(x + 7)^2 + k

Demonstrated above shows how plugging in a negative number (-) with another negative (-) changes the value into a positive (+). This follows the rule of how two negatives equals a positive.

In addition, the “h” value also represent the horizontal shift of the parabola. In this case, for my given equation, the vertex of the parabola will shift 7 points to the left towards -7 from the origin of the parent vertex (0,0). This is because when the shift in a parabola equation is negative, it will shift to the left, and when it is positive, it will shift to the right.

Significance of “k”:

In my equation, “k” is represented as – 4. In any quadratic equation, the h value determines the y-value of the vertex in the parabola. In this case, my given equation shows that the parabola’s vertex is (-7, -4). The “k” also affects the vertical shift of a parabola. For instance, if it is positive (+) it will shift upwards along the y-axis, and if it is negative (-) it will shift downwards. In this case, my given parabola equation shows that the vertical shift will move down by 4 spaces on the graph.

What my given equation would look like without an “a” value:

y = (x +7)^2 – 4 :

The parabola is now opening upwards rather than downwards as it doesn’t have a negative “a” value.

What my given equation would look like without an “h” value:

y = -1/2(x)^2 – 4 :

Since there is no horizontal shift, the vertex’s x-value stays at 0. The parabola does not shift left or right. The vertex stays at (0, -4).

What my given parabola would look like without a “k” value:

Self-Assessment:

y = -1/2(x + 7)^2

Since there is no “k” value, the parabola will have no vertical shift along the y-axis. “K” resembles the y-value of the vertex so if there is no “k” the vertex will stay at (-4, 0).

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

While completing this assignment, I represented the same mathematical idea when demonstrating what my given equation would look like without the “a,” “h,” and “k” values separately in order to evaluate the differences and how each of these values affect the parabola in significant ways.

2. Give an example of this assignment where you used mathematical vocabulary to demonstrate your understanding.

During this assignment I was able to use mathematical vocabulary to demonstrate my understanding when explaining the purposes/significance/roles of each “a,” “h,” and “k” values. Specifically, I used mathematical vocabulary to explain the horizontal and vertical shifts of my given equation and they have shifted in that direction. In addition, I also used mathematical vocabulary when explaining why my “h” value/horizontal shift is represented as +7 when the x-value of the vertex (h) is actually -7. In order to explain why the +/- signs changed, I discussed how two negative numbers equal a positive, and I showed it by written formulas and bolding/colouring what numbers were being affected.

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

In this assignment, I used formatting to share the information in a clear and organized way by visual images, typed equations, bolding and highlighting/colouring important texts, etc. As a visual leaner myself, I found it helpful and easier to use DESMOS and screenshots to show my thinking and understanding revolving parabolas. I was able to use these images, as well as bolding/highlighting text to explain the significance of a, h, and k in my equation and also what the parabola would look like without/if I changed one of these values.

Facing a Challenge

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Section 1.5 – Question 6. j)

The first time I tried this problem I found it challenging because I had never attempted to solve an equation by adding two fractioned radicals without the help of a peer or teacher. The whole concept of working with radicals by themselves was still new to me so adding fractions to the equation made it a bit more challenging to solve.

During my first attempt at solving this equation, I was able to factor out numbers from the numerators and also the “x2” in the denominator of the second fraction. However, I got stuck when I had to make the denominators the same before adding the fractions together. This was quite a simple step that I had learned previously but forgot to do; in order to add fractions, the denominator must be the same – you can multiply the denominator and numerator by a common multiple so that both denominators from each fraction are the same. After completing and understanding this step, I made another mistake by adding both the coefficients in the numerator as well as the radicands in the numerators. This step is incorrect and led me to a false answer as when you add the same radicals with coefficients, you only add the coefficients and must keep the radials and radicands the same. This is because if a radical has the same index and radicand, you can add or subtract as normal. However, if they were different, you cannot add or subtract.

To find the correct solution and solve this question properly, I used a variety of resources. First, I reviewed my notes with my peers so we could all understand and figure it out together. The notes did help show where I went wrong, but I also consulted with my math tutor so she could fully explain why I was wrong and why the correct steps make more sense (more description).

In order to remember how to solve this equation, the concepts/skills I needed were that when you add fractions with radicals, you first need to make the denominators the same (by using common multiples). In addition, I needed to remember that when you add the radicals together, if they have the same radicand, all you do is add the coefficients.

Next time I encounter a difficult problem, I might try to use other strategies such as use the answer key to work backwards or watch a video on YouTube so someone can explain the steps to me and the reasoning behind them. All in all, I feel that the strategies I used to solve this challenging question were useful, helped me get the correct answer, and made me learn from my mistakes.