While working on the glucose solution lab, I effectively communicated with my partner to coordinate our tasks for setting up the beaker. My responsibility was getting the dialysis tubing, and my partner handled the string, and together, we skillfully tied the string to the dialysis tube. Collaborating on estimating and pouring 10 mL of the starch solution into the tube required teamwork and good communication.

Engaging in critical and reflective thinking was crucial throughout the experiment. I focused on finding the best technique to tie the string, ensuring no air bubbles in our cell. Submerging the cell in the beaker presented challenges initially, but pouring more water in the beaker proved to be a helpful solution. Upon observing the results after 24 hours, we identified a leakage issue with the glucose solution, likely stemming from not tying the knots tightly enough. This became a valuable lesson for improvement in future experiments.

The process of analyzing our findings involved critical thinking as we speculated on which molecules diffused in or out and which ones did not. Using reasoning and deduction based on our 24-hour results, I drew conclusions about the diffusion of different molecules. This experience not only honed our laboratory skills but also sharpened our ability to think critically and draw informed conclusions from experimental outcomes.

CORE COMPETENCY REFLECTIONS

Working collaboratively with others

In my pre-Cal 11 class, I always participated in daily group work, using my ability to collaborate effectively with others. Together with my classmates, we solved new math problems everyday, supporting and helping each other when we encountered difficulties. This approach approach improved my learning as it exposed me to different perspectives and problem-solving techniques. Through our discussions and shared insights, I gained a deeper understanding of the math lessons and discovered new strategies to solve problems. At the beginning it was hard to do group work and collaborate with my peers because I have never done that in math before, but then I noticed it really helped because when I was confused I had people who could help me. Overall, I really liked the group work sessions in our it not only bettered my teamwork skills but also enhanced my mathematical skills and enriched my learning journey.

Committing to Individual practice

To build my learning in math, I made a dedicated commitment to practice at hime. Consistently setting aside time outside of class, I engaged in focused independent study sessions. This time that I took for myself really helped me achieve a better grade, since I struggle with focusing in class. I used this method specifically when we were introduced it the graphing unit, I really struggled in this unit and couldn’t understand the lessons. But when i took the time at home ad watched YouTube videos, did more workbook questions, and reread the lessons it made a huge difference. Through these deliberate efforts, I was able to change my understanding of key concepts, strengthen my problem-solving skills, and improve my overall mathematical understanding. This practice allowed me to be more comfortable with challenging topics and gain confidence in tackling complex math problems, leading to significant growth in my learning outcomes.

Treating myself and others with respect

I consistently treated my classmates and teacher with respect by speaking to them kindly and listening attentively. I made sure to communicate in a considerate and respectful manner, and showing genuine interest in their thoughts and ideas. I think when learning math the its very important to be aware ad respectful to everyone. This is especially important because when learning math everyone works at different paces and understands concepts n a different way. So I was always respectful to everyone because of the way we all learn differently. By fostering a this environment, I encouraged open dialogue and I hoped to create a space where everyone felt valued. This respectful approach contributed to a good classroom atmosphere and making it a supportive learning environment for all of us.

Managing time effectively

I made sure to manage my time effectively when studying math at school. Whenever I felt confused, I set aside specific periods to focus on it. This was definitely my biggest obstacle in this course that’s why i want to talk about it. Honestly pre-Cal 11 is not as hard as its made out to be but the harder thing is time management, its easy to get confused in math really quickly. Not doing the workbook questions could be a big problem when we move on to a different lesson the next day. But through this course I learnt how to improve my time management and this was by making sure to finish work book questions everyday. By doing this, I could dig deeper into challenging concepts and problems. This approach helped me set clear goals for my study sessions and make the most of my learning time. Through effective time management, I established a routine that allowed me to address my confusion and make significant progress in understanding math.

ADVICE TO FUTURE STUDENTS

I think there’s a few things that next year’s students need to know. First is part of the core competency I talked about “time management”, time management is super important in this class because you never wanna fall behind . To mange your time always make sure to finish work book questions, study when you’re finished, and take the time to study ahead of the exams. My second piece of advice is to ask questions, sometimes a part of a lesson or problem just doesn’t make sense to you and that’s completely okay. Asking questions can completely open up your eyes and make sense of a chunk of a unit, so don’t be scared to ask questions! And my last piece of advice is to get to know your classmates, talking to your classmates can help because when you’re not understanding a problem they can’t can give you a new perspective to solve it. And when doing group questions you can also contribute to helping your classmates so you can all be successful with your learning.

Communication Skills

During the Titration lab, effective communication was key to successfully conducting the experiment. Given the need for accurate observation of the solution, we engaged in frequent discussions, sharing our observations and coordinating the addition of NaOH drops throughout the process. Through collaborative dialogue, we conducted multiple trials, refining our approach by exchanging ideas on how to achieve greater accuracy and effectiveness. By actively listening and articulating our thoughts clearly, we seamlessly executed the titration lab.

Critical thinking skills

In addition, our critical and reflective thinking abilities played a significant role in achieving our desired outcome in a comprehensive manner. As we encountered challenges and encountered unexpected observations, we engaged in critical thinking to analyze the unforeseen outcome. Throughout multiple trials, we engaged in reflective thinking by drawing upon our past laboratory results, utilizing them to enhance the accuracy of our procedures and ultimately obtain the best possible result. We diligently evaluated the data, identified sources of error, and made efforts to prevent the recurrence of such mistakes in future endeavors .

Curricular Competency Explanation: 

Cover the following points in one paragraph. This will take the place of a conclusion for your lab write-up. 

• What is a titration? 

A titration is a laboratory technique used to determine the concentration of a substance in a solution by reacting it with a known concentration of another substance (titrant). The reaction is usually a chemical reaction that involves a measurable change, such as a color change or the formation of a precipitate.

• What was a titration used for in this lab? 

In this particular lab, the titration was used to determine the concentration of an acid or a base in a solution. The titrant, which is a solution of known concentration, was slowly added to the solution being analyzed until the reaction between the acid and base was complete. By measuring the volume of the titrant required to reach the endpoint, the concentration of the unknown acid or base could be calculated.

• What is the endpoint (or the equivalence point) of a titration? 

The endpoint of a titration is the stage where the stoichiometrically equivalent quantities of the reactants, in this case, NaOH and HCl, have been combined. It signifies the completion of the reaction. At the endpoint, the NaOH and HCl have reacted in the precise stoichiometric ratio required for the reaction to reach its conclusion.

• How do you know that you have reached the endpoint of the titration? 

If phenolphthalein is specifically used as the indicator in a titration, the color change at the endpoint would be from colorless to pink. Phenolphthalein is initially colorless in acidic solutions, but as the titration progresses and the solution becomes more basic, it undergoes a distinct transition and turns pink, indicating the endpoint of the titration.

• What is a systematic error of this lab? 

Two systematic errors can occur in titration experiments when using phenolphthalein as an indicator. The first error involves the pH of phenolphthalein, which is ideally expected to be 7, but can sometimes measure at 8.2. This discrepancy can result from impurities in the indicator solution or inaccuracies in pH meter calibration. The deviation in pH can lead to inaccuracies in determining the endpoint of the titration and calculating concentrations. The second error occurs when the color change observed during the titration is excessively pink. This can make it difficult to accurately identify the endpoint, potentially leading to errors in volume measurements and concentration calculations. Minimizing these systematic errors requires precise calibration of the pH meter, high-quality indicator solutions, careful observation of color changes, and conducting multiple trials to ensure consistent and accurate results in titration experiments.

I can think about different issues in the world and make a project reflecting the problem, to create awareness for my social awareness assignment. 

I had to think about the different important issues in the world and pick one I could accurately represent. I picked drunk driving because I think its an issue that not talked about enough and I made a video about it. It’s a very important issue because thousands of drivers in Canada get into drunk driving incidents and its important to me to lower those numbers. It’s a issue not talked about enough until it happens to someone you love, and I want to change that. I want my Ad to evoke sad emotions to urge viewers to make responsible choices. I also promoted alternative options such as taking a cab home. I wanted to show a  relatable story because I wanted to show that it can happen to anyone. I also used split framing to show the story where both these relatable individuals are having the same story but then showing how drastically their life could differ with a simple choice, driving drunk vs picking a responsible alternative. 

Parent function -> 𝑦=𝑥^2

Vertex : (0,0)

Axis of symmetry : x=0

x intercept(s) : (0,0)

y intercept(s) : (0,0)

Domain: all real numbers

Range: y≥0

Minimum Value : 0

My equation -> 𝑦=4(𝑥+1)2−2

Vertex : (-1,-2)

Axis of symmetry : x=-1

x intercept(s) : (-1.7,0) (-0.29.0)

y intercept(s) : (0,2)

Domain: all real numbers

Range: y≥-2

Minimum Value : -2

COMPARISON

There’s plenty of ways where the parent function is different from my given equation and I will explain the different ways my parabola was transformed.

Starting with the “k” which transforms the parabola because it effects the vertical shift of the parabola .The value for my equation the “k” value is -2 which means the parabola shifts down by 2 as seen in the picture. This is different from the parent function because it doesn’t have a “k” value therefor the parabola doesn’t shift up nor down. Next, the “h” value for my equation which effects the horizontal shift of the parabola, in this case it’s +1 this means that the parabola shifts 1 to the left. This is different from the parent function because there is no “h” value in the equation therefor the parabola doesn’t shift to the left nor right, Also if my coefficient was -4 instead of 4 the parabola would flip upside-down but since its positive it shares something with the parent function in which both parabolas are going up. Finally the parabola from my equation is more compressed than the parabola of the parent function, this is because the bigger the value of the coefficient the more compressed the parabola will be, so since the coefficient 4 from my equation is bigger than 1 the coefficient from the parent function it explains why its more compressed.

SELF REFLECTION

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

I represented the same mathematical idea with a visual representation, written, and numerically. First I used a visual representation by going to Desmos and plugging my different equation. My given equation and the parent function each had their own visual parabola, and then a separate one with both the parabola together for comparison. Then I wrote a paragraph about how the 2 different equations of the graph affected the difference between the parabolas. And finally to show the differences numerically I wrote the different components (range, domain, vertex, etc. of the 2 different parabolas under both graphs

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

I used mathematical vocabulary when in my paragraph where I was explaining the difference between the 2 parabolas( vertical shift, horizontal shift, parent function, compress, transformation, coefficient.) I also used mathematical vocabulary when I was describing the different characteristics of the 2 parabolas. ( y intercept(s), vertex, axis of symmetry, x intercept(s), minimum value, domain, range.)

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

I made the key titles bolded so it would be easier to read and more visually pleasing. I also made sure my different graphs were cropped properly and easy to see, and finally made sure my paragraphs were neatly spaced.

1. The variable “4” affects the steepness of the parabola. Specifically, the larger the value of “4”, the more compressed the parabola will be, and the smaller the value of “4”, the more stretched the parabola will be.
2. The variable “(x + 1)” represents the horizontal shift of the parabola. Specifically, the “1” in the expression “(x + 1)” means that the vertex of the parabola is shifted to the left by one unit.
3. The variable “2” represents the vertical shift of the parabola. Specifically, the “2” in the equation means that the vertex of the parabola is shifted upward by two units.

Overall, changing the values of these variables will change the shape and position of the parabola. For example, increasing the value of “4” will make the parabola steeper, shifting the vertex to the right of the origin will move the entire parabola to the right, and increasing the value of “2” will shift the entire parabola up.

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

I represented the same mathematical idea in 3 different ways. I represented the math equation i got by putting it into a graph and having a visual representation. Also the equation itself is a representation of the different elements of the graph. And finally I talked and explained how each part of my equation effects the graph ion my own words.

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

I used mathematical vocabulary when explaining how the different value of “a” whether it be a bigger or smaller value contributed to the graph being “compressed” or “stretched”. I also used mathematical vocabulary when explaining how the “h” and “k” value of an equation can determine the vertical or horizontal shift of the parabola.

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

I went on canva to try to project my understanding in a fun and organized way, but found it to be difficult to use. In the end I shared my information by pointing arrows to the two different graphs and also sharing my understating of the different values of an equation and how it can effect the parabola in steps.

1. Include your answers to the following questions in your reflection: 

1. What is your Inquiry Question? Has the focus of your inquiry shifted or changed since you wrote your Personal Learning Plan? Explain. 

My Inquiry question was “Can I build my dream house” but Im shifting in a new direction and changing my question to “ How many new skills can I learn by may and which one is the hardest” I realized I wanted to learn more like ASL, cooking, ect 

2. How is your time management? Are you using CENT time weekly to work on your Inquiry, or are you finding other time during the week? 

So far time management has been hard. But from now on I’m going to be focusing on learning a new skill each week and using Cent time especially for that process. 

3. What resources (people, websites, apps, videos, etc.) have been most helpful? 

Using Pinterest and YouTube has been the most helpful in learning and getting inspired. 

4. What challenges are you currently facing with your Inquiry? What challenges have you overcome? 

Challenges Im faciong with my inquiry is finding time to work on my inquiry. I am now trying to overcome this by catching up and getting my work done and organized. 

5. Describe your growth of a Core Competency through this inquiry process. 

I used my critical thinking skills when I was using SketchUp and had difficulty using the program, I looked on YouTube and used my thinking to build my project. 

6. How will you share what you have been learning, creating or planning in this Inquiry? Are you on track to share your learning by the end of May or early June? 

I’m still not quite sure if I can finish this by may but maybe by June. Ill present my project through PowerPoint. 

7. Will you continue working on this Inquiry, or parts of it, for your Capstone next year? 

Maybe, I’m hoping that through learning different skills I will find something I’m passionate about and further explore it next year. 

When I first tried to solve this problem I kept making small mistakes and never ended up getting the correct answer. This question may look very easy but when there’s a lot of small details it’s easy to mess up. The first time I encountered this problem I multiplied the the first radical by 3 to match the second one, but this is a mistake because I didn’t think of the of how a square root has a two in front of it, therefor both radicals would both have to be multiplied by the least common multiple between 2 and 3 which is 6. My second mistake was not multiplying the exponent inside the radical, I thought just multiplying the number outside the radical was the correct way to do it. After a lot of trial and error I figured out the equation, I also read the book about this chapter and it truly helped me understand the rules of solving this equation. After I solved this question correctly to make sure I understood the concept, I did a lot of similar questions in the workbook.

The main skill I used to solve this problem is Critical Thinking. I think Critical Thinking is generally really important when it comes to math because you will encounter a lot of problems, and have to use your thinking skills to try to think of new ways to get through the equation. When tried this problem as I said I made a lot of mistakes but from my mistakes I slowly realized where I was going wrong and what I was doing right which led me to get the correct answer.

In our groups we were supposed to tape a slinky to the table and track its wave patterns. Group work was important for this project because it was difficult task, and collaboration was important because we all had different levels of understanding. As you can see from my work, I am aware of the distinction between collaboration and straightforward “group work.” When my group ran into trouble, I worked with other groups in addition to talking and solving the issues within my own. When flustered I thought of solutions for our group that would continue our research.    In this lab, we had to sort everything out amongst ourselves, thus it was a perfect opportunity to practice my groupwork and critical thinking skills.