Archive of ‘Grade 11’ category

The Crucible – Project Based Learning

This is an art project Gianna and I created based on The Crucible by Arthur Miller:

Guiding Question: How is manipulation within governments today similar to authority influence in the past? 

Manipulation is present in both The Crucible as a major theme, and today within our society. Although power, authority, reputation, and religion are all important themes that guide the story and our current world, we have chosen manipulation to be showcased in our art. We also included other meaningful references within our artwork, such as the coffee-stained paper, colour scheme, and torn background. 

In Arthur Miller’s The Crucible, manipulation plays a major part in the accusation of witches. Abigail influences others, including people of power, to make them think someone else is a witch when she is really the one to blame. This is shown in our art piece as people hanging from Abigail’s arms, as if she is controlling over them. The background also has a significant meaning, as it is pages from the novel torn and dyed to look like they were from the novel’s time period. This ties together with the other side, which has newspapers in the background talking about dictatorship in the world today. The highlighted words are important as they relate to our overall theme. A dictatorship is when the leader of a nation has complete control, and there is no freedom of speech or opinion within that society. Anyone speaking out against laws in this kind of country is punished, sometimes severely. Governments in Russia, North Korea, and some areas of Africa are a few examples of how minorities can be manipulated to believe a certain thing, leading to corruption, war, and violence. Examples of leaders who have done this are Kim Jong Un, his father Kim Jong-il, Vladimir Putin, Trump, and many others throughout history. Sometimes this thirst for control is simply based on the goal of gaining power though money. The control of news, propaganda and information can be a way to take over people’s minds and only input the information one wants them to read. This is seen in our art as people climbing up towards powerful leaders, as if they need them to survive. They are like zombies, who are manipulated and “brain-dead” to individualism. However, they are being deprived of freedom, individualism and rights. This is also common in a dictatorship when mass hysteria breaks out, and the dictator makes it seem as if they are the solution to the problem, when they actually caused it. This is exactly what occurred in The Crucible when Abigail says she sees “a bird” (114) to prove her innocence, convincing everyone of something that does not exist.  

What can we do to combat this problem? Changing some aspects of social media may help to remove bias on current events or government. Creating a website that is purely educational with no bias could be a solution for people to get updated, accurate information on an event or person. Raising awareness in the education system could also have a positive impact on teenagers, so they can grow up to make their own decisions rather than being influenced by the media. Staying properly informed as a provincial or national voter makes a major difference because each individual can vote for their personal choice of leader, not who they have been influenced to vote for by the media or other people. According to Insead Knowledge, “abdicating personal responsibility cripples’ freedom of expression and derails democratic processes” so to combat dictatorship we can also strive for a more equal democracy. This is possible through peaceful protests and large groups coming together to create change. 

In summary, manipulation is a major issue occurring in The Crucible, and currently today. Dictators can greatly influence people, depriving them of freedom of speech and making it seem like they must follow a certain leader or law. Our art piece depicts the feeling of manipulation in a way that both separates and combines the past and present. However, we can make a change today so that this no longer is a problem in the future. Through peaceful protests, proper elections, and equal democracy, society can become a place where rules are important, but do not take over freedom of speech. 



Chandra, Ravi. “How Political Leaders Strategically Manipulate US.” Psychology Today, Sussex Publishers, 12 Mar. 2020, 

“Dictatorship Countries 2022.” World Population Review,  

Kets de Vries, Manfred. “Fighting against Dictatorship.” INSEAD Knowledge, 18 Jan. 2018,  

Niiler, Eric. “How Dictators Keep Control.”, NBCUniversal News Group, 21 Dec. 2011, 

Poetry Talks – Allusion, Apostrophe, and Cliché

Here is the video Gianna and I created explaining Allusions, Apostrophes, and Clichés:


Allusions, apostrophes, and clichés are all literary terms commonly used in both everyday conversations and in poetry to bring a deeper meaning. Allusions in poetry are short references to something that is known to the reader or listener; an event, person, place etc. Allusions are a subtle hint at something meaningful and can bring a certain value or emotion to the writing. For example, “I’m listening to the king” alludes to the singer Elvis Presley. Apostrophes in poetry are not punctuation, but rather something that directs the attention of the reader to something else. They reference a dead or absent person, as if they were present. Apostrophes are like writing to an object, idea, or person that will not ever be able to receive it. An example would be the poem “Twinkle, Twinkle, Little Star”, where the star is being spoken to, even though it is an inanimate object. Finally, clichés are expressions or phrases that are overused and have therefore lost meaning over time. They lack creativity and can be annoying to the reader. For example, “it is what’s on the inside that counts”. This saying is a cliché because of its overuse in literature and conversation. 

I Can Statement Write – English Honours 11

As an English student, I would describe myself as someone who is hard working, creative, and often an over-achiever. I love to write both creatively and persuasively, always aiming to receive the highest mark I can. I strive to improve on my mistakes and I can act on feedback as something to work on in the future. My strengths in English include creative writing, as well as proper grammar and punctuation. I can analyze online or written sources to check if they are accurate or not. I also enjoy working in a group and can respectfully share my ideas while still listening to others, or helping them if they need. If I am passionate about something, I can pursue that interest and carry it into my writing as something of importance to me. This semester I would like to work on improving my skills of essay writing, specifically planning and organizing the points before writing the essay itself. I would also like to practice editing my writing so it is more concise and less wordy. Overall, I am excited to experience this semester of English and I look forward to every new skill I will learn.

TOP 5 Things I Learned in Precalculus 11

These are the top 5 things I learned this year in my Precalculus 11 class. I chose some of the most important topics from this semester that I didn’t know how to do in previous years of math. Below are the 5 topics with a definition of each, a few examples, and the reasons why I chose them as part of this blog post.

1: Mixed and Entire Radicals

Mixed and entire radicals are both forms in which to write a radical (root of a number). Entire radicals are simply the root of any numbers, written normally. Mixed radicals are a simplified form of these, where a number is multiplied by a root. For example:

Entire Radicals:

√3  √17 ∛44

Mixed Radicals:

2√7   3√5   2∛4

As you can see, the mixed radicals are usually smaller numbers, as they were originally large numbers that were distributed outside the root sign. To write an entire radical as a mixed radical, follow these steps. √45  –  find multiples of the number, with at least one square (or cube) root. Since 9 x 5 is 45, and 9 can be square rooted, these numbers will work. (If no multiples are squares, then creating a mixed radical is not possible). Find the square root of 9, which is 3. Put the 3 outside the root symbol, leaving the remaining number inside, which was 5. It now looks like this: 3√5   To go back to the original entire radical, multiply the outside number by itself, since the symbol is a square root (and not a cube or fourth root). This would be 9. Put it back inside the symbol and multiply by the number there  –  √9×5 = √45

Here is one more example, using a cube root. ∛16  –  find multiples that include a cube root. You could also make a factor tree for 16. Since 8×2 is 16, you can make this into a mixed radical. The cube root of 8 is 2, so put that outside the symbol: 2∛2   To go backwards, multiply the outside number by itself two times, because it is a cube root. This makes 8. Then put the 8 inside and solve: ∛8×2 = ∛16

I chose this topic as one of my top 5 because it was something unique I hadn’t learned about until grade 11. I found this interesting because if there is a question or answer with a root, you can simplify it to make it easier to read. Personally, I find math more straightforward if it is written in lowest or most simple terms, and this is one way to do that.


2: Rationalizing the Denominator

Rationalizing the denominator is helpful when there is a fraction with a root on the bottom. This technique puts the fraction into a simpler form, with an integer on the bottom instead. Here is an example of a non-rationalized fraction:

To rationalize the denominator, just multiply the top and bottom of the fraction by √3. Because you are multiplying the top and bottom by the same value, it is as if you are multiplying by 1. This doesn’t change the ratio of the fraction, it just makes it easier to read.

Here is a final example, where I have continued simplifying the fraction:


This skill was in my top 5 because it is a quick, easy technique that I find super useful. I still remember it today, even after learning it a few months ago. I also think it makes any answer look cleaner and easier to read.


3: Graphing a Parabola

This is something new that I only learned in precalc 11. A parabola is a u-shaped line that curves on a graph. I learned that every quadratic function or equation creates a graph of a parabola, with certain characteristics. Equations can come in standard, vertex, or factored form. Vertex form is the easiest to graph. It looks like this: y = (x – p)². This is an example of a simple equation in vertex form, and it’s resulting parabola. y = x² – 3

See the source image

The middle point, at the highest or lowest spot, is called the vertex. This is either at the top or bottom of the parabola. A parabola is symmetrical, with the axis of symmetry being in the center. Based on the sign (positive or negative) of the x², the parabola will open upwards or downwards. Here are a few other examples:

For the first graph, the equation would be y = -x². The negative means it opens downward. The vertex, or highest point, is at the coordinates (0,0), and the axis of symmetry is x = 0. The second graph below shows the equation y = -(x – 3)² + 2. The vertex is (3,2), and the axis of symmetry is x = 2. As you can see the -3 turned into +3 when finding the vertex. Make sure you switch to the opposite sign when finding the number for the x-coordinate in vertex form.

See the source image  See the source image

Parabolas are a new and interesting way of graphing, making them one of my top 5 things I learned. When I could see the relation between the equation and a graph, it made it much easier for me to read and understand a question because there was a visual.


4: Multiplying & Dividing Rational Expressions

This was one skill that I found really fun once I learned to properly solve the expressions. When multiplying and dividing these expressions, you can cancel out like terms, or terms that are the exact same. These terms must be either in both the numerator and denominator of the same fraction, or in opposite fractions, with one on the top and the other on the bottom. Here is an example showing the usual way to multiply fractions, which can take a while. Below it is a more efficient way, where the 4 is cancelled out to find the same answer.

Sometimes you have to factor an expression first, to check for any terms that can be cancelled out. Remember that terms in brackets are connected, and cannot be cancelled out unless another term in brackets is the exact same. For example, (x + 3) and x are not like terms, but (x – 4) and (x – 4) are. When you have cancelled out all like terms, always check to make sure a fraction cannot be simplified any further. Don’t forget to include restrictions on your answer (values that would be impossible because they would make the denominator 0). With dividing, just flip the second fraction to it’s reciprocal, and continue. These examples show more complicated questions:

This technique turns a complicated equation into a simple fraction, without having to do lots of difficult calculations. That is why I chose it for one of the top things I learned, because it is so simple and fun!


5: The Cosine Law

The cosine law is a way to find the angles and side lengths or a non-right triangle. This law is a formula which works for any non-right triangle where there are 3 sides and no angles, or finding a third side when 2 sides and the angle between them are given. The cosine law looks like this when you need to find a side:

To find an angle instead, just switch the same formula to this:

Here are 2 examples using the cosine law to find a missing side/angle:


This was one of my top 5 because I didn’t realize trigonometry was possible with non-right triangles before math 11. The cosine law makes it easy to find missing values on a triangle by putting them into a simple formula.

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