Newton Would Be Impressed

Newton’s First Law 

Unless acted upon a large enough force, an object in motion will stay in motion. In this example, the cart moves in a more or less straight line and will do so presumably forever. However, Jaya standing in the path of the cart acts as a strong enough force to stop the cart, as her mass is greater than that of the cart.

Considerations: If there are unbalanced forces present the object will not continue in the same path of motion. Jaya stood in the way and applied a strong enough force to stop the moving cart. Even if Jaya wasn’t standing in the way, the cart would have eventually slowed down due to friction between the wheels and the floor. 

 

Newton’s Second Law

Newton’s Second Law is built off of the First Law. It states that the acceleration of an object due to unbalanced forces will depend directly on the unbalanced force (referred to as net force) and inversely on the mass of the body. In other words, the more mass an object has, the more net force is needed to cause it to accelerate. The formula for Newton’s Second Law is a=F/m, where F is net force, a is acceleration, and m is mass.

Considerations: There was a force of friction between the wheels and the floor. This would cause the cart to slow down quicker for each situation separately. There is also friction present between the wheels and the surface of the cart; since each cart is only supposed to support one person. This would cause the cart to slow down much quicker in the second situation. 

 

 

Newton’s Third Law 

For every action, there is an equal and opposite reaction. This can be represented by the equation F1 = F2, or m1a1 = m2a2, where F=force (N), m=mass (kg), and a=acceleration (m/s2). In this example, the cart is pushed towards the wall, which it then hits. Upon impact, the cart is pushed backwards due to the equal and opposite force being exerted from the wall.  

Considerations: In ideal conditions, this cart would rebound off the wall with the same amount of force as it hit the wall and continue going in the opposite direction forever. However, this is clearly not the case because the cart does not travel at the exact same speed directly back to the pusher. This is due to the force of friction between the wheels and the floor acting on the cart after the point of impact with the wall, and potentially the inability of the wheels to quickly change direction of rolling. Also, if the wall had any elastic properties, the cart would experience less force on the rebound become some of the initial force would be absorbed by the wall.  

 

Tech Team Passion Project

a) Briefly describe your new and improved idea, by incorporating ideas and/or feedback.

The main focus of the Support Team is to provide tech support to anybody who needs it and maximise the use of technology in the school. This year, we would like to work on building up the general knowledge of school staff surrounding technology and teach them how to use programs that will be helpful in the classroom, as well as give them the resources and knowledge to teach their students how to use their digital devices effectively.

We would also like to inform parents and visitors to the school about the 1:1 program and all that entails.

 

b) Answer the following questions:

– What problems might I run into?

Most of the main goal will rely on teacher cooperation. It may be difficult to be able to set aside times to sit down with teachers and help with their familiarity with digital educational tools. All teachers will also have varying levels of proficiency with technology, so identifying the needs of the teachers regarding technology may be tricky.

– What skills do I need to complete this project? How can I attain these skills?

We will need to have a lot of patience and the working knowledge of programs that we will be teaching people. These skills can be acquired with researching programs that will be helpful in classrooms and figuring out the most effective ways to teach them, as well as working in the WAVE and always being opening to helping others with their digital devices.

 

c) Create a brief timeline of key things that need to happen to ensure successful completion of your project. What happens next?

The first step will probably be the upcoming Pro-D day where we will talk about the core competency reflections and how those will happen with Edublogs. If necessary, we can hold sessions for teachers on how to maximise the use of Edublogs (especially regarding new plug-ins), and proceed from there. What programs we intend to teach will depend on the school and what administration and the LIF team would like to see in classrooms. This may also be influenced from visiting delegations from other schools and companies who want to learn more about the 1:1 program.

Math11PCQuadraticFunctions2017

In this unit, we built upon what we learned in the previous unit about quadratic equations and learned how to analyse these equations on graphs, how to model quadratic equations on graphs, and how to interpret those graphs. 

My lifeline this unit has been the following key:

General form: y=ax^2+bx+c 

Standard form: y=a(x-p)^2+q

To convert between general form and standard form, complete the square (we learned how to do this in Unit 3.) 

a:

  • a > 1 = vertical expansion (becomes thinner)
  • 0<a<1 = vertical compression (becomes wider)
  • a>0 = minimum value (open up)
  • a<0 = maximum value (open down)

p:

  • p>0 = horizontal translation to the right
  • p<0 = horizontal translation to the left
  • p determines the x value of the vertex and the axis of symmetry

q:

  • q>0 = vertical translation up
  • p<0 = vertical translation down
  • p determines the y value of the vertex.

Math and Philosophy

This is actually from Semester 1 of Grade 10, but I read it again and I’m genuinely proud of it so I’m posting it here so it may be immortalized on the internet. 

The link between mathematics and philosophy was my entire inquiry project, so I apologize if you don’t read something incredibly profound about how math is actually grounded in unanswerable questions, just like philosophy. If you are looking for that, please see my inquiry project write-up. Instead, I’m going to go really in depth into specific mathematically philosophical questions.

Language is one of those human concepts that are simultaneously infuriating in its limits and exhilarating in its possibilities. I’ve often felt betrayed by the English language, as I search for a word that perfectly describes what I’m feeling, only to discover that it doesn’t exist. However, as a lover of literature, it’s difficult to stay angry for long. Humans are able to describe nearly everything in our visible universe, and we like to feel that we know everything there is that needs to be known, and then some. But that feeling doesn’t really matter to discoverers and inventors, so it inevitably always gets ignored. Us humans have the concept of infinity, defined as something with no ends and no limits. It just goes on and on and on (like me!), and it is impossible for humans to fully grasp this concept. We rely so heavily on physical representations of ideas, thus making complex concepts, like time travel and infinity, unimaginable to us. We can’t imagine something that doesn’t exist to us, and that is to be expected. So, why do we talk about the infinite so much, when it doesn’t even apply to us?

One perspective is the mathematical side. We use concepts like infinity in, say, graphing, because we logically know that there no boundaries to a function like x + 1 = y. We can represent this on a graph or in a table of values, but all the values of y are impossible to list, because they’re infinite. You can add one to any number an infinite number of times, and you will still get a possible y value. This concept also applies to fractions and negative integers, even irrational numbers. Pi plus one is just π + 1, shortened to 4.1415… Even irrational numbers, that we use so often in mathematics, go on infinitely! An irrational number is defined as a non-terminating, non-repeating decimal, therefore it goes on infinitely. We use these little infinities constantly: pi, phi, certain ratios and fractions. We also find these irrational numbers in nature – the Golden Ratio can be seen almost everywhere in nature, and is directly linked to the Fibonacci sequence. Therefore, this tells us that some form of infinity must exist outside of humans, that there are situations where never-ending and limitless concepts exist.

However, (there’re a lot of those in this little composition) we can also look at infinity philosophically. When we talk about something that never ends, we begin to erase the basic aspects of life itself – as morbid as it sounds, death and decay. If, for example, human beings were infinite, we would either never die or our bodies would never decompose. Either one. But then there’s the idea of souls, or some sort of aspect of humanity that is separate than the total sum of our parts. It is my belief that, if one were to completely clone a living person, give them the exact same memories and emotions as the original, you would still get someone completely different. This new person would not be the old one in all shapes and forms, but that missing aspect is unknown. I’m not sure if this missing aspect is infinite in its existence, but it’s definitely possible. We can also think about infinite time philosophically. Often, we ask ourselves if anything we do is worth it, if it’s all towards some purpose or if it’s even going to remain. Logically, we may know that whatever we make and everything we do will eventually disappear, but we don’t know when. Our brains are hardwired so that the idea of humanity perishing, of us just ceasing to exist, terrifies us. There’s the survival instinct, of not wanting to die, but we also don’t like the idea of putting all this work, effort, and time into the things we’re proud of, and thinking that they will have been for nought. I know I don’t like thinking about it.

Our brains tell us that time isn’t infinite, but science tells us that the universe itself might be. According to multiple theories, proposed by those much more educated than I, there are an infinite number of possibilities in an infinite number of dimensions in an infinite universe. This is described as the multiverse theory, and it gives a certain amount of hope that things are better somewhere in our supposedly infinite universe. Although, this also means that things are worse, but good and bad are all relative and depend on our definitions, so it’s inevitably a language issue, which I touched on earlier, and this whole mind-screwing idea is a topic for another composition. Anyway, according to this theory, literally anything is possible, and that sounds like something you’d see on a poster with a sunset in the background, but it’s also a mathematical goldmine. In inequalities that state x ≥ y, x can be equal to or larger than y, meaning x can be equal to almost anything other than y. However, if y is equal to negative infinity (-∞) x can be anything, including negative infinity. Because infinity (even negative infinity) is, you know, infinite.

Some infinities are larger than other infinities, but that’s per our current definition of infinity. This definition might change with more concepts introduced over time or more “mathematical evidence”, but it always just comes down to language and how we interpret it. When I think of the word “infinity”, I think of the multiverse theory. Other people might think of infinite time, of wormholes, of graphs. The thoughts that come into our minds when we think of infinity are, dare I say it, endless. Does this imply our own thoughts, the little electric shocks zooming through our brains at thousands of miles per hour, are infinite? Who knows? Why do we even care? If they are infinite, why? Why wouldn’t they be? I can come up with multiple answers to each of those questions, but none of them are definitive, which is really cool. This implies that even our most logical field, mathematics, isn’t definitive. It implies that current science isn’t definitive, and it’s all just theory, when you really think about it. Philosophy as we know it has managed to worm its way into every aspect of logic with its unanswerable questions, almost always beginning with “why”. Maybe this explains why we use “y” as a variable. Maybe it doesn’t, but that’s okay. (If the multiverse theory is to be believed, then there is a Sara who knows why, or has at least convinced herself that she does.)

I think what I took away most from these philosophical discussions in math class was accepting that sometimes there isn’t an answer, that math isn’t necessarily the say-all, do-all. It’s mostly about discussion and exploring all these ideas. Maybe it’s naïve of me to think about, but how much could we do if we acknowledged that not everything is clean-cut with a simple answer and a picture? If we did things out of pure curiosity (as I do most of the time), and because we think there might be a positive outcome? Is there any better way of doing things?

TechTeamEdublog

  1. What Widgets and Plugins did you choose?
    1. Calendar+
    2. Footnotes
    3. Image Widget
  2. What are their strengths?
    1. Online platform to keep track of school events, tests, homework assignments, etc.
    2. Great for students to keep track of their sources and where information in their work is taken from, or for those like me who tend to put little comments in their work and don’t like using brackets.
    3. Offers opportunity for additional customization to blog (which I needed more of). Very user friendly and can add multiple additional images
  3. What are their weaknesses?
    1. No way to sync it with normal Calendar widget to make upcoming school events, tests, etc. public to those who view the blog. Widget is mostly for personal use.
    2. In the published version of a post with footnotes, there’s a less-than-aesthetically-pleasing blue symbol at the end of each footnote.
    3. No opportunity to preview how image looks on site, or add additional content without the presence of an image.
  4. Can these programs be used in a classroom setting to enhance student learning? Would you use it and/or recommend it?
    1. It’s good for students who would like an easy-to-use online platform to keep track of all their upcoming events and due dates. I wouldn’t personally use it because I use my phone calendar to keep track of these things, but to each their own.
    2. It’s an excellent tool for sourcing work (helps students keep track of what they used their sources for, etc.). Would definitely recommend.
    3. I would recommend it to students who want to add a bit more flair to their blog, especially those interested in photography/art and would like to show their work on their homepage.

Math 11 Sequences and Series Blog Post

 

Arithmetic
General Term: t_{n} = a + (n-1)d
To figure out the value of any given term (t_{n}), a (the first term), d (the common difference), or n (the term in which a certain value appears).
Sum of Terms: s_{n} = [(a+t_{n})n]\div2
To figure out the sum of any given arithmetic series (S_{n}), n (the last term), or a (the first term).

Geometric
General Term: t_{n} = ar^{n-1}
To figure out any given term (t_{n}), a (the first term), r (the common ratio), or n (the term in which a certain value appears).
Sum of Terms: S_{n} = [a(r^n-1)]\div (r-1)
To figure out the partial sum of any geometric series if not given the last term, the last term, the first term, or the common ratio OR
S_{n} = (rt_{n} - a)\div (r-1)
to do the same thing, but if given the last term of the series.

You can have two types of geometric series: convergent (terms come closer together) or divergent (terms become further apart).
When you have a convergent series, the common ratio is greater than -1 but smaller than 1 (and cannot equal zero). Convergent series have infinite sums (the number in which the sum of all the terms converge at), which can be calculated with the formula S_{\infty} = a\div (1-r).
Divergent series don’t have infinite sums.

Langston Hughes, Poetic Genius

I think Langston Hughes wrote about the African-American experience of the early 20th century best because his poem, “The Negro Speaks of Rivers”, is directly emotional. It is a poem that is meant to be quickly understood, and the feelings within it comprehended by those who share the same struggle. Hughes wrote the poem in simpler language so his purpose isn’t lost in complicated vocabulary and allusion. In a few short lines, Hughes uses broad allusions and emotional phrases to emphasize a point. He conveys the emotions of his ancestors and the weight he feels from his own history, making “The Negro Speaks of Rivers” an incredibly powerful poem.

Photo 

When Men Find Comfort in the Land of Mice

When Men Find Comfort in the Land of Mice

The novella Of Mice and Men would be a fast-paced tragedy, arrival of the main characters quickly giving way to darkness, if it weren’t for how author John Steinbeck inserts long paragraphs with vivid descriptions of nature. This describing of forests, swamps, and animals tend to be the only peaceful points in the story, with every setting outside of nature plagued by distress and worry.

Steinbeck uses this method, of writing his story so that nature is almost synonymous with calm, incredibly well and, frequently, not so explicitly. One of the first scenes of the story features the two main characters, George and Lennie, lounging next to a pond as the day winds down. George begins to talk about a farm that he and Lennie will one day have, with “a big vegetable patch and a rabbit hutch and chickens,” (p.14). This dream is a recurring element of the story, with George detailing it multiple times throughout the novella and Lennie speaking about how he will get to tend the rabbits.

For Lennie, the farm is an opportunity for him to pet soft things whenever he pleases, but for George, it is something to look forward to. Typically quite angry, George calms down when he thinks of his farm (“[George’s] voice was growing warmer. ‘An’ we could have a few pigs. I could build a smoke house the one gran’pa had…’” p.57). After Candy’s dog is brought out to be shot, George eventually begins to talk about the farm, with Candy himself catching on to the idea: “We’ll fix up that little old place an’ we’ll go live there.’ […] They all sat still, all bemused by the beauty of the thing, each mind was popped into the future when this lovely thing should come about,” (p.60).

Aside from the farm, however, the nature in the character’s current environment of Soledad is a more physical source of refuge. After Lennie kills Curley’s wife, he runs to the spring where he and George first arrived. He kneels down and drinks the water, and Steinbeck sets the scene acutely differently to the chaos of the barn: “When a little bird skittered over the dry leaves behind him, his head jerked up and he strained toward the sound with eyes and ears until he saw the bird, and then he dropped his head and drank again.” (p.100)

But why did Steinbeck create an environment where the characters’ only salvation from their struggles is nature? It’s possible he was attempting to answer the question of what is man’s connection with nature. In Of Mice and Men, Steinbeck relates nature to a life without struggle, an outlet for serenity. Perhaps, nature is a way for man to detach himself from a life of hard-work with nothing to yield. Perhaps Steinbeck thought that the forests and ravines are places to go when in need of a refresh, a way to return to our roots. Regardless, it’s clear that the author instills a sense of importance to man’s unique connection with nature; despite consistently being deprived of it, nature is almost always a way for us to find salvation from the hardships of human existence.

 

Photo courtesy of: mtran on serendip studios.