Everyone would want the power to predict the future. Just imagine, you could calculate the exact amount of money you need for that dream house you’ve always thought about, find a place that will be the perfect temperature for a vacation in 20 years from now, or even predict and help avert disasters. Surprisingly, you actually can do this in real life, and no, you don’t need magic or a radioactive accident. All you need, is a small but powerful equation, and a graph. Want to learn more? Then read on about our latest Scimatics Unit, Flow Like Water.

What is a Linear Equation?

A linear equation is pretty much self explanatory. It is an equation, which through the use of two variables, can connect and predict the future of linear trends. We learned a little about them last year, but what made this time different, was we dove a lot more in depth into the concept of functions:

Functions can be something such as the rate of money you earn per hour, where each time that an hour (the independent X variable) is put into the function, money (the dependent Y variable) is put out. This rate of change will stay consistent no matter how high the variables get, until something new occurs with the trend, such as in the example of hours = money, a raise. When a change occurs, you will need to create a new function to model it. Now you may be wondering, well what happens if there is other data in the equation, such as going back to the previous example, a Christmas bonus? Well, if you want to include data that does not alter a function, or are planning to plot your findings on a graph, you need to use…

Slope Intercept Form

Slope Intercept Form is an equation which uses the slope of a line (M), the Y intercept (B) and the independent variable to determine the dependent Y value. It is drawn out as you can see below:

Using the slope intercept form can also help you locate points on a graph, which is shown in the example graph for the rate of a glacier melting vs time below:

Our Project

Now that we understood the tools of predicting the future, it was time to actually get onto doing it. Our project for this unit was to research a body of water around the world that is experiencing a linear trend of change (increasing, decreasing, heating up, cooling down, etc), and then graph it to find a point of no return where the damage would cause a significant downfall. My partner Alivia and I chose to do the Canadian Great Lakes for our water body, and the results we found were shocking:

Keep in mind that this linear rate of change will most likely shift in the future due to global weather patterns and the extent of the damage from climate change.

Reflection

Science, math, or something in between; all projects teach us something valuable. During this brief unit, our project work and what we learned from our worksheets has been quite valuable in the sense of utilizing curricular competences, and developing new skills. Here are the four main mathematical curricular competencies I feel I have demonstrated most during this project:

Explore, analyze, and apply mathematical ideas using reason, technology, and other tools.

From day one to the time of our presentation, Alivia and I utilized, explored, and analyzed mathematical concepts in a variety of ways. Starting off with the research segment of our project, I used the tool of checking diverse sources to make sure our graph’s data was accurate. We recorded data from six total sources, along with checking each other’s previous work to make sure we understood the material. Next, when we had our data, we used the tool of keynote to create mock graphs (graphs with only 2 rough data points) to help us analyze and predict the potential impact of the rising water. This then lead us to creating our final graphs in Desmos, where we ran into some problems finding that most of the lakes did not have specific elevations points listed online. To fix this issue, we looked at the general elevation from the shore to a few KM inwards, and applied logic and an online map tool to best predict the elevation of our locations.

Apply Flexible and Strategic Approaches to Solve Problems

During this project, my partner and I solved problems both inside and outside of the felid of mathematics, and in our own workspace. When we first began searching for a body of water, we quickly realized that there were limited articles that could be found by looking up “bodies of water with rapid rate of change”. To solve this, we decided to think flexibly and change our approach, looking up general water data instead, and drawing our own conclusions about rates of change. At one point, I was also confused by the term function and how it related to the slope intercept form equation, which caused some issues in my overall grasp of the unit. However, looking back to the point I had made in my PGP about learning by doing, I decided to try once again thinking flexibly by conceptualizing what a function is with concrete examples (such as thinking about hours = amount of money), and this helped wonderfully. Finally, as the due date approached and I realized that I would not have time to complete our project’s original vision, I used the competency once more by thinking strategical about what the point of the project was, and focusing only on the most important aspects.

Represent Mathematical Ideas in Concrete, Pictorial, and Symbolic Forms

Our project showcased numerous examples of mathematical concepts depicted in a variety of ways. For one, we used a variety of graphs to model a variety of slope intercept form equations (1 for each of the lakes). We also demonstrated how a function worked with a pictorial example of X values producing Y values, which then supported our later example of our slope intercept form equation. Throughout our presentation, we also represented our mathematical data through pictures of it’s effect, such as the picture of the flood damaged town of Bridgman which was effected by the rising water levels demonstrated on our graphs.

Engage in Problem Solving experiences connected with place, story, cultural practices, and perspectives relevant to local First Peoples communities…

What I feel made our project stand out was the connections it made to the local environment, communities, and First Peoples of Canada. Instead of just listing the rate of change of a body of water, we explained in great detail the harm that this change will cause, and gave examples of where the damage is already occurring. We also used this to problem solve, and came up with examples of ways that we in Vancouver can help to prevent similar issues. Throughout our presentation, we made connections to the First Peoples of the Great Lakes area as well, stating how the lakes are an important part of their travelling history, and that changes to them may result in a loss of these historic routes.

Here is my Unit End Mind Map, which outlines my overall journey of learning for this unit: