I decided to keep focusing on the fx-991EX Classwiz Scientific Calculator this week, since it’s one of my favorite calculators, in particular because of the added capability to show a visual representation through the QR code, which is something most scientific calculators can’t provide. Multiple representations are so important to helping students see relationships, recognize patterns, understand solutions, etc. Particularly to understand what it means to ‘solve’ an equation or system of equations – i.e. what does the ‘solution’ represent? Being able to see it numerically and visually is important for overall understanding. Especially if you are not just doing ‘naked math’, but have provided a context (problem-solving) for the functions/equations you are solving, where students really need to explain the solution in relation to the context.
With that in mind, I wanted to share a system of equations activity from the open-source curriculum, Illustrative Math, which has some great problem-solving tasks that allow students to apply mathematical skills, explain their thinking, and think beyond just skill-based practice. For this particular posting, to show how the fx-991EX can help support finding solutions and visualization, I searched the Illustrative Math tasks for simultaneous equations, and found the task Kimi and Jordan. This is a grade-8 task that provides information about two kids, Kimi and Jordan, who both earn weekly allowances and also work jobs where they get paid a certain amount per hour. The problem asks students to create a table that matches total earned to hours worked each week, and also to compare who is saving more money if they work the same number of hours. This last question really is the ‘solve the system’ question, but involves more than just a single answer, since there can be several answers dependent on the number of hours. This is where having the ability to both visualize the equations and look at the graphs and really explain what is happening in the context of the problem. What does the intersection of the graphs represent? When, if at all, would Kimi earn more? When, if at all would Jordan earn more. So, adding the context of the situation makes this a beyond skill-practice problem, since they have to explain their thinking and there isn’t just one solution (i.e. the intersection point). This a nice problem to use with a graphing calculator or dynamic math software, but also if you have the fx-991EX as your technology tool, you can do the multiple representations as well, including a visualization. Below are some images from the fx-991EX on this specific task.
I like this problem because it goes beyond a single solution for (x, y), and instead forces students to explain the different possible solutions based on hours worked. Real applications of mathematical skills require students to analyze, justify and understand that mathematics is just a way to model situations and help you make decisions.
Here’s the link for the activity on the Illustrative Math website, which also includes a discussion of the solution, and also a link to the Youtube video that shows you how to use the fx-991EX Classwiz to solve simultaneous equations and look at the visualization with the QR code option.
- Kimi and Jordan Task (Illustrative Math)
- Video How-To: fx-991EX ClassWiz Solving and Visualizing Simultaneous Equations
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