![]() No previous knowledge of solving systems-by graphing, substitution, or elimination-is expected or required. Students should already be proficient at solving linear equations in one variable, and should also be familiar with graphing points and lines in the coordinate plane. The best method often depends on the structure of the equations involved.Īctivities in this bundle are designed to help students develop a conceptual understanding of systems of linear equations, with an emphasis on the graphical, numerical, and algebraic meaning of the solutions to those systems. There are multiple ways to solve a system, including: graphing, substitution, and elimination. Likewise, a solution to a system of linear equations can be interpreted in two ways: (a) graphically, as a point that lies on each line in the system, and (b) algebraically, as an ordered pair that satisfies each equation in the system. Search Follow A Best-Case Scenario on WordPress.Key Understandings A solution to a linear equation can be interpreted in two ways: (a) graphically, as a point on the line, and (b) algebraically, as an ordered pair that yields a true statement when substituted into the equation. Here is a graph of mine from Desmos, with only a little of the data: Play with the sliders and all the other features of this site.You can change the range of sliders by clicking the limits at the slider ends.You can type values in, even if you have sliders.If you leave parameters in the formula, it will ask if you want sliders.You can change the variable names if you want. Click the “<” button under the little panel, upper left, where you will eventually enter a function. Measure the long legs of the triangles as suggested on the handout.Download the PDF with the one-page handout.The draft of the book (link above) is free for now, but it occurred to me that you could do at least one activity (integrates trig, geometry, data, exponential functions) easily using Desmos’s cool new technology. To show how you can use the Desmos graphing calculator to do the graphing and calculation. ![]() How does the length of the “spokes” of this spiral depend on the spoke number? The idea of the book is that there are geometrical constructions that have relationships under them-usually a relationship about length-that you can model using a symbolic formula. Continue reading “Chord Star: Another Geometry-Function-Modeling Thing” Author Tim Erickson Posted on 29 January 2014 30 January 2014 Categories content, curriculum development, modeling Tags Desmos, geometry, mathematical modeling, modeling 5 Comments on Chord Star: Another Geometry-Function-Modeling Thing Modeling a Spiral, and enjoying DesmosĪt a recent meeting, I got to tell people about an old, non-finished book, EGADs (Enriching Geometry and Algebra through Data). Pick a point not near the center, but not too close to the circle itself. Oddly, it took a while to figure out what to plot against what to get a revealing function, but here we go. To that end, remember teaching geometry and that cool theorem where if you have two chords that cross, the products are the same? That’s where this comes from. So one strategy is, think of some theorem or principle, and see if you can find the relationship. And what I mean by that is, where do you have two quantities (in geometry, often distances, but it could be angles or areas or…) where one varies when you change the other. What does it take to turn something from geometry into a function? This is an interesting question in my explorations here I’ve found it helpful to look for relationships. ![]() Last time I wrote about a super-simple geometry situation and how we could turn it into an activity that connected it to linear functions.
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