I always favor teaching as much about the connections between the functions/equations and their graphs, so I agree with Glenn on that. Michael Paul Goldenberg Octoat 10:22 pm.That’s what I get teaching topics for the first time. I don’t know that I have the grasp on this conception of polynomials and rationals to teach it well, but I really like it. I think I may introduce those big ideas to start, and then move deeper and deeper, reasoning through end behavior and other interesting properties, linking polynomial and rational functions together whenever possible. It seems like two big ideas at the heart here, which will echo through calculus, are that factored terms in the numerator are zeros, factored terms in the denominator are vertical asymptotes, and factored terms that appear in both the numerator and the denominator are removable discontinuities. Link here.Īs a side note, I’m unconvinced that polynomials need to come strictly before rationals. In Desmos Activity Builder, students graph a number of functions that meet specific criteria. Equations are written in a variety of forms - some standard, some factored. Each card is either an equation, a graph, or a few statements about the function. Students label each as always true, sometimes true, or never true, and justify their answer.
Link here.ġ0 statements about polynomials. Students open a Desmos graph and record characteristics of 8 different polynomial graphs written in standard form.
Graph 6 polynomials written in factored form, with linear and square factors, using technology if students find it helpful.
COMPOSITE FUNCTIONS DESMOS ACTIVITY HOW TO
I’m not sure how to order them, and what instruction to give before, during, and after the tasks. Here are five tasks that I have for students to work through. We just wrapped up some time working with function transformations, composition, inverses, and touched on even and odd functions, as well as plenty of time on quadratics. Most also don’t remember polynomials very well. I’m moving into graphing polynomials in one section of Pre-Calc.
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