Saturday, January 19, 2013

Polynomial Questions

Normally, I post questions like this to Twitter, but I need to use more than 140 characters to ask it. Please feel free to tweet me (@lmhenry9) your answers or post them in the comments. Thanks!

We are starting the polynomial unit in Algebra 2. I have some students who have graphing calculators. We do not have BYOD and cell phones and i-devices are not permitted in school. I have four computers in my classroom. We do have a computer lab, but there are not enough computers for all of my students to have access at the same time. Some students have access to computers at home. My district has about 55-60% of its students on free or reduced lunches. I have students of many ability levels in my classroom.

So, given that background knowledge... how would you deal with the graphing polynomials (and eventually exponential and logarithmic equations as well as rational and radical equations) with these students? Common Core says (from here):

  • CCSS.Math.Content.HSF-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
    • CCSS.Math.Content.HSF-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
    • CCSS.Math.Content.HSF-IF.C.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
    • CCSS.Math.Content.HSF-IF.C.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
    • CCSS.Math.Content.HSF-IF.C.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
    • CCSS.Math.Content.HSF-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude

    So, how would you do it? In the past, I have always used the graphing calculator as a part of the process. I have asked my principal for permission to use other devices in and she is thinking about it, but I am not confident I am going to get a yes answer. What would you do? Thanks for your thoughtful answers.


    Jimmy Pai said...

    I've done a couple of things in the past before. Here's one that might help?

    Students get a string (of various length), a paper with only the xy axis on (no scale).

    Students are instructed to think about the least number of tape (small strip each) they need in order to fit their string on the piece of paper.

    Once they agree on a number, they come to me to get it. Then they have to tell me about the properties of what they make. Each group has to present their product and show me what's going on.

    I've used this as a consolidating activity, but also as an intro activity. Hope that's helpful! I have done several other things before too, but I have to dig through my files to check.

    Let me know what you think via twitter at @paimath

    Simplifying Radicals said...

    I have to give some thought to your situation and don't have a suggestion for you right now.

    Have you heard of

    You could ask for donations of graphing calculators for your classroom. I have had two projects fully funded this school year alone. Many of the donations I received were from strangers. Good luck!

    Amy Gruen said...

    I have been meaning to comment on this for a while . . . I actually teach the majority of graphing in Algebra2 without graphing calculators. I don't have anything against them, but I don't have a classroom set. I think graphing by hand helps students have some intuition about what a graph looks like without grabbing for a calculator.

    I start the year by drawing the graphs of all the major parent functions by plotting points by hand. Students practice these quite a bit and end up memorizing their shapes and transformations.

    Later on, when they encounter an absolute value or quadratic or a radical equation, they can usually graph it by hand using transformations and solve it graphically by finding the x-intercepts. I like to have them do a graphical solution and an algebraic solution side-by-side.

    For more complex graphs, I will eventually use graphing calculators. (I will borrow some from here and there and some students have their own, but I do not have a classroom set).

    I haven't done trig functions in algebra2 yet, but I plan on adding it this year. I think I will take a similar approach, though. We will start by sketching the basic graphs of sin and cos by hand and then use transformations.