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Mathematical Repesentations, Part 2

If I examine every other entry, starting from the first, I get 1.047..., 7.330...,  13.613... This sequence has a common difference of 6.283 or 2*pi. Likewise, the other sequence has 2.094..., 8.377..., 14.660... These terms also have a common difference of 2*pi. I am now in a position to write the two solutions as X=pi/3 + 2*pi*n or X=2*pi/3 + 2*pi*n, where n is any integer.


I can return to Symbolic view now and enter both Y=sin(X) and Y=sqrt(3)/2 (Figure 6). In Plot view (Figure 7), I see the larger context. I can use this in my next lesson.


Blog6.png     Blog7.png

                                                 Figure 6                                                                                                    Figure 7


In Figure 7, the tracer is set to jump from one intersection to the next of V2 and V3.


In this blog, we have used a set of mathematical representations to promote a conceptual understanding before focusing on the computations and algorithms required to obtain the solutions by hand. This is a fundamental aspect of my own teaching style. Although I am an HP employee and a member of the team that developed the HP Prime graphing calculator, what I have expressed here are my own views and not those of HP.


If you are going to the NCTM AAnnual COnference in New Orleans, please stop by the HP booth and say hello!

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About the Author
  • Jim Vanides is responsible for the vision, strategy, design, and implementation of education technology innovation initiatives. His focus is the effective use of technology to create powerful learning experiences that help students around the world succeed. He has been instrumental in launching over 1200 primary, secondary, and higher education projects in 41 countries, including the HP Catalyst Initiative - a 15-country network of 60+ education organizations exploring innovations in STEM(+) learning and teaching. In addition to his work at HP, Jim teaches an online course for Montana State University on the Science of Sound, a masters-level, conceptual physics course for teachers in grades 5 through 8. Jim’s past work at HP has included engineering design, engineering management, and program management in R&D, Manufacturing, and Business Development. He holds a BS in Engineering and a MA in Education, both from Stanford University.
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