## Monday, May 12, 2014

### Desmos Advanced Algebra Exploration -- Power Functions, Inverses and Graphs

NOTE: CLICKING ON THE GRAPH ABOVE SHOULD NOW LOAD THE DESMOS activity...

Hope you enjoy this new Common Core Investigation...

Students will examine the relationships among the graphs of y = kx^n, the inverse x = ky^n and their graphs. Beginning with particular values k=2, n=2 students will observe how the graphs are reflection images of each other over the line y=x. They will be asked to observe how the number of points of intersection vary over positive integer values of n, according to whether n is even or odd.

They will then determine the coordinates of these points first by estimating from the graphs, then by obtaining exact values using a system of equations.

Finally, they will use more advanced algebra tools to solve in terms of k and n. Some students will recognize the BIG IDEA that the points of intersection must lie on the graph of y=x, therefore the algebra is simplified by using y=x to replace x=ky^n when solving. This is crucial.

Thus, there is a blend of discovery and application of exponent skills. This is to me is the best use of technology - to enhance not replace instruction.

Desmos empowers the student to probe deep beneath the surface but the teacher must carefully plan and guide this process, otherwise many students will make pretty graphs and not get beyond moving sliders left and right. My opinion of course...

Desmos is a powerful teaching/learning tool because it enables students to discover important mathematical relationships and formulate key concepts for themselves. However, it is the expertise of the instructor which will determine WHAT they are learning. This is GUIDED self-discovery!

In this activity I included a detailed overview and guide for the instructor but I left it to the professional to tailor the investigation to the students and the curriculum. In other words, I did not provide a student worksheet. I encourage the professional to modify as he/she sees fit.

Your feedback is very important to me as I continue to develop these. Feel free to comment below or contact me directly using the new Blogger contact form. Also follow me on Twitter @dmarain.

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I don't see the lesson. Is there supposed to be a link somewhere?

Dave Marain said...

Thanks, Denise. Now I know how to generate comments!

I posted a temporary link below the graph but it's not live. You have to copy/paste it. When I get home I'll fix it.