For example 1 students might use the embedded Geogebra link to add points of interest to a graph and use the pen tool to connect the points of interest. I'm not convinced this is better than paper and pencil for this particular problem, but at the same time I might use this example as an opportunity to teach students these two Geogebra skills that we will use throughout our course. If we want to compare sketches I can teach students to take a screen shot and embed on a given slide in this Google Presentation. This will be day 3 of students looking at elevation versus time graphs, so introducing additional tech skills might be appropriate with students feeling comfortable with content. The screenshot below shows the pen tool, as well as the input area where students would add points.

Given the time it takes to teach students to use new technology, I am more likely to spend class time on the exploratory challenge problems (1-3). For these problems I want students to do all of the graphing on Desmos. My question is whether I am changing the task too much by moving to Desmos. In the paper and pencil version of problem 1, students watch this video (I couldn't load on Chrome, but Safari worked), scale the y-axis, and then plot by hand. They will notice that at 0 seconds, there are 2 bacteria, at one second there are 4 bacteria, at two seconds there are 4 bacteria (etc.). I want students to go to this prescaled Desmos graph and plot the points in pre-loaded table of values on a pre-scaled graph.

For problem 1 I am more concerned with students' ability to interpret the situation and extend the pattern. If this is my goal, then asking students to choose the y-axis scaling and draw their own table of values seems like a lot of extra steps. They can generate the graph below in about 30 seconds if starting with the blank graph above.

Problem 2 is an extension of problem 1, with students noting that 20 minutes of real time are covered by 1 second in the video (this info is not included in the student version of text, so you have to refer to the teacher version for how to lead the lesson). They could go back to their Desmos graph and show understanding of this fact by changing the times in the x-column of the table of values. Then we can walk through how to change the scale of the x-axis so the data points are visible. Adding additional points necessitates a rescaling of the y-axis if you want to see all of the points. We can rescale by clicking on the wrench icon towards the top right and changing the minimum and maximum values for each axis.

What do you think of these digital additions to the lesson? Are they too much for students? Does this change the task in a way that takes away from the mathematical goal? (Students choose and interpret the scale on a graph to appropriately represent an exponential function. Students plot points representing the number of bacteria over time, given that bacteria grow by a constant factor over evenly spaced time intervals.)

Download or make a copy of the Google Doc here. Original source is here. Engage NY is a great resource even if you aren't using it as your primary curriculum, and you can modify this document to use in your class.

This lesson is part of one of the summer work projects at my school, and includes making a few interactive lessons for our Algebra class. We are piloting the Engage NY curriculum for the first time next year. We are also in the Google Domain and will have access to Google Classroom for the first time, in a one-to-one environment. We'll primarily use Google Docs and other Google Apps for Education as we learn how to meaningfully incorporate technology into our math classes.

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