# Engaging students: Graphing Square Root Functions

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my student Alexandria Johnson. Her topic, from Algebra II: graphing square root functions. An interesting word problem that students should be able to solve after completing a lesson on graphing square root functions would be: “The Chandra satellite detected x-rays coming from the region of the sky containing the galaxy cluster JKS041. The electrons in the gas are emitting the X-rays, and colliding at high speed with the protons in the gas. The energy of the x-rays at the time they were emitted by the hot gas was 21,400 electron Volts (eV). This energy is shared equally between the electrons and protons. The speed of a proton is related to its kinetic energy by E = 1/2mV^2 where E is the energy in Joules, V is the proton speed in meters/sec, and m is the mass of a proton (m = 1.7 x 10-27 kg). About how fast are the protons moving? (Note: 1 eV = 1.6 x 10^-19 Joules)”. Students can arrange the problem into a square root function to solve for velocity: V=sqrt(2E/m). Using the information provided students can convert eV to E and solve for m. Once this information is found, students can plug in the numbers to solve for V. Note: this question is difficult and some students may struggle with the calculations. A simpler question about the relationship between kinetic energy and velocity could be used in place of this one. Question provided by https://spacemath.gsfc.nasa.gov/weekly/6Page70.pdf. In Physics, students will be able to use square root functions to describe the relationship between different variables. Having the knowledge of graphing square root functions will allow students to represent these relationships graphically. For example, to find kinetic energy, students use the formula E=(1/2)*m*v^2, where m=mass and v=velocity. Students can manipulate the equation to find v which would be v=sqrt(2E/m). Given m, students should be able to graph the relationship between v and E. When solving for volume, students can rearrange the equation into the form y=a*sqrt(x-h)+k, where h=0, k=0 y=v, x=E, and a=sqrt(2/m). knowing how to graph a square root function, students can graph this equation. A useful resource when creating a lesson about graphing square root functions is https://teacher.desmos.com/. This website provides teachers with existing activities that the students can complete. Also, it allows the teacher to create activities for the student. An activity that is already created for teacher use is called Polygraph: Square root functions. In this activity, students play a game similar to the board game Guess Who. Students pair up and are given a set of graphs of square root functions. Partner 1 chooses a graph. Then, Partner 2 asks questions about the graphs to try to find the graph that Partner 1 chose. Students compare various graphs and communicate these differences. Though the website doesn’t offer any other premade activities at this time, teachers can use the activity type “marble slides” to create an activity that shows how a, h and k affect the parent function of square roots. Work cited

“Chandra Spies the Most Distant Cluster in the Universe.” Space Math, NASA, Chandra Spies the Most Distant Cluster in the Universe. Accessed 15 Sept. 2017.
“Square Root Functions.” Desmos Classroom Activities, teacher.desmos.com/polygraph/custom/560ad29158fd074d156300b6. Accessed 15 Sept. 2017

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