Unit 2: Incorporating Desmos and Desmos Activities into Mathematics Lessons
Objective: Given a learning standard that includes a graphing component, the participant will be able to locate a Desmos Activity that could be integrated into a lesson the specific standard and then explain how the activity would enhance student learning.
When I share Desmos and Desmos Activity Builder with other math teachers, each one has a unique idea of how to incorporate the technology tools into their own classroom. The possibilities are nearly endless. Each teacher can design the activities and projects to fit their own teaching style and the needs of their students.
The Desmos Graphing Calculator allows for registered user to save and share any creation. Upon seeing the capabilities of Desmos Graphing Calulator, a colleague shared with me that he was planning on creating sample graphs to use in his lesson presentations so that students could manipulate the graphs as he demonstrated their characteristics for the whole class. Desmos also allows for users to insert sliders into the graphs. Sliders allow for the user to illustrate how a graph changes as a specific values varies.
Here is a sample graph that I created: https://www.desmos.com/calculator/rgj7pmzqwe This particular graph allows students to manipulate the vertex form of a quadratic equation to see how each value changes the graph.
Inquiry Based Learning
Discovery based learning or inquiry based learning is a great technique that can be used to engage students and teach for understanding in mathematics. Desmos Activity Builder opens the door to build more and better inquiry based learning activities. With the interactive features available within Desmos Activity Builder, students can manipulate graphs and equations to build understanding. With the existing and public activities that have been built by Desmos and other mathematics teachers, mathematics instructor across grades 7-12 can find ready to use activities that will encourage student discovery. Watch this video to see what a few of the possibilities are for discovering learning with Desmos: https://www.youtube.com/watch?v=lMUuXMsrBP8
Click on this link to explore the numerous activities already available for teachers to use: https://teacher.desmos.com/
Mathematical Language Building
A personal goal I have for my math students is to build mathematical language. In order to develop that language, learners must be given opportunities to communicate mathematical. Activity Builders called Polygraphs have enabled me to encourage mathematical communication. As shown in Unit 1, Polygraphs are a mathematical Guess Who? game. One students chooses a graph or image and the other asks yes/no questions to eliminate and choose the correct image. Having to create yes/no questions requires students to utilize the terminology used in class. In graphing, pupils may use vocabulary such as quadrant, vertex, slope, intercepts, and axes. Here is a sample Polygraph on Transformations created by Mike Waechter https://teacher.desmos.com/polygraph/custom/560c53f5441172070b26220a Students would be required to use vocabulary such as reflection, translation, dilation and rotation to successfully complete the activity.
As math teachers, it is important to gauge student understanding as we progress through a unit. Desmos Activity Builder provides a teacher dashboard for instructors to tract an entire class of responses or view an individual student's answers. While students work through the activity, teachers have a direct connection to each learner. If there is a common misconception among students or more instructions need to be given, the teacher may pause the entire class. Students' names may be displayed or alias names can be listed. Next to each name there is a status bar. This bar allows for the instructor to see how fast students are moving through the lesson. A quick assessment determines when one learner is moving too quickly or is much slower than his/her classmates. Desmos has created a great feature to assist teachers in formative assessment. Watch this video for more specific details concerning the teacher dashboard: https://www.youtube.com/watch?v=8c7Xpv99nvE
David Ebert shared Graphing Project ideas through his article on the National Council of Teachers of Mathematics. You can read the article here: http://www.nctm.org/Publications/mathematics-teacher/2014/Vol108/Issue5/Graphing-Projects-with-Desmos/ As David points out students will explore various aspects of graphing throughout the high school years. Learners begin with linear equations and progress through rational functions, trigonometric functions, conic sections, and more. Adding Desmos into the classroom allows for students to manipulate and connect the various graphing skills. A commonly assigned project for upper level student is to combine the multiple levels of their graphing skills to create a picture. This project utilizes the save feature on the Desmos Graphing Calculator. Students must create their own account, save their project as they build it, and share it with their instructor once finished. The sample project on the left was created by Luke Boudreau and displayed on the Desmos Art page listed below. This project allows learners to bring in their interests outside of math class and is a great idea as a culminating project for upper level math courses that emphasize graphing.
Here is the assignment as laid out by Thomas Lee in a Prezi presentation: https://prezi.com/bftg3d754gnq/copy-of-year-10-mathematics-desmos-graphing-project/
Check out the creative designs by mathematics students around the world https://www.desmos.com/art
Do you ever have students who excel in math who need some extra challenge to advance their math skills? Desmos Activities has great ideas for all levels of students. If you want to see your top students continue to move forward with their math skills, try searching your current topic on the Desmos Activity Builder page. Here are few examples:
- In Polynomial Equation Challenge created by Jonorr, students try to create a polynomial that will meet the given requirements including hitting all the given points. https://teacher.desmos.com/activitybuilder/custom/561582ecbd554ea00760f933
- In Building Conic Sections created by Dylan Kane, learners attempt to create specific conic sections that separate sets of colored points. https://teacher.desmos.com/activitybuilder/custom/56030ac728462f1706872e72
- With Marbleslides such as this one created by the Desmos staff, students explore using piecewise functions to guide marbles on a specific path. https://teacher.desmos.com/marbleslides-lines
After viewing the various options for activities, discuss the following questions with a partner:
1. In what manner do you foresee utilizing Desmos and Desmos Activity Builder in your classroom?
2. What needs could Desmos meet for your unique students?
3. Find an existing activity on Desmos and build a lesson around that activity for your specific students.
Please enter your response into this Google Form: https://docs.google.com/forms/d/e/1FAIpQLScqYkJcXIJqv3K8Nts3E8EL1DQcOXM42EOVNiZ6onYRJn9okQ/viewform You will also be able to read responses from other teachers who have participated.
Resources and References
Desmos. (2016, Jan 22) TEACH: Using the desmos teacher dashboard. [Video file]. YouTube. Retrieved from https://www.youtube.com/watch?v=8c7Xpv99nvE
Desmos. (n.d) Desmos creative art. Retrieved from https://www.desmos.com/art
Desmos. (n.d.) Marbleslides: Lines. Retrieved from https://teacher.desmos.com/marbleslides-lines
Ebert, D. (2014) Graphing projects with desmos. Mathematics Teacher, 108. Retrieved from http://www.nctm.org/Publications/mathematics-teacher/2014/Vol108/Issue5/Graphing-Projects-with-Desmos/
Garcia, J. (2015, August 12) Teacher activities with desmos. [Video file]. YouTube. Retrieved from https://www.youtube.com/watch?v=lMUuXMsrBP8
Jonorr (n.d.) Polynomial equation challenge. Retrieved from https://teacher.desmos.com/activitybuilder/custom/561582ecbd554ea00760f933
Kane, D. (n.d.) Building conic sections. Retrieved from https://teacher.desmos.com/activitybuilder/custom/56030ac728462f1706872e72
Lee, T. (2015, September 9) Copy of year 10 mathematics desmos graphing project. [Video file]. Retrieved from https://prezi.com/bftg3d754gnq/copy-of-year-10-mathematics-desmos-graphing-project/
Waechter, M. (n.d) Polygraph: Transformations. Retrieved from https://teacher.desmos.com/polygraph/custom/560c53f5441172070b26220a