Instructional Software Lesson Idea

Lesson Title Hunting for Discontinuity

Content Area Precalculus & 12th grade

Content Standards PC.FGR.2.5 Graph rational functions and identify key characteristics.
Technology Standards 1.1 Empowered Learner: Students leverage technology to take an active role
in choosing, achieving, and demonstrating competency in their learning
goals, informed by the learning sciences.
1.1.c. Students use technology to seek feedback that informs and improves
their practice and to demonstrate their learning in a variety of ways

Integrated Technology Desmos

Type of Instructional Drill and practice
Software
Software Feature screen reader compatibility and keyboard navigation

Collaboration: Desmos allows for multiple users can edit and interact with a
shared graph or activity in real time Customization: Users can customize the
appearance of graphs by changing colors, line styles, and labels, making it
easy to create clear and visually appealing graphs.

Multiple-Language Support: it supports multiple languages, making it

accessible to users worldwide.

Educational Activities: Desmos provided a library of pre-made educational

activities and lessons created by educators to engage students in interactive
math experiences.

Graphing functionality: Desmos allows user to graph equations, inequalities,

and functions both 2D and 3D
Reference or Chat gpt supported me in the creation of this idea by providing me with
Supporting Resources information on how Desmos enhance the learning experience for all students,
the software features, how students can apply this topic to discontinuity

Bloom’s Taxonomy Remembering, understanding, applying and creating

Levels
Integration Level Level 3 infusion

Universal Design Desmos enhances the learning experience for all students in several ways:
Rationale
Visualization: Desmos provides interactive graphing capabilities that help
students visualize mathematical concepts. This visual representation makes
abstract concepts more concrete and easier to understand.

Interactivity: Students can manipulate graphs and equations in real time. This
interactivity fosters engagement and allows students to experiment with
mathematical concepts, leading to deeper understanding.

Immediate Feedback: Desmos provides instant feedback as students make

changes to equations and graphs. This allows them to quickly see the effects
of their actions, reinforcing their understanding of mathematical relationships.
 Students can use Desmos to explore mathematics at their own pace and it
provides customization options, such as sliders and adjustable parameters,
allowing for personalized learning experiences tailored to individual needs
and abilities.

Collaboration: Desmos allows for collaborative learning. Teachers can create

activities that encourage students to work together on math problems and
share their insights, fostering a sense of community and peer learning.

Engagement: The interactive and dynamic nature of Desmos tends to capture

students' attention and interest. This can lead to increased motivation to learn
and explore mathematical concepts.

Scaffolding: Desmos provide scaffolded activities that can be gradually

released with independent skills.
Lesson Idea In this lesson, students will be finding the discontinuity of rational functions
algebraically. The teacher would guide the students on how to find the
different discontinuities with guided notes that will have the definition of
rational functions, examples and non-examples of rational functions,
information on how to find the vertical asymptotes, holes, and horizontal
asymptotes, and independent practice. After students learn how to identify
those specifics discontinuity, they will participate in a Desmos activity that
reinforces what they have learned. The Desmos activity will have students
find the discontinuity algebraically and either identify it on a graph or they will
have to graph it. Then the students will explain why this discontinuity occurs
with rational functions based on what they observed graphically and
algebraically
Now once students make sense of discontinuity graphically and
algebraically students in groups will create real-world applications that involve
the discontinuity of rational functions by modeling and visualizing scenarios
where rational functions exhibit jumps, holes, or vertical asymptotes. They will
do this by first selecting a real-world scenario, for instance, population
growth, or decay, financial investments and returns, etc. Next, students will
develop a rational function that represents their scenario. After that, they will
use the Desmos graphing calculator to visualize the function’s behavior. Then
the students will Use Desmos' slider feature to create sliders for the
parameters and variables in your rational function. This will allow the young
scholars to interactively adjust these values and see how they affect the
graph. They will have to Pay attention to the points on the graph where there
are jumps, holes, or vertical asymptotes. Lastly, students will have to analyze
these discontinuities in the context of their scenario and will have to present
their findings by creating a presentation. Students will share their findings
with their peers.
This presentation will be scored on a rubric and in return will give them
feedback on how well they understood the lesson on discontinuity in which
this lesson will be used to inform learning. I will give my students a week to
finish this project, however I will give them 2 days out of the school week to
work on it in class.
Design Reflection The combination of theoretical understanding, Desmos exploration, and
real-world application is likely to engage students and make the concept of
discontinuities more tangible and applicable. Students are not only learning
the theory but are also actively using technology and applying their
knowledge to real-world scenarios. Not to mention, Desmos provides an
interactive platform for students to visually explore and manipulate functions.
This hands-on experience enhances their understanding of how changes in
parameters affect the graph, promoting a deeper level of learning.
 To extend this lesson, I can establish connections to other mathematical
concepts or units of study. For example, I can illustrate the relationship
between rational functions and concepts like limits, creating a more
comprehensive understanding of mathematical principles. Additionally,
students can be encouraged to independently explore further real-world
applications. This autonomy allows them to delve into scenarios beyond the
provided examples, tailoring the learning experience to their interests and
promoting a more personalized approach.Furthermore, the integration of
additional technology tools can enhance the overall lesson. For instance,
Wolfram Alpha can complement Desmos activities by offering a platform for
computational exploration and verification. Through inputting functions and
analyzing results, students can deepen their understanding and reinforce the
concepts explored in the Desmos activities. This multi-tool approach ensures
a well-rounded and comprehensive learning experience for the students.