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1. TPACK MODEL
LESSON PLAN

2. LessonTitle: Graphing Equation of a Line: Slope-Intercept
Form
Grade: Grade 8
Lesson Length: 90 minutes

3. Learning Styles
Students comes from a variety of economic and social backgrounds and
their learning styles vary from: auditory, visual, tactile and kinesthetic.
However, some students have difficulty maintaining focus during class. In
order to overcome this issue, lesson must accommodate the students’
attention span and also to facilitate their individualized preferred needs.
Entry Skills
Students already knows the basic concepts of slope and intercepts of a
line; however they cannot carry out the task in graphing an equation of a
line in slope-intercept form.
LEARNERS CHARACTERISTICS

4. STATE OBJECTIVES
At the end of the lesson, students should be able to:
• Demonstrate understanding on slope-intercept form of the
equation of a line
• Restrict, reposition, and rotate lines with the slope-intercept
form using the Desmos Graphing Calculator and Marbleslides:
Lines
• Develop accuracy and teamwork in making tutorial video
about graphing linear equations in slope-intercept form

5. LESSON DESCRIPTION
The information contained in this link:
https://teacher.desmos.com/marbleslides-lines will be used to
facilitate the discussion. This contains is an interactive game called
Mathslides: Lines and Desmos Online Graphing Calculator developed
by the team of educators at the Desmos Labs. This interactive activity
makes students manipulate series of linear equations in order to
collect the 4 stars on a given page. Once students have completed
collecting the four stars they can then move on to the next slide.

6. LESSON DESCRIPTION
To start this activity, a teacher would create a class code from
activity launch page, then they would need to distribute the class
code so students could access the activity. Once students are inside
the activity, the first slides inform them of how the activity works. The
first slides include how to use the launch bottom, how to change one
of the parameters of a linear equation (slope or y intercept) to collect
the stars, and how to reset the equation is you make a mistake. These
first sets of activities are called “Fix-it” tasks.

7. LESSON DESCRIPTION
Besides having to have some prior knowledge about the basic
properties of linear equations, students will also be introduced to
creating restrictions on a line to make it start or stop at a given point.
Teachers can use built in tools like the thumbs up mode, or the pause
button so they can lead a whole class discussion to intervene when
students are struggling.

8. LESSON DESCRIPTION
After students complete the “Fix-it” challenges, they move on to the Predict
and Verify section of tasks. In the Predict and verify sections, students are asked to
anticipate what would happen to a graph if some value is changed, and justify their
answers in writing. When students reach each of the slides they can see their
classmates’ responses. A teacher can review any of these responses and pause the
class to ask more probing questions as to why students think their answers is true.
Students also have the ability once they make a prediction, to see on the next slide
if their prediction is correct by changing the values asked in the prediction section.
Students can start to understand why certain changes to a given equation
transforms a linear equation.

9. LESSON DESCRIPTION
After students complete the 4 predict and verify questions, they
move to the last section of the Marbleslides lab, the Challenge slides.
On each of the challenge slides students need to use all of the skills
they have learned in the previous slides to come up with a solution to
collect all four stars. For all of the challenge slides students must
generate their own equations, including parameters, to achieve the
goal. After a few students have a solution to a given problem, the
teacher could showcase to the class inventive solutions that their
classmates have created.

10. LESSON DESCRIPTION
There are eight challenge slides total. If some students complete
all of the activities they are given a free play screen where they graph
and design whatever they choose. The controls that Desmos provides
can help any teacher navigate through the activity. Teachers can see
each student’s progress by viewing the thumbs slide, or they can
select any given slide and see an overlay of all students’ responses, or
see responses from each individual student.

11. LESSON DESCRIPTION
Teachers can also pause the entire class at any time, so they can
lead a class discussion or help students understand difficult concepts.
Teachers can also enable teacher pacing which forces students to
walk through each activity at the teacher's pace, rather than the
students pace.

12. TPACK Specific Questions
T – Desmos Lab—MathSlides: Lines and Online Graphing Calculator
P – Inquiry-based learning
C – Graphing Linear Equations: Slope-Intercept Form of a Line

13. Pedagogical Content Knowledge
Definition of PCK:
The Inquiry-based learning is an effective method on teaching linear equations.
This concept is challenging for grade 7 students taking algebra 1. Students have
struggled on visualizing how manipulating slopes and y-intercept can change a
graph.
Description of PCK:
The inquiry-based lesson has students manipulating linear functions in the
form of y=mx+b and restricting slopes and y-intercepts to make inferences on how
the graph is affected. Changing any or all of the parameters will make the linear
equation translate, reflect, or shift. This lesson has students virtually manipulate
values in an equation and see the effects happen instantly.

14. Pedagogical Content Knowledge
Support of PCK:
Some of the traditional methods in mathematics instruction do
not allow for much questioning, investigation, or developing
understanding. The Inquiry-based instruction in mathematics,
however, allows for this to take place and opens doors for students to
answer their own questions, explore meaningful problems, and
incorporate several mathematical concepts into one problem (Kyle
Ferguson, 2010).

15. Technological Content Knowledge
Definition of TCK:
Desmos technology supports student learning in graphing linear equations.
Description of TCK:
Desmos is a free online graphing calculator that allows users to manipulate
various equations and represent them visually. The Desmos Labs allows teachers to
create learning environments for their students to explore mathematical concepts,
as well as utilize pre-created lessons that explore specific concepts. In this
environment, we selected a lesson on linear functions that gamifies students
learning about slope, domain restrictions, and y-intercepts. With the support of
Desmos will be allowed to play and discover more on linear equations.

16. Technological Content Knowledge
Support TCK:
“We have learned that calculators cause changes in the way we teach and in
the way students learn. Before computers and calculators, it was necessary for
students to spend time mastering and becoming proficient in the use of paper-
and-pencil computational and manipulative techniques. Today much of this time
can be spent on developing deeper conceptual understanding and valuable critical-
thinking and problem-solving skills. Calculators reduce the drudgery of applying
arithmetic and algebraic procedures when those procedures are not the focus of
the lesson. They provide better ways to compute and manipulate symbols. For
example, if the problem is to find the area of a region bounded by the graphs of
two functions, then the essential challenge for the student is to understand that a
definite integral is needed, determine the limits of integration, and setup the
specific definite integral. Finally, the student needs to determine whether the
answer obtained makes sense in the problem situation. All these tasks require
serious thinking and thorough understanding.

17. Technological Content Knowledge
Support TCK:
The actual computation of the integral is often best done with (or feasible only
with) calculator or computer technology. Calculators with computer interactive
geometry allow for investigations that lead to a much better understanding of
geometry (Laborde 1999; Vonder Embse and Engebretsen 1996). Calculators help
students see that mathematics has value. Students using calculators find
mathematics more interesting and exciting. Texas Instruments first introduced a
handheld calculator-based-laboratory (CBL) device in 1994 that connects to the link
port of graphing calculators. This device allows students to make precise
measurements of many scientific phenomena and store the measurements in their
calculators for mathematical analysis.

18. Technological Content Knowledge
Support TCK:
Thus, more than any other classroom innovation in the past, calculator-based
laboratories have connected school mathematics to the real-world phenomena
around the student. The excitement and interest in both mathematics and science
generated by these real-world connections is impressive (Bruneningsen and
Krawiec 1998). The use of the Desmosapplications and all of its features brings the
older, yet effective, graphing calculator into more relevant with today’s students.
Calculators make possible a “linked multiple-representation” approach to
instruction. A graphing calculator makes graphical and numerical representations
practical learning strategies”(Burke, 2000).

19. Technological Content Knowledge
Support TCK:
Thus, more than any other classroom innovation in the past, calculator-based
laboratories have connected school mathematics to the real-world phenomena
around the student. The excitement and interest in both mathematics and science
generated by these real-world connections is impressive (Bruneningsen and
Krawiec 1998). The use of the Desmosapplications and all of its features brings the
older, yet effective, graphing calculator into more relevant with today’s students.
Calculators make possible a “linked multiple-representation” approach to
instruction. A graphing calculator makes graphical and numerical representations
practical learning strategies”(Burke, 2000).

20. Technological Pedagogical Knowledge
Definition of TPK:
Desmos is not only an effective and helpful technology in facilitating inquiry-
based learning, but also it helps create an environment where students can share
knowledge with their classmates. The use of Desmos allows the student to get a
deeper understanding of how different parameters affect the equation of a line. If
students had to do this activity with paper and pencil, for each equation they would
have to construct a table and a graph. The “human error” factor is either reduced or
eliminated when using this technology. Students can easily make changes and see
immediate results, therefore, gaining the knowledge of the concept on graphing
linear equation in slope-intercept form more concretely.

21. Technological Pedagogical Knowledge
Description of TPK:
This Desmos Lab allows students to input linear equations and
see the graph automatically. This technology allows the student to
manipulate the equation in exploring how the graph is affected. In
this lab the student is trying to catch all of the stars. The Desmos Lab
allows students to explore the linear equations concepts in more
detail and make their own inquires.

22. Technological Pedagogical Knowledge
Support of TPK:
“Math instruction can be the most resistant to changes in pedagogy
— even schools that have had success with project-based learning or
inquiry-centered approaches can struggle to teach math in ways that
help students understand the rich connections and complexity of the
subject. That’s why some educators are excited to see Desmos — an
ed-tech product best known for offering an online graphing
calculator — adding features that promote inquiry” (Katrina Schwartz,
2017).

23. Technological Pedagogical Content Knowledge
Define TPCK:
Teaching linear equations through inquiry-based learning while using a graphing
calculator like desmos promotes learning in a math classroom.
Description of TPCK:
Students can use the Desmos Lab as an introduction to linear equations. They
have a basic knowledge of linear equations from 8th grade or pre-algebra. This
Desmos Lab will allow students to make inquiries based on the lesson and develop
conclusions and connections about how the graph of a linear equation is affected by
changing the slopes and the intercepts.

24. Technological Pedagogical Content Knowledge
Support of TPACK:
“Students can be more investigative as the constructivist approach and
student centered learning were implemented in the teaching process in
understanding the mathematical concepts, thus can boost higher order
thinking skills. There is a pedagogical impact in incorporating the latest trend
in mathematics education namely, integrating the graphing calculator to
maximize the mathematical and pedagogical benefits to students” (Tajudin.,
& Zarkasi, 2014)

25. REFERENCES
• Ferguson, K. (2010). Inquiry Based Mathematics InstructionVersusTraditional
Mathematics Instruction:The Effect on Student Understanding and
Comprehension in an Eighth Grade Pre-Algebra Classroom.
doi:10.15385/tmed.2010.5
• Schwartz, K. (n.d.). CouldThis Digital MathTool Change Instruction For the
Better? Retrieved March 12, 2017, from
https://ww2.kqed.org/mindshift/2016/04/06/could-this-digital-math-tool-
change-instruction-for-the-better