A lesson plan for a high school
geometry class that I felt would be an excellent example for technology integration
is called “Hands-On Geometry: Using Manipulatives in Math 10: Lines and Line
Segments Angles and Polygons,” written up by Kathleen Bracken. The idea
of the lesson is to increase student understanding in the area of lines, line
segments, angles, and polygons. For this particular assignment, I chose to
stick with sections one and two, “Mira Constructions: Lines and Line Segments” and “Pythagorean
Puzzles.” The total completion time of this unit plan is four hours or
approximately one week of lecture, modeling, and practice, given the length of
a class is approximately forty-five minutes.
Sessions 1 and 2: Access/Analysis
The
first mathematics standard I found based on this lesson plan is one about
rotation, reflection, and translation of lines and line segments using physical
technologies and virtual geometry software. Students will be using a tool
called a Mira, a transparent device that creates a reflection of a written line
or shape which acts as a mirror, for constructing reflections of given lines or
line segments. Students would be actively participating in discussion based on
their findings and constructions using this tool. There is also a basic mirror tool online which acts similarly to the Mira which can be used for simple
simulation and modeling. As an alternative, students can use Geometer’s Sketchpad,
computer geometry software, to construct lines and shapes in order to perform
reflections, rotations, and transformations. This is a tool I am very familiar
with and would be used for any and all geometry plans. It is useful for giving students
a more accurate representation of geometric ideas and can help with
understanding.
The
second standard which corresponds to the lesson is about explaining the
criterion for two triangles being congruent. As a teacher I would lecture about
the criterion for triangles to be considered congruent. Then, in order to
better students understanding of triangle congruency, students will be asked to
work in groups using rulers and protractors to collaboratively construct congruent
triangles based on the criterion for triangle congruency. They can also use
Geometer’s Sketchpad to construct congruent triangles as well as add the
correct markings which could be used to show congruency when triangles are not
drawn to scale. After students complete their work they will be asked to use
the Smartboard to interactively display their findings to the rest of the
class. The Smartboard will allow for manipulations of their work in case there
needs to be correction.
The
third standard is about students knowing how to make constructions using a
variety of tools. They will use tools such as a straightedge and a protractor
to construct shapes such as triangles, squares, and other shapes with larger numbers
of sides and angles. They will also use a compass and string to construct
circles. For more complicated constructions such as using circles to construct
an equilateral triangle, students can use the geometry software which can
create more perfect circles which would lead to more accurate constructions of
more complicated figures. As a teacher I would model for the students, using
these technologies, how to perform these constructions and from there, students
will work either at their desks or at computers to individually complete the
work. After completion there would be a group discussion about how the
constructions were completes as well as sharing the difficulties some students
may have experienced.
Sessions 3 and 4: Communication/Evaluation
The
final standards covered in this lesson plan are proving theorems about
triangles and using the Pythagorean theorem to solve right triangles.
Essentially this is leading into the basic understanding of the Pythagorean theorem.
What students will do is use Geometer’s Sketchpad to use the congruency of
triangles to show relationships between them, more importantly, those for right
triangles. There is an online tool known as NOVA which gives a clear demonstration
of a proof of the Pythagorean theorem by breaking down squares which have side
lengths of that of the triangles and fit the leg’s squares into the hypotenuse square. As a teacher I
would lecture about the proofs of triangles and about the basic of the
Pythagorean theorem. Students would then individually use NOVA or Geometer’s Sketchpad
to practice basic proofs of triangles and solve problems using the Pythagorean
theorem. After they practice I would check for understanding by administering a
brief examination about their understanding of triangle congruence and the
Pythagorean theorem.
It
is clear that technology can be easily and effectively integrated into this
lesson plan and using them, along with specific teaching strategies, would make
mathematics more interesting and enjoyable.
Link to Speadsheet
Link to Lesson Plan
Link to Speadsheet
Link to Lesson Plan
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