According to the Montana Common Core State Standards, the
Pythagorean theorem is a critical area for eighth grade students. It is also a concept that is used in
many real life contexts. For
example, a 22-inch TV has a diagonal length of 22 inches, which is the
hypotenuse of a right triangle.
Also, painters and construction workers need to know the size ladder to
use to get to the top of a wall.
Geologists use the Pythagorean theorem to find the center of an
earthquake. Surveyors use the
theorem to calculate the height of a mountain. Triangulation is a more complex version of the Pythagorean
theorem that helps pinpoint locations on earth.
There is no doubt that it is an important concept for
success in adult life.
However,
the traditional method of teaching it would most likely involve direct
instruction.
A teacher would
demonstrate the skill; students would practice and then there would be a
quiz.
See
original lesson plan.
Substituting technology still keeps the lesson direct
instruction but it is more engaging and interesting for students.
See
substitution lesson plan.
Augmentation cleans up the substitution
plan but still only enhances the original direct instruction plan.
See
augmentation lesson plan.
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| Student Work - Google Earth |
To transform the lesson, one has to think outside the
box.
Flipping the classroom is one
such idea.
In a flipped classroom,
the direct instruction is done outside of the classroom as homework.
Students watch videos that introduce
concepts.
In class, students work
on activities or investigations that apply those concepts.
For a significant redesign from the
original lesson see
modification lesson plan.
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| Student Work - Wheel of Theodorus |
A Menu is not a new pedagogy.
It has its roots in the elementary classroom’s
stations.
However, redefining a
menu takes the best of the old pedagogy and makes it rich with technology.
A menu is a way to organize the
classroom for instruction that includes problems, activities, games and
investigations.
It allows students
to have choice that helps them work within their own strengths as well as
challenges them to step outside their comfort zone.
An internet-based menu uses their world to help students
have success.
The menu in my
lesson is located on a Google web page so that students have access to it
anywhere.
It consists of an
appetizer, a main dish and a dessert.
The appetizer introduces the Pythagorean theorem.
The main dish consists of activities
and investigations that use and apply the Pythagorean theorem.
The desserts allow students to be
creative with triangles.
For a
more in-depth description see
redefinition lesson plan.
Most students are highly motivated as they work their way
through the menu.
They begin by
watching several YouTube videos that reinforce their fragile understanding
gained from watching the stop-motion movie that I created to introduce the topic. (The Pythagorean Theorem Movie).
The students are required to choose two main dishes.
A favorite activity is the Pythagorean
Triples and Google Earth Activity.
When students get to the desserts, the have a good grasp of the
Pythagorean theorem and are ready to have some fun.
Since I have used and revised this menu, I have never had a
student fail the culminating quiz.