Trig in the Village
Name: Jason Cearley
Date of Lesson: any
Length of Lesson: 50 minutes
Description of Class: HS Geometry
Source of Lesson: Self Created
TEKS addressed:
(a)
Basic understandings.
(2)
Students use geometric thinking to understand mathematical concepts and the
relationships among them.
(4)
Students perceive the connection between geometry and the real and mathematical
worlds and use geometric ideas, relationships, and properties to solve
problems.
(6)
As they do mathematics, students continually use problem-solving, computation
in problem-solving contexts, language and communication, connections within and
outside mathematics, and reasoning, as well as multiple representations,
applications and modeling, and justification and proof.
(d)
Dimensionality and the geometry of location: knowledge and skills and
performance descriptions.
(1)
The student analyzes the relationship between three-dimensional objects and
related two-dimensional representations and uses these representations to solve
problems. Following are performance descriptions.
(A)
The student describes, and draws cross sections and other slices of
three-dimensional objects.
(B)
The student uses nets to represent and construct three-dimensional objects.
(C)
The student uses top, front, side, and corner views of three-dimensional
objects to create accurate and complete representations and solve problems.
(3) The student
uses functions and their properties to model and solve real-life problems. The
student is expected to:
(A) use
functions such as logarithmic, exponential, trigonometric, polynomial, etc. to
model real-life data;
The Lesson:
I. Overview:
This lesson will be an intro to basic trigonometric
properties (sin, cos, tan) that I will tie into the 6 weeks project by linking
it to the construction of the Olympic Village structures.
II. Performance or learner outcomes:
The students will be able to work basic
trigonometric problems involving missing parts of right triangles. They will
also be able to use this knowledge to aid them in finding appropriate roof
angles for the structures they will design in the future for the project.
III. Resources, materials and supplies needed:
Nothing special required.
IV. Supplementary materials, handouts:
Practice handout.
Five-E Organization
|
Teacher Does |
Student Does |
|
Engage: The teacher will begin by reminding the students that in
only a few days they will FINISH the design of the first structures in the
Olympic venues and that initial design starts today. ÒBut before we can begin
the design it is important that we learn a few new concepts that we can use
to help us along the way. One of these very important tools is the use of
basic trigonometry to help us find missing lengths and angles of right triangles.Ó |
Hoped for student response: Students paying attention to my introduction and picture of the roof section that I have on the board. |
|
Questions:
For this project we are restricted to certain roof
angles for our design due to local building codes. When looking at the roof
section here, why would it be beneficial to know how to figure out missing
angles or lengths? And for our project, why do we care about the angle? |
Expected Student Response: Well, when we get done
designing the roof, we can take the measurements and find the missing angle. Because you said we have to
keep it within a certain range because of building code. |
Student responses to the questions give me an idea that the students understand the purpose of the lesson.
|
Explain: The teacher will begin by stating the 3 main trig
functions and what they help us to do. (for our purposes, finding missing
elements of a right triangle) |
Students will listen to my brief description of the properties. |
|
The teacher will then work examples of each type on
several triangles and have students come up to the board to work some of the
final examples. |
Students will be watching me and coming up to the board to work some examples. |
|
Once the examples have been worked, the teacher will then distribute
a sheet of paper to each group that has various building code restrictions
placed on it. (I.e.: the minimum
building width 20 meters, roof angles must be 20-25 degÉ..) |
Students will receive worksheet. |
|
|
|
|
Questions: What
function can we use here? Is there more than one trig function that we can use? Why did you choose this function? |
Expected Student Response: Answers specific to example. |
Student responses to questions as well as participation during examples will give me an idea of general understanding.
|
Explore: The teacher will now tell the students that the worksheet they possess has their own group specific restrictions for building Olympic village houses. ÒThe design of the roof for the athlete houses begins here. As long as you donÕt violate the building code anything is fair game.Ó In the remaining time the teacher will let the groups go free
to work on starting the design of Olympic houses. Questions:
I expect various questions about wild designs and will need to be
flexible in handling various proposals. I am aware that some kids might choose circular houses
and if they do I will allow this but still insist on a certain angle roof and
building width.(the roof would obviously have to be a cone but trig is still
applicable)
|
Expected Student Response: Students will listen. Students will begin design to
meet building code and the teacher will walk around and help those that are
having troubles. |
Here I will be looking to see that all groups are on task and looking for ÒquietÓ students who might not understand the trig.
|
Extend / Elaborate: The teacher will tell the kids that they are doing well
and to be sure to save all calculations/dimensions and info from the day in
their group folders because they will tie this into their overall design in
the next few days. |
Students will put group work and calculations in the allotted group project folder. |
I will be emphasizing the continuation of the project and making sure students know that this is an ongoing exercise.