Lesson Plan (non-inquiry)

 

Name: Elizabeth Berlinger

 

Title of Lesson: Triangle Simulation

 

Date of Lesson: Thursday/Friday of the 1st week of the Unit

 

Length of Lesson: 50 minutes

 

Description of the class:

            Name of course: Pre-Calculus

            Grade Level: 11th or 12th

                  Honors or Regular: Regular

 

Source of the lesson:

 

http://argyll.epsb.ca/jreed/math9/strand3/3103.htm

 

TEKS addressed:

(b3B) The student constructs and justifies statements about geometric figures and their properties.

 

(c3) The student identifies and applies patterns from right triangles to solve problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

 

(e1C) The student develops, extends, and uses the Pythagorean Theorem.

 

(f3) In a variety of ways, the student develops, applies, and justifies triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples.

 

 

            I. Overview:

            The goal for this lesson is to give students a way to review and solidify their    understanding of the use of trig to find missing angles and sides, the use of the             Pythagorean Theorem and other basic concepts of trigonometry, with the help of a     simulation.  

 

 

            II. Performance or learner outcomes:

                        Students will be able to:

                                    1). Use sine, cosine, and tangent ratios to calculate angles in a right                           triangle with and without scientific calculators.

                                    2). Use the Pythagorean Theorem to calculate angles in right                                      triangles.

                                    3). Define and explain trig vocabulary such as sine, cosine,                                                     hypotenuse, tangent, opposite angle, ect.

 

            III. Resources, materials and supplies needed:

                        1). Computers with internet access for each student

 

 

 

 

 

Five-E Organization

 

ENGAGEMENT:

 

       Teacher Does                         Probing Questions                    Student Does

Since this lesson is a review of concepts learned in previous courses, I will start the lesson with a discussion about what they should, but may not, already know. Through this I will be assessing prior knowledge as well.

What are the names of the three types of triangles, and what characteristics make them unique? How many degrees do the angles inside of any triangle sum to? How do you know this? Is there a way to find the length of a missing side of a triangle if you have the length of the other two sides and the angle measures? How would you go about doing this? Can anyone tell me what the Pythagorean Theorem says and why it is useful? Has anyone heard or seen the acronym SOHCAHTOA? What does it stand for, and how is it used?

Student responses will reflect any misconceptions about how to calculate angles measures and side lengths. It will also let me know how solid or shaky their understanding of these concepts are.

Briefly discuss how these “old” concepts will be useful to them when thinking about and answering the driving question.

 

 

 

EXPLORE:

 

       Teacher Does                       Probing Questions                      Student Does

We are going to be using the computers today to work on some simulations to see how well you remember the concepts you learned in Geometry. This will act as a review for most of you, but it will be helpful in the next coming weeks. Please everyone find a computer and go to the following website: http://argyll.epsb.ca/jreed/math9/strand3/3103.htm

 

 

Students do as they are told, and use this time to ask any preliminary questions they might have.

There are many different links on the website that all have different activities and games for you to play that address right triangles and other geometry concepts you have learned. Some of your options are:

1. Vocabulary matching game

2. Exercises utilizing SOHCAHTOA, with explanations

3. Trigonometry flash cards

4. Manipulation of triangles and use of trig to calculate angles

5. Exploration of trig ratios and patterns

I will be walking around the room helping whoever needs it, but please use your peers as sources of guidance first.

 

Students explore the website choosing activities that deal with the concepts they feel weakest in.

 

EXPLAIN:

 

        Teacher Does                        Probing Questions                   Student Does

After the students work on theses activities for a majority of the time, we will conclude with a discussion about what they learned, how much of what they did was a review, and did they find something out that they never knew before

Were there any concepts covered in the simulation that you had never seen before? If so, which ones? Did these activities/games help solidify your understanding of triangles and the geometry behind them? Did you find the vocabulary game helpful at all, or was the terminology more confusing than it was beneficial? What would you guys say was the major theme of this entire simulation, and if you had to describe it someone else, what would you say?

Students respond to probing questions hopefully leading to more questions left uncovered by the simulation. Students respond and discuss with each other as much as with me.

 

EXTEND/ELABORATE:

 

       Teacher Does                      Probing Questions                   Student Responses

Now that we have done a fairly thorough review of the concepts needed to start your projects, let’s discuss how you might apply these concepts to your sundials.

Which concepts do you think will be most important, and in what ways do you think you will use them?

Students will respond with guesses that they will need some knowledge of circles (for the base), isosceles triangles (for the time increments), etc. They will not know at this point that the Law of Sines and Cosines will be needed when constructing the gnomon. I would also like them to note that some knowledge of latitude and longitude will be necessary.

 

 

EVALUATE:

 

      Teacher Does                         Probing Questions                      Student Does

I will be doing the “Misconception/Preconception Check” from our list of CAT’s as an assessment for this lesson. I chose this one because most of the students will be coming into this review with different Geometry backgrounds. This will help me to gauge how far along everyone is. I will create a list of common misconceptions that I believe the students will have, and from that I will create a questionnaire to elicit their ideas on these concepts.

 

Students fill out the questionnaire to the best of their abilities and turn them into me to evaluate. From there I can create a plan for what I should plan to cover again or in a different way.