Content and Instructional Strategies

Right Triangles

Context: / This lesson is designed for a pre-calculus class in high school. The class includes 24 10th through 12th graders, all with grades of B or better in all previous math courses. Most of the students are college bound and are preparing to take Calculus in high school or in college. The class is held in the math lab in a high school, so each students has an individual computer in the classroom.
Objectives: / ñ  Student will find the values of trigonometric functions of acute angles.
ñ  Student will solve for all aspects of right triangles.
ñ  Student will solve applied problems of right triangles.
SOL: / MA.13 The student will identify, create, and solve real-world problems involving triangles. Techniques will include using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines.
Resources/ Materials: / Worksheets
Computers
Calculators

Approximate Time Required: 85 minutes

Content and Instructional Strategies:

1.  (10 minutes) Students will complete a free-write on the following prompt:

◦  What do you remember about right triangles? What are some examples of right triangles in the real world? Spend 10 minutes writing/drawing everything you can remember and be ready to share your answers.

2.  (5 minutes) Have students share their answer and the teacher should write the key points on the board. - Discussion

◦  The teacher will not remark on the answers provide, just write them on the board and refer back to them later.

3.  (2 minutes) Then the teacher will hand out the first worksheet containing the four vocab words and the chart of trigonometric function as ratios for the students to complete.

4.  (15 minutes) The teacher will then instruct the students to move to the computers and complete both parts of the worksheet. - Read Text

◦  Along with their definition, the students should provide the website address, as a form of citation/reference.

◦  The students should use a math-related websites and use their best judgment when selecting definitions.

◦  Plan B: Have student read the section 7.1 in their textbook. For information not provide in textbook, the teacher will provide the information.

5.  (13 minutes) The teacher will then have students provide, orally, their definitions and formulas to the rest of the class. - Discussion

◦  The teacher will write each word on the board, and have two volunteers give their definition.

▪  The students will decided which definition is the best and the teacher will write the definition on the board.

◦  The teacher will then, with the help of the students, fill in the chart for all the trigonometric functions as ratios.

6.  (2 minutes) The teacher will handout the next worksheet.

7.  (3 minutes) The students will be guided to the website http://nlvm.usu.edu/.

◦  Once there, have the students select the box for Geometry, 9 – 12.

◦  The students should scroll down and open the manipulative, Right Triangle Solver.

8.  (5 minutes) The teacher will then demonstrate how to use the manipulative, showing how to selecting the unknown, determining the method, place the variables into the equation and finding the solution.

◦  Note: the questions are randomly generated, so the students might have a different question from the teacher, so it would be best to note and explain this to the students.

9.  (5 minutes) Then the teacher should point out that this manipulative does not have the students solve for all aspects of a right triangle, so they need to find the rest.

◦  Most are provided on the website, but they will to find all measurements for sides and angles.

◦  The teacher will also provide an example of finding all the trigonometric functions as ratios for one of the angles, using the chart created earlier.

10.  (15 minutes) Students should use their worksheets and completing three problems on their own, not only finding the unknown that the manipulative is asking for, but the measurements of all of the sides and angles, as well as, the ratio of the trigonometric functions of one angle. - Do Drill and Practice

11.  Plan B: If technology will not work, the teacher should have ready 4 different triangle so the student can complete the worksheet.

12.  (5 minutes) The teacher will refer back to the prompt from the beginning of class and will look at the list of real-life examples of right triangles. - Discussion

◦  The teacher will ask if the students could provide any more examples.

13.  (5 minutes) The teacher will finish the class by complete the following real-world example:

◦  A lamp post is 10 feet tall and casts a shadow. The distance from the top of the lamp post to the tip of the shadow is 20 feet.

◦  The teacher will find the all angles, the hypotenuse, and the trigonometric ratios of the one angle for the triangle.

Evaluation:

Homework: Pages 491 – 492: 9 – 17 odd, 29 – 41 odd, 43, 45, 48, and 51

Differentiation and Adaptations:

ñ  For a hearing-impaired student, everything will be written on the board, as well as, they can work along with partner.

ñ  If a student has a reading impairment, then a fellow student or the teacher can read aloud to him/her from the website.

Citation:

Utah State University (2010). National Library of Virtual Manipulatives. Retrieved from http://nlvm.usu.edu/