Subjects:  Mathematics, Language Arts 

Learner Outcomes:
1.  The student will discover the relationships between the sides of 30-60-90 and 45-45-90 triangles.
2.  The student will express these relationships in complete sentences.
3.  The student will solve problems involving these types of triangles.

Duration of Lesson:  One fifty-minute class period.
 
Materials:  Protractors, rulers, Special Right Triangles Discovery Worksheet, Special Right Triangles Exercise Worksheet,  Special Right Triangles Exercise Worksheet Key Part 1 and Part 2, calculators,  and computers

Technology Tools/Courseware:  Internet

Teacher Notes:
1.  Schedule the computer lab.
2.  Check for any students who do not have a signed Technology Use Consent Form on file.
3.  Assess prior knowledge for understanding of ratio and simplest radical form.

Procedures:
1.  Distribute rulers and protractors.
2.   Ask students to draw a square that measures ten centimeters on each side and write the measurements on each side.  Have students draw one diagonal of the square and label the measures of the angles in one of the triangles formed.  Direct students to find the length of the diagonal as an exact answer (simplest radical form) and then as a decimal approximation.
3.  Have the students to repeat the above steps for a square measuring eight centimeters on each side.

4.  Ask the students to draw an equilateral triangle that measures ten centimeters on each side.  Have students draw the altitude from one vertex and label the measures of the angles of one of the smaller triangles formed.  Students are to find the lengths of the sides of the small triangle as an exact answer and as an approximation.
5.  Have the students repeat the above steps for an equilateral triangle measuring seven centimeters on each side.
6.  Distribute the Special Right Triangles Discovery Worksheet and ask students to use the computer to access M.Yates site.  The site has an  interactive Java Sketchpad activities for 45-45-90 and 30-60-90 triangles.  Students should follow the steps on the worksheet and answer the questions.
7.  Ask students to write a conjecture about the relationship between the sides of a 45-45-90 and 30-60-90 triangle.
8.  Have the students verify his/her conjecture at one of the following sites.  Go to Braddock Math and scroll to page nine of fourteen or visit UCES Archive.  Then students should draw and label the 45-45-90 and 30-60-90 triangles in their notes.  Require the students to use complete sentences to state the relationships between the sides of these special right triangles.
9.  Distribute the Special Right Triangle Exercise Worksheet.  Work two or three of the problems with the class.  Assign the remaining problems as independent practice.

Modifications:  The teacher should consult any Individual Educational Plans and make indicated accommodations.  The teacher should give individual help to any student having difficulty with the protractor or ruler.  The teacher may assign preferential seating to encourage peer tutoring.

Enrichment Activities:
1.  Have the students visit the Math Puzzle.  Scroll down the page and find Sawblade and Pinwheel by Bob Harris.  Make a puzzle of your own design using pieces formed by 30-60-90 triangles.
2.  For a challenge, ask the students to go to Sat math.  Students should copy the problem and solve before scrolling down to the solution.

Evaluation/Assessment:  Use teacher observation to evaluate drawings and calculations.  Score worksheets by percent accurate.  Use a rubric to evaluate the conjectures and notes.

West Virginia IGOs:
       Mathematics:  7.40, 8.36, Al.4, Al.18, G.12
       English/Language arts:  7.57, 8.49, 9.47
 

National Standards:
    Mathematics:
        Uses a variety of strategies in the problem solving process
        Understands and applies basic and advanced properties of the concepts of geometry
        Understands and applies basic and advanced properties of functions and algebra
    English/Language Arts:
        Uses the general skills and strategies of the writing process
        Uses grammatical and mechanical conventions in written compositions

Workplace process skills:  PW.2, PW.8, PW.9, PW.10, PW.27, PW.28, PW.36, and PW.44
Job/Career Cluster:  Engineering/Technical.

References:
Homework Help 1

Geometry Words
Math Study Strategies
Sketch
McCallie/Yates

Authors:  Dianne Smith
               Donna Pittman
               Teresa Lester
               Shady Spring Junior High School