Math 8 Standard 7 08-30
9/5/02
11:32 AM
Page 193
TIMSS
NAEP
Standard Indicators
8.7.1-8.7.12
Trig Discovery
Purpose
Students will solve problems by choosing strategies, explaining their
reasoning, making calculations, and checking results.
connecting
across the
curriculum
Materials
For the teacher: chalkboard, chalk, protractor
For each student: copy of Black Line Master (BLM) Triangle Lab,
paper, pencil, protractor, ruler
Activity
A. Pre-Activity Preparation
Research on the Internet or at the library to find some interesting
historical information about the study of right triangles to present
to the class.
B. Introducing the Problem
1. Give a presentation on the study of right triangles in a historical
perspective.
2. Tell students that mathematicians as far back as 2000 B.C.E.
have studied the relationships between sides and angles of
right triangles.
3. Draw a right triangle on the chalkboard. Label the vertices
“A,” “B,” and “C,” with C at the right angle.
4. Use the drawing to clarify the meaning of the terms adjacent
and opposite. Name and label the side opposite ∠A as side “a.”
Do the same for ∠B and ∠C.
5. Show and explain which sides are opposite and adjacent to
each angle.
6. Explain that side c, the side opposite the right angle, is called
the hypotenuse.
7. Ask students to name relationships they are aware of between
the sides of a right triangle. Discuss each named relationship
with the class and list it on the chalkboard.
8. Tell students that they will be searching for additional
relationships in today’s Triangle Lab.
English/
Language Arts
Have students write
a persuasive paragraph
using the findings from
the BLM Triangle Lab.
Explain that they are
charged with the
building of an animal
shelter in the shape
of a 45-45-90 isosceles
right triangle. Instruct
students that two sides
of the shelter need to
measure 80 feet each.
Tell students to find the
length of the third side
of the structure and
explain in detail why
this is the only possible
measurement for the
third side.
(continued)
Standard 7 / Activity 6
Indiana Mathematics Grade 8 Curriculum Framework, October 2002
Standards Links
8.2.1, 8.4.1
page 193
Standard 7
C. Solving the Problem
1. Divide the class into groups of three students.
Math 8 Standard 7 08-30
9/11/02
11:12 AM
Page 194
Activity (continued)
2. Ask each group member to draw a right triangle on his/her own
paper. Tell them to use one 90°, one 30°, and one 60° angle.
Explain that this triangle is commonly referred to as a 30-60-90
right triangle.
3. Ask them to vary the sizes of the triangles so that one group
member draws a small-sized right triangle, one draws a mediumsized right triangle, and one draws a large-sized right triangle.
4. Have students trade the drawings within their group and
measure the angles to confirm they are of the correct
measurement.
5. Distribute one copy of the BLM Triangle Lab to each student.
Ask students to complete the table entries for the 30-60-90
right triangle.
6. Have students repeat steps 3 through 5, this time drawing a
45-45-90 right triangle and ask students to complete the table
entries for the 45-45-90 right triangle.
7. Allow ample time for groups to complete the BLM.
8. Write the following questions on the chalkboard:
How do your ratios compare to the ratios of your group
members? [They should be the same.]
Using your Triangle Lab as a reference, make a prediction
about the ratio of the legs of any 30-60-90 triangle.
[Ratio is 1: 3 ]
Using your Triangle Lab as a reference, make a prediction
about the ratio of the legs of any 45-45-90 triangle.
[Ratio is 1:1]
side 2
adjacent side 2
Find the value of ( opposite
hypotenuse ) + ( hypotenuse ) for each angle.
What do you notice about each value? [equal to 1]
9. Lead a class discussion of students’ findings.
Classroom Assessment
Basic Concepts and Processes
While students complete the BLM, ask the following questions
to gauge their understanding of the Standard Indicators:
What is the side opposite the right angle called?
Explain why each triangle in your group is a different size
but the angle measurements are the same.
Standard 7
Which side is opposite [indicate angle of student’s triangle
by name]?
Which side is adjacent to [indicate angle of student’s triangle
by name]?
page 194
Standard 7 / Activity 6
Indiana Mathematics Grade 8 Curriculum Framework, October 2002
Math 8 Standard 7 08-30
9/5/02
11:32 AM
Page 195
Name:
Triangle Lab
Complete the tables below based on the measurements of your triangles.
30° angle
60° angle
45° angle
30° angle
60° angle
45° angle
Measure of opposite side
Measure of adjacent side
Measure of hypotenuse
Ratio
opposite side
adjacent side
opposite side
hypotenuse
adjacent side
hypotenuse
Standard 7 / Activity 6
Indiana Mathematics Grade 8 Curriculum Framework, October 2002
Black Line Master 1
page 195
Math 8 Standard 7 08-30
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11:32 AM
Page 196
Triangle Lab
Teacher Directions
Give each student a copy of the BLM Triangle Lab. Ask each group member to draw one 30-60-90
triangle and one 45-45-90 triangle. Have students measure the triangles, complete the table
entries on the BLM, and answer the problems written on the chalkboard. Use results from
the BLM to lead a class discussion.
Answer Key
Answers will vary, but should be close to trigonometry ratios for 30°, 60°, and 45° angles.
Black Line Master 1
page 196
Standard 7 / Activity 6
Indiana Mathematics Grade 8 Curriculum Framework, October 2002