Download Export To Word

Rockin' Right Triangle Ratios
Resource ID#: 28821
Primary Type: Lesson Plan
This document was generated on CPALMS - www.cpalms.org
Special Right Triangles and the ratios that work when you have to do to learn those ratios for 3060-90 and 45-45-90 triangles.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Instructional Time: 1 Hour(s) 30 Minute(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: Right Triangle, Special Right Triangles, Applied Ratios of right triangles
Instructional Component Type(s): Lesson Plan, Worksheet, Formative Assessment
Instructional Design Framework(s): Confirmation Inquiry (Level 1)
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
GreenAM1 WarmupSRT1.docx
GreenAM1ClassWorkSRT2.docx
GreenAM1ClassWorkSRT3.docx
GreenAM1SRT5.doc
GreenAM1ClassWorkSRT4.docx
LESSON CONTENT

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this
lesson?
Students will be able to use 30-60-90 and 45-45-90 ratios to solve for the lengths of the sides of a right
triangle with these angle measures and understand that by similarity, side ratios in right triangles are
properties of the angles in the triangle.
The objective of this lesson is to have a student given any single side of one of the special right triangles,
will be able to find the other two side lengths using ratios related to the triangle given.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should understand what a right triangle is and be able to recognize isosceles right triangles,
scalene right triangles and angle measures of triangles. They should also have an understanding of extended
ratio and how to solve equations involving them.

Guiding Questions: What are the guiding questions for this lesson?
If a triangle is a 45-45-90 triangle is it also and Isosceles right triangle?
It a right triangle has an angle measure of either 30 or 60, is it also a 30-60-90 triangle?
When can we not use these ratios to solve right triangles?
What is the pattern of these triangles that make up an extended ratio?
How can knowing the extended ratios of these triangles make finding the missing two sides of the triangle
easier?
What is the easiest way to remember when to use or into the equation? (45-45-90 has two angle measures
and gets 30-60-90 has three angle measures and gets )
When might a contractor or architect need to use these skills?

Teaching Phase: How will the teacher present the concept or skill to students?
Special right triangles can take one or two days depending on time limitations. The material can be done in
one 50 minute class or each type of special right triangle can have its own day, in which case a second
warm up would be needed.
The lesson begins with a warm up exercise to practice the prior knowledge as given in the warm-up
worksheet. These problems should concern finding the values in extended ratios, on sides of triangles.
GreenAM#1WarmupSRT1: Assign problems 1 - 4 Pythagorean theorem problems on just 45-45-90
triangles with one side missing. GreenAM#1ClassworkSRT2: As they are working ask students look for a
pattern in the length of the sides. Have them attempt to set up an extended ratio using the information the
students have gleaned from this exercise. Set up ratios in 45-45-90 triangles in a prominent place on the
board where students can look up to see it. Have students go back to look at their previous problems
making sure this extended ratio works.
Assign students a few more problems for practice. Have the answers ready so students who finish first are
able to check their work while you walk around and help those who are still struggling. At least 80% of the
students should be proficient before you move on. Also have new problems for students who understand
the above can go on and work ahead on their own. Assign a few Pythagorean theorem 30-60-90 problems
with one side missing. Remind students to look for a pattern in the lengths of the sides. Have them attempt
to set up an extended ratio of the length of the sides. Set up ratios in a prominent place on the board for a
student reference point. Have students compare and contrast the two sets of ratios. Talk about how the
students can remember which ratio set goes with which type of these special right triangles. Give students a
set of problems that requires them to determine which set of ratios to use and to solve for the two different
types of Special right triangles.

Guided Practice: What activities or exercises will the students complete with teacher
guidance?
The students will do a warm up exercise to prepare them for the lesson.
They will do practice problems with 45-45-90 triangles.
They will do practice problems with both 45-45-90 problems and 30-60-90 problems.

Independent Practice: What activities or exercises will students complete to reinforce
the concepts and skills developed in the lesson?
Activities and exercises are included in the classwork, homework and extra practice sheet provided.
Students will get 15 to 20 problems that use special right triangles. At least 10% of those problems should
be extended use of the skill.
GreenAM#1 WarmupSRT1
GreenAM#1ClassWorkSRT2
GreenAM#1ClassWorkSRT3
GreenAM#1ClassWorkSRT5

Closure: How will the teacher assist students in organizing the knowledge gained in the
lesson?
Teacher will have students compare and contrast the two types of triangles and they should discover that
the 45-45-90 triangle has a ratio of x:x:x sqrt(2) and the 30-60-90 triangle has a ratios of x:2x:x sqrt(3).

Summative Assessment
Student assessment would be in the test at the end of the chapter.

Formative Assessment
By observing students work on problems, as in problems with lesson, at their desks, teachers can stop a
student mid-work and point them in the right direction. Sending students to the board, in pairs, gives a
weaker student someone to bounce ideas off of, and helps cognitive learning of the stronger student. A
teacher can reteach, the parts of the lesson the majority of students are struggling with.

Feedback to Students
Students should get a short quiz at the end of the lesson to help them determine how well they know the
material taught. I often have the students grade their own quizzes with red pens that are passed out for this
activity. Homework should always be gone over. Answers are posted for students to check their own work,
and questions are answered up to 10 minutes of a 50 minute class.
ACCOMMODATIONS & RECOMMENDATIONS

Accommodations:
Students with special needs will receive guided notes, can do a few less problems in the class work and
homework. They can use the ratios on tests, and will not be expected to memorize the ratios, while regular
students have to memorize the ratios and how to recognize them.

Extensions:
Extensions can be in the form of a riddle page of triangles that deal with Pythagorean theorem and special
right triangles. SEE Attachment: GreenAM#1SRT4.

Special Materials Needed:
Document camera, LCD projector, Paper, Pencil, white board or chalk board

Further Recommendations:
This lesson is used in Geometry, but is an important part of Pre-Calculus or Trigonometry.
Additional Information/Instructions
By Author/Submitter
This lesson is for 45-45-90 and 30-60-90 triangles in geometry, but is an important part of PreCalculus or Trigonometry.
SOURCE AND ACCESS INFORMATION
Contributed by: Annetta Green
Name of Author/Source: Annetta Green
District/Organization of Contributor(s): Seminole
Is this Resource freely Available? Yes
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-SRT.3.6:
Description
Understand that by similarity, side ratios in right triangles are
properties of the angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.