Download Rockin Right Triangle Ratios

Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 28821
Rockin' Right Triangle Ratios
Special Right Triangles and the ratios that work when you have to do to learn those ratios for 30-60-90 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 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 )
page 1 of 3 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 3060-90 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 Pre-Calculus or Trigonometry.
SOURCE AND ACCESS INFORMATION
Contributed by: Annetta Green
page 2 of 3 Name of Author/Source: Annetta Green
District/Organization of Contributor(s): Seminole
Is this Resource freely Available? Yes
Access Privileges: Public
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.
page 3 of 3