Beacon Lesson Plan Library
30-60-90 Right Triangles and Algebra
Johnny Wolfe
Santa Rosa District Schools
Description
This lesson covers right triangle relationships of the 30-60-90 triangle.
Standards
Florida Sunshine State Standards
MA.A.1.4.4
Understands that numbers can be represented in a variety of equivalent forms using integers, fractions, decimals, and percents, scientific notation, exponents, radicals, absolute value, or logarithms.
MA.A.3.4.1
Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.
MA.A.3.4.3
Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).
MA.C.3.4.1
represents and applies geometric properties and relationships to solve real-world and mathematical problems including ratio, proportion, and properties of right triangle trigonometry.
Florida Process Standards
Numeric Problem Solvers
03 Florida students use numeric operations and concepts to describe, analyze, communicate, synthesize numeric data, and to identify and solve problems.
Materials
- Overhead transparencies (if examples are to be worked on overhead) for 30-60-90 Right Triangles and Algebra (See Attached File)
- Marking pens for overhead
- 30-60-90 Right Triangles and Algebra Examples (See Attached File)
- 30-60-90 Right Triangles and Algebra Worksheet (See Attached File)
- 30-60-90 Right Triangles and Algebra Checklist (See Attached File)
Preparations
1. Prepare transparencies (if teacher uses overhead for examples) for 30-60-90 Right Triangles and Algebra Examples. (See Attached File)
2. Have marking pens (for overhead).
3. Have 30-60-90 Right Triangles and Algebra Examples (See Attached File) prepared and ready to demonstrate to students.
4. Have enough copies of 30-60-90 Right Triangles and Algebra Worksheet (See Attached File) for each student.
5. Have enough copies of 30-60-90 Right Triangles and Algebra Checklist (See Attached File) for each student.
Procedures
Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals and solving equations.
Note: This lesson does not address percents, scientific notation, absolute value, and logarithms on MA.A.1.4.4. This lesson does not address ratio and proportion on MA.C.3.4.1.
1. Review with students on naming angles and sides of a triangle. (See #1 on Examples.) Answer student questions and comments.
2. Describe to students why we call these 30-60-90 triangles. Make sure students understand what an acute angle is. (See #2 on Algebra Examples.) Answer student questions and comments.
3. Ask students to analyze the equilateral triangle and to come up with the measure of angle B. Make sure students know what constitutes an equilateral triangle. (See #3 on Examples.) Answer student questions and comments.
4. Ask students to draw a perpendicular to the base of triangle ABC. Then have students determine what type of triangles are formed. Make sure students understand what a perpendicular line segment is. (See #4 on Examples.) Answer student questions and comments.
5. Discuss Thought Provoker. Make sure students understand the term bisect. (See #5 on Examples.) Answer student questions and comments.
6. Discuss the measure of the side opposite the 30-degree angle. (See #6 on Examples.) Answer student questions and comments.
7. Discuss how we label triangles. (See #7 on Examples.) Answer student questions and comments.
8. Work #8 example. (See Examples.) Answer student questions and comments.
9. Work #9 example. (See Examples.) Answer student questions and comments.
10. Work #10 example. (See Examples.) Answer student questions and comments.
11. Work #11 example. (See Examples.) Answer student questions and comments.
12. Work #12 example. (See Examples.) Answer student questions and comments.
13. Have students do the Thought Provoker. (See #13 on Examples.) Answer student questions and comments.
14. Work #14 example. (See Examples.) Answer student questions and comments.
15. Work #15 example. (See Examples.) Answer student questions and comments.
16. Work #16 example. (See Examples.) Answer student questions and comments.
17. Work #17 example. (See Examples.) Answer student questions and comments.
18. Work #18 example. (See Examples.) Answer student questions and comments.
19. Work #19 example. (See Examples.) Answer student questions and comments.
20. Distribute the 30-60-90 Right Triangles and Algebra Worksheet. (See Attached File)
21. Distribute the 30-60-90 Right Triangles and Algebra Checklist. (See Attached File) Describe what constitutes an A, B, C, D, and F in the Checklist.
22. The students write their responses on the worksheet.
23. The teacher moves from student to student observing their work and lending assistance.
Assessments
Student worksheets are taken up and scored according to 30-60-90 Right Triangles and Algebra Worksheet Key and Checklist. (See Attached File)
Extensions
Have students take a protractor and measure objects that have 30-60-90 degree angles. Then, using the concepts learned when using a 30-60-90 triangle, determine the length of the diagonal. Then have students measure the diagonal and compare with their computations.
Web Links
Web supplement for 30-60-90 Right Triangles and Algebra Hamilton-Math To Build On- 30 60 90 Right TranglesWeb supplement for 30-60-90 Right Triangles and Algebra Topics in Trigonometry 30 60 90 Triangle
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