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# Problem Solving with Triangles

Lesson 7 of 13

## Objective: SWBAT solve problems involving triangles.

*45 minutes*

#### Bell Work

*5 min*

Today students need time to solve problems with the Law of Sines and the right triangle ratios before learning the Law of Cosines. To start class students work on a bell problem. In this problem students will need to do multiple steps to find the value of x.

Once students have had time to problem solve for 2-3 minutes I have a student share the answer and the process for solving. We discuss the process I ask questions like:

- Why did we find angle B?
- Couldn't we have used tan 60=70/20?
- Why not use the Pythagorean Theorem?

The last 2 questions are common errors. Students forget to consider whether the triangle is a right triangle. By asking these questions I am clarifying issues that some students are too afraid to ask.

#### Resources

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#### Problem solving

*35 min*

After the bell work students are given contextual problems to solve. Today is an opportunity for students to work on problems using the concepts we have learned so far in this unit. Unlike many book problems, these problems do not have diagrams. The more practice students get with drawing their own sketches, the more proficient they will become with modeling with mathematics.

Students will need to determine the the best method to solve the problems. At this point students will look at the diagram to determine if the triangle is a right triangle or oblique. Once this is determined students will be able to use the appropriate process to solve.

After about 20 minutes of work. Students are asked to share their diagrams with the class. This is done in a couple of ways. The first way is to begin with problem 1 and move through the problems. The second is to take a poll on which problems students need help and only put those problems on the board. The second approach is more engaging for students since they do not need to wait for their question to be answered.

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#### Closure

*5 min*

Students answer two questions to be turned in when they leave today. This is a student assessment of what material is going well.

For standard based grading I can use this to informally assess the level of proficiency. Questions 1, 4 and 5 of the worksheet I consider a level 2 proficiency while 2 and 3 are at a level 3 proficiency due to the complexity of the drawing and the context. If a student says they are confused with questions 2 and 3 I can document that at this time the student is at a level 2 for the first learning target of the unit.

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- UNIT 1: Introduction to Learning Mathematics
- UNIT 2: Functions and Piecewise Functions
- UNIT 3: Exponential and Logarithmic functions
- UNIT 4: Matrices
- UNIT 5: Conics
- UNIT 6: Solving Problems Involving Triangles
- UNIT 7: Trigonometry as a Real-Valued Functions
- UNIT 8: Graphing Trigonometric Functions
- UNIT 9: Trigonometric Identities
- UNIT 10: Solving Equations
- UNIT 11: Vectors and Complex Numbers
- UNIT 12: Parametric and Polar graphs and equations

- LESSON 1: Review of Angles
- LESSON 2: Solving Right Triangles
- LESSON 3: Law of Sines Introduction
- LESSON 4: Ambiguous Case Day 1 of 2
- LESSON 5: Ambiguous Case Day 2 of 2
- LESSON 6: Finding the Second Solution
- LESSON 7: Problem Solving with Triangles
- LESSON 8: Law of Cosines Day 1 of 2
- LESSON 9: Law of Cosines Day 2 of 2
- LESSON 10: Area of Triangles
- LESSON 11: Review of Solving Triangles Day 1 of 2
- LESSON 12: Review of Solving Triangles Day 2 of 2
- LESSON 13: Solving Triangles Assessment