Navigating Bearings: Mastering Directional Math Problems

Algebra 2 Grades High School 3:59 Video
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Lesson Description

This lesson plan uses Mario's Math Tutoring video to teach Algebra 2 students how to solve bearing math problems, including converting between different bearing notations and using the Law of Cosines to find distances.

Video Resource

Bearing Math Problems

Mario's Math Tutoring

Duration: 3:59
Watch on YouTube

Key Concepts

  • Bearing notation (clockwise from North, and North/South with degree East/West)
  • Cardinal directions (North, South, East, West)
  • Law of Cosines
  • Angle measurement and conversion

Learning Objectives

  • Students will be able to convert between the two different bearing notations.
  • Students will be able to apply the Law of Cosines to solve for unknown distances in bearing problems.
  • Students will be able to accurately sketch bearing directions based on given notations.

Educator Instructions

  • Introduction (5 mins)
    Begin by introducing the concept of bearings and their importance in navigation. Briefly explain the two main ways bearings are expressed: clockwise from North, and using North/South with degrees East/West. Show the first minute of the video as an introduction.
  • Understanding Bearing Notations (10 mins)
    Explain the two types of bearing notations in detail. For the 'clockwise from North' notation, emphasize that the angle is always measured clockwise starting from the North direction. For the 'North/South with degrees East/West' notation, explain that the first direction (North or South) is the reference, and the angle indicates how many degrees to turn towards the second direction (East or West). Refer to video (0:12-1:40).
  • Example Problems: Graphing Directions (10 mins)
    Work through examples of graphing directions based on given bearing notations. Use the examples in the video (1:41) - (2:02) to illustrate how to accurately sketch the direction. Emphasize the importance of starting from the correct cardinal direction (North or South) and turning the correct number of degrees towards East or West. Provide additional examples if needed.
  • Law of Cosines and Distance Calculation (15 mins)
    Introduce the Law of Cosines. Explain when it is applicable (side-angle-side triangle). Go through the example problem presented in the video from 2:03 - 3:05, breaking down each step. Emphasize how to identify the included angle. Discuss the importance of accurate calculations and using a calculator correctly. If necessary, review basic calculator skills.
  • Practice Problems and Wrap-up (10 mins)
    Provide students with additional practice problems involving different bearing notations and applying the Law of Cosines. Have students work individually or in small groups. Circulate to provide assistance as needed. Conclude by summarizing the key concepts and answering any remaining questions. Mention the importance of understanding these concepts for real-world applications.

Interactive Exercises

  • Bearing Notation Conversion
    Provide a list of bearings in one notation (e.g., '250 degrees from North') and ask students to convert them to the other notation (e.g., 'South X degrees West').
  • Ship Navigation Simulation
    Create a simulated scenario where two ships are traveling on different bearings. Provide the bearings and distances traveled. Ask students to calculate the distance between the two ships using the Law of Cosines. Students can use online graphing tools or physical graph paper to visually represent the problem.

Discussion Questions

  • In what real-world scenarios would understanding bearings be important?
  • What are some potential sources of error when calculating distances using bearings and the Law of Cosines?
  • Can you think of situations where you could apply knowledge of bearing to solve navigation problems?

Skills Developed

  • Spatial reasoning
  • Problem-solving
  • Trigonometry application
  • Mathematical modeling

Multiple Choice Questions

Question 1:

What is the bearing of 135 degrees measured clockwise from North?

Correct Answer: South 45 degrees East

Question 2:

Which direction do you initially face when given a bearing of South 60 degrees West?

Correct Answer: South

Question 3:

What mathematical concept is primarily used to find the distance between two points given side-angle-side information in bearing problems?

Correct Answer: Law of Cosines

Question 4:

A ship heads North 30 degrees East. What is the angle between the ship's path and the North direction?

Correct Answer: 30 degrees

Question 5:

If two ships leave from the same point, one traveling South 50 degrees East and the other South 30 degrees West, what is the included angle between their paths (at the starting point)?

Correct Answer: 100 degrees

Question 6:

Which of the following is equivalent to a bearing of 270 degrees clockwise from North?

Correct Answer: West

Question 7:

What is the purpose of drawing a coordinate axis when solving bearing problems?

Correct Answer: To accurately represent and visualize directions

Question 8:

What formula is x^2 = a^2 + b^2 - 2ab * cos(C)?

Correct Answer: Law of Cosines

Question 9:

Which tool is most helpful for accurately calculating the distance between two ships using the Law of Cosines, especially with non-integer values?

Correct Answer: Calculator

Question 10:

How does bearing notation typically start when using cardinal directions?

Correct Answer: North or South

Fill in the Blank Questions

Question 1:

A bearing is measured ________ from North.

Correct Answer: clockwise

Question 2:

When given the notation 'North X degrees West,' you first face ________.

Correct Answer: North

Question 3:

The formula used to find a missing side when you know two sides and the included angle of a triangle is the Law of ________.

Correct Answer: Cosines

Question 4:

In bearing problems, the directions North, South, East, and West are known as ________ directions.

Correct Answer: cardinal

Question 5:

A ship heading South 45 degrees East is traveling towards the ________ quadrant.

Correct Answer: Southeast

Question 6:

To find the angle between two paths when given bearings such as 'South 20 degrees East' and 'South 30 degrees West,' you need to determine the ________ angle.

Correct Answer: included

Question 7:

The value of 'a', 'b', and 'c' in the law of cosine represent the length of the _______ of a triangle.

Correct Answer: sides

Question 8:

When a ship has a bearing of 0 degrees from North, the ship is heading ________.

Correct Answer: North

Question 9:

The Law of Cosines is helpful when dealing with _______ triangles.

Correct Answer: non-right

Question 10:

If a ship heads South and then travels 90 degrees West, it is now heading ____.

Correct Answer: West

Educational Standards

A2.A.1:Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context. A2.F.1:Understand functions as descriptions of covariation (how related quantities vary together).

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