Goals: Each student will be able to find magnitude and direction of vectors.
Objectives: Students will be able to use vectors to describe distance (or speed) and direction a particular object has traveled. Students will be able to describe the effects wind speed and direction has on the bearing of an object.
State Standards: MACC.912.N-VM.1.1 Recognize vector quantities as having both magnitude and direction.
Engage: Vectors are applied in many areas of science and engineering. They are often used to represent velocity and direction of a moving object. Vectors can also be used in reading maps. It is helpful to have a working knowledge of following and giving directions. For example, if you take a boat out on the water, you should be able to determine the direction and distance of where you are from where you began.
Lesson Procedure:
1) Students must review the trigonometric ratios using the mnemonic SOHCAHTOA
Sin = Opp Cos = Adj Tan = Opp
Hyp Hyp Adj
2) Explain vectors to students. Show them that there is magnitude (which could be length or speed depending on the application) and direction. Review basic map directions (North, East, South, West).
3) Show students how to place a vector on a coordinate system in standard position.
4) Work through this example on board with students: Given the vector < -15, 20 > in standard position, determine its magnitude and direction angle.
Have student begin by plotting the vector and form
a right triangle to the x-axis.
5) Work through this example on board with students: Write the component form of a vector whose magnitude is 50 and is positioned at 25◦ E of N.
Students will need to know that this vector lies in Quadrant I of an xy-plane. Show them how to sketch a figure. I will explain to students to drop a vertical segment (y) down to the x-axis to create a right triangle. Remind students to find the angle inside the triangle at the origin (65◦).
6) Show video "Overview of Trigonometry and Bearings" to students. Bring up practice problems for determining bearing and distance to have students do in class. Select students at random to work problems on smartboard.
7) Show video "Direction Angles" to students. Bring up practice problems on finding magnitude and direction angle to have students do in class. Select students at random to work problems on smartboard.
Exploration/Assignment: Students will sign up for a braingenie account and use class code v1i6p2z7 to join my class. Once they are logged in, they need to complete two lessons: Find the component form of vector and using vectors to find speed and direction.
Closure: This lesson should take one to two class periods for instruction. Students will be given web assignment to complete before the next class. Provisions will be made for those that need to use school computer lab after school to complete assignments.
Extension/Elaboration: To give students an opportunity to see more application of vectors, I will use my smartboard to put up "Vector Investigations" from NCTM's Illuminations website. This is an interactive game in which students must use their knowledge of magnitude and direction of vectors to steer a boat towards an island and find a school of fish while not crashing the boat. I can also use www.nctm.org/standards/content.aspx?id=26778 as another application of vectors. This one has students steer a car without crashing, then has the car chase a tornado. I think both of these are excellent example to encourage discussion about vectors.
Evaluation/Assessment: Students’ results will be sent to me through the braingenie website. Students will be given their scores/results to determine how well they understand the lesson. The website allows the student to redo the lesson until they can successfully answer each question. As the teacher, I will be able to see how many times it takes a student to complete the lesson.
Objectives: Students will be able to use vectors to describe distance (or speed) and direction a particular object has traveled. Students will be able to describe the effects wind speed and direction has on the bearing of an object.
State Standards: MACC.912.N-VM.1.1 Recognize vector quantities as having both magnitude and direction.
Engage: Vectors are applied in many areas of science and engineering. They are often used to represent velocity and direction of a moving object. Vectors can also be used in reading maps. It is helpful to have a working knowledge of following and giving directions. For example, if you take a boat out on the water, you should be able to determine the direction and distance of where you are from where you began.
Lesson Procedure:
1) Students must review the trigonometric ratios using the mnemonic SOHCAHTOA
Sin = Opp Cos = Adj Tan = Opp
Hyp Hyp Adj
2) Explain vectors to students. Show them that there is magnitude (which could be length or speed depending on the application) and direction. Review basic map directions (North, East, South, West).
3) Show students how to place a vector on a coordinate system in standard position.
4) Work through this example on board with students: Given the vector < -15, 20 > in standard position, determine its magnitude and direction angle.
Have student begin by plotting the vector and form
a right triangle to the x-axis.
5) Work through this example on board with students: Write the component form of a vector whose magnitude is 50 and is positioned at 25◦ E of N.
Students will need to know that this vector lies in Quadrant I of an xy-plane. Show them how to sketch a figure. I will explain to students to drop a vertical segment (y) down to the x-axis to create a right triangle. Remind students to find the angle inside the triangle at the origin (65◦).
6) Show video "Overview of Trigonometry and Bearings" to students. Bring up practice problems for determining bearing and distance to have students do in class. Select students at random to work problems on smartboard.
7) Show video "Direction Angles" to students. Bring up practice problems on finding magnitude and direction angle to have students do in class. Select students at random to work problems on smartboard.
Exploration/Assignment: Students will sign up for a braingenie account and use class code v1i6p2z7 to join my class. Once they are logged in, they need to complete two lessons: Find the component form of vector and using vectors to find speed and direction.
Closure: This lesson should take one to two class periods for instruction. Students will be given web assignment to complete before the next class. Provisions will be made for those that need to use school computer lab after school to complete assignments.
Extension/Elaboration: To give students an opportunity to see more application of vectors, I will use my smartboard to put up "Vector Investigations" from NCTM's Illuminations website. This is an interactive game in which students must use their knowledge of magnitude and direction of vectors to steer a boat towards an island and find a school of fish while not crashing the boat. I can also use www.nctm.org/standards/content.aspx?id=26778 as another application of vectors. This one has students steer a car without crashing, then has the car chase a tornado. I think both of these are excellent example to encourage discussion about vectors.
Evaluation/Assessment: Students’ results will be sent to me through the braingenie website. Students will be given their scores/results to determine how well they understand the lesson. The website allows the student to redo the lesson until they can successfully answer each question. As the teacher, I will be able to see how many times it takes a student to complete the lesson.