Teaching Mathematics through Navigation Summer Teacher Institute
Lessons developed by 2011 Participants
ELEMENTARY
1. Marine Navigation Using a Compass Rose, by Julie E. Junttila
4th Grade, Social Studies and Math
Unit Overview
Students will become familiar with using cardinal and intermediate directions to describe relative locations of significant places in the U.S. by viewing and listening to information on the compass rose, practicing with a compass on locating objects/reference points inside/outside the classroom, and using directional skills to guide a fictional ship through U.S. water bodies.
2. The Route of the Edmund Fitzgerald, by Julie E. Junttila
4th Grade, Social Studies and Math
Unit Overview
Students will be able to draw upon stories, photos, artifacts, and other primary sources to compare the life of people in towns and cities in Michigan and in the Great Lakes region during the time period of 1975-2011.
Students will be able to use geographic tools and technologies, stories, songs, and pictures to answer geography questions about the U.S. by listening to, viewing, and discussing a story and song about the Edmund Fitzgerald, a map of Lake Superior, and studying latitude and longitude with dividers and roller plotters.
Students will be able to measure using common tools and select appropriate units of measure by using dividers and roller plotters to map the points of latitude and longitude of the actual route of the Fitzgerald, and alternative route points, which may have been safer choices.
3. Learning Directions and Degrees of Movement by Jeff Adamick
5th Grade, Special Education Math
Unit Overview
Students will become familiar with a starting direction and respond correctly given a degree and rotation. This lesson involves a hands-on activity and is great for hyperactive students that need to move around.
MIDDLE SCHOOL
8. Learning Directions and Degrees of Movement by Jeff Adamick
6th Grade, Special Education Math
Unit Overview
Students will measure a route, find the distance, figure the direction in degrees and solve the time it takes for each leg of a boat trip.
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HIGH SCHOOL
1. Using Vectors to Navigate (Day One), by Randall L. Elenbaas
9-12 Grade, Geometry or Algebra 2
Unit Overview
This lesson should be presented after the students have worked with vectors in the coordinate plane.
Students will research the concept “to navigate” including vocabulary words heading, bearing, direction, and distance. Students will be able to compare and contrast headings in navigation and the direction of a vector in a coordinate plane. Students will use charts to plot a course, giving the heading and distance for each leg and then convert each heading to a direction and distance for the coordinate plane.
2. Using Vectors to Navigate (Day Two), by Randall L. Elenbaas
9-12 Grade, Geometry or Algebra 2
Unit Overview
Students will plot a course diagonally across the gym floor around set up obstacles using (1) vectors from Algebra2 and (2) headings from navigation.
3. Plotting a Course through the School, by Randall L. Elenbaas
11th grade Trigonometry
Unit Overview
The overall goal of this lesson is for students to plot a course through the school from one end to the other using navigational techniques. The students will use a blueprint of the school as a map for planning the course. The First day will be spent learning about plotting a course. The second day will be spent actually plotting the course through the school and then testing the course by going through the school.
4. Finding Locations on a Chart with Polar Coordinate, by Randall L. Elenbaas
11th grade Trigonometry
Unit Overview
The overall goal of this lesson is for students to gain an understanding of polar coordinates through use of navigational charts. Students should be able to convert rectangular coordinates to polar coordinates.
5. Getting Your Fix: How to Determine One’s Location Using Lines of Position, by Serena Gay
9-12 Grade, Geometry
Unit Overview
In this lesson, students will learn about navigation as it applies to the compass and how bearings to three different objects can be used to identify the location of an unknown object or person. They will learn the difference between magnetic and true headings by constructing a compass rose (reinforcing previous knowledge of central angles in a circle) and use it to draw three lines of position and identify an unknown location on a map of the local area. They will also apply the geometric constructions for the perpendicular bisector of a segment and erecting a perpendicular through a given line and point on that line as part of an activity that uses a Snellius construction (which is an alternate method of using three known bearings to identify an unknown location). With this lesson, I hope to generate enthusiasm for navigation and show an application of the constructions they’ve learned. The lesson should take no more than two 80-minute class periods, allowing time for warm-ups, discussion and working on their projects.
6. Plotting and Adjusting Your Course: Using Vectors and Trigonometry in Navigation, by Serena Gay
9-12 Grade, Precalculus
Unit Overview
In this lesson, students will use their previous knowledge of trigonometry and vector representations of motion to perform the operations of addition and subtraction on given sets of vectors. Students will represent the paths of boats and planes using vectors and investigate the effects of current and wind on these paths using vector addition (i.e. find the altered path). They will also determine a path necessary to keep them on an intended path given the constraints of the current/wind using subtraction of vectors. We’ve used navigation applications in the past to teach vector operations, but this lesson will hopefully generate more enthusiasm by letting them learn about and actually use a nautical chart as part of the learning process. This lesson should take about two or three 80-minute class periods, given time for a warm-up review of the trig and vectors, introduction to new concepts, learning how to read and use the nautical charts and investigation of vector operations through the activities.
7. Oblique Triangles, by Nathaniel Heralde
9-12 Grade, Geometry
Unit Overview
The students will use the law of cosine in order to calculate the measure of the missing side of a triangle.
8. Right Triangles, by Nathaniel Heralde
9-12 Grade, Geometry
Unit Overview
The students will use the angles of elevation and depression and trigonometric ratios in order to solve problems.
9. Lines of Latitude and Longitude, by Keith Johnson
9-12 Grade, Math
Unit Overview
This lesson plan will introduce students to latitude and longitude along with local and universal time. Students will learn how any location on Earth can be defined by its latitude and longitude. Students will also learn the difference between local time and universal time, and the various adjustments made to "clock time," e.g. time zones, daylight saving time and the use of the international date line.
10. Plotting Points in Baltimore Harbor, by Fiel Angela Jose
9-12 Grade, Math
Unit Overview
At the end of the session, the students will be able to use a nautical chart of Baltimore Harbor to give the approximate coordinates of specific markers, navigational aids, and other points o f interest.
11. Convert Decimal Degrees into Degrees, Minutes, Seconds, by Fiel Angela Jose
9-12 Grade, Math
Unit Overview
At the end of the session, the students will be able to use conversion of units to write Decimal Degrees into Degrees, Minutes, Seconds form and vice versa.
12. Vector Resolution, by Robert Madigan
11-12 Grade, Physics
Unit Overview
This lesson will cover vector resolution, magnitude and direction, vector components and the vector resultant. We will use real life examples to calculate correct resultants involving polar coordinates and distance.
13. Dimensional Analysis, by Robert Madigan
11-12 Grade, Physics
Unit Overview
This lesson will be our first physics lesson chapter one section one and define what physics is. Physics is the branch of science that involves the study of the physical world; matter and energy and how they are related. Physics uses math as it language. The last statement is one of the most powerful physics statement made. We must have a firm understand of dimensional analysis before we can continue on our quest for physical knowledge. While taking ED5661 one of the most important concepts was doing conversions from degrees minutes and seconds and also statue miles and regular miles and the understanding on knots and the relationship to miles per hour.
14. Correcting for Magnetic Variation, by Kevin Murphy
11-12 Grade, Physics
Unit Overview
In this lab activity, students will determine the magnetic variation both from a rose wheel on a map and for their exact location (using an Internet source). Also, given a particular displacement (relative to True North), students will convert to a displacement (relative to Magnetic North).
15. Average Velocity and Speed on a Boat Trip, by Kevin Murphy
11-12 Grade, Physics
Unit Overview
In this lab activity, students will use vectors to determine the average velocity and average speed during a boat trip.
16. Calculating Time When Travelling by Water, by Tiffany Scullion
9-12 Grade, Introduction to Algebra
Unit Overview
Students will calculate the time it will take to travel between two or more navigational aids when given distance between (in statute miles) and speed traveled (in knots). The purpose of this lesson is to provide students with an opportunity to use rate conversions and dimensional analysis in a real world situation while providing them with knowledge of nautical charts and map reading skills.
17. Wave Speed and Wind Height on Lake Superior, by Tiffany Scullion
9-12 Grade, Introduction to Algebra
Unit Overview
Students will gather data (wave height and wind speed) from one of MTU’s collection buoys on Lake Superior. They will then use this data to complete a chart, create a scatter-plot, and answer questions regarding the data they collected. The purpose of this lesson is to provide students with an opportunity to practice their data collection skills and graphing in a real world situation.