Algebra II

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Calculus (A.P

COURSE: BASIC COASTAL NAVIGATION

TOPIC: Position and Course Line on a Nautical Chart

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: CT Frameworks: a) A wide variety of functions can be used to model real world situations. b) Tables, graphs, and equations can be used to analyze linear functions as well as non-linear functions, for which the rate of change is not constant. NCTM Standards: a) Develop a deeper understanding of very large and very small numbers and of various representations of them.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
Small scale charts cover a large area of the earth’s surface and show little detail and large scale charts cover a small area and show more detail Heights in a tide table are given in mean low water form Position on a nautical chart is given in Degree Minute Second format with reference to latitude and longitude. Course line is measured using degrees from the compass rose. Distance on a nautical chart is measured in nautical miles (nm) with dividers Time on a piloting worksheet is given in military time.	What is the best type of chart to use for navigating? How can we determine position on a nautical chart? What is the best way to measure course line on a nautical chart? What is the appropriate scale to use when measuring distance on a nautical chart?
Knowledge and Skills What students are expected to know and be able to do
Students will know… How to interpret the scale on a nautical chart How to locate water depth on a tide table	Students will be able to… Locate position on a nautical chart Measure the course line with a compass rose Measure a distance using dividers
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
Given a sample piloting worksheet, the students will be able to plot a course on their nautical chart.	Have students answer review questions at the end of the chapter. Quizzes and assignments Classwork on simulated navigational problems
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: Use of T-120 Teaching Chart to discuss scale of a nautical chart. Locating a position: The students will be able to find a position given a fixture and also given a position find a fixture. Given two fixtures on a chart, the students will be able to calculate a bearing and distance between the two. Complete review exercises from Ch. 1-8 of Basic Coastal Navigation.

COURSE: BASIC COASTAL NAVIGATION

TOPIC: Distance, Speed, Time, and Bearing

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: CT Frameworks: a) A wide variety of functions can be used to model real world situations. NCTM Standards: a) Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitude of quantities. b) Judge the reasonableness of numerical computations and their results.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
Military time is commonly used for labeling course lines. Calculating distance, speed, and time is necessary for plotting an accurate course Converting a true course to a compass course is necessary for proper navigation	Why is the method of calculating time, distance and speed necessary to know in order to plot a course? Why is the true course bearing different than the compass course bearing?
Knowledge and Skills What students are expected to know and be able to do
Students will know… What the formula is for dead reckoning. What the formula is for course conversion.	Students will be able to… Convert standard time to military time. Add and subtract time. Calculate distance, speed, and time given two of the three variables. Label a dead reckoning position given distance, speed, and time. Convert true course to compass course.
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
Given the legs of a typical day cruise the students will be able to plot their course on a nautical chart.	Have students answer review questions at the end of the chapter. Quizzes and assignments Classwork on simulated navigational problems.
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: Students will solve estimated time of departure and arrival using military time. Students will calculate for the missing variable when solving for time, distance, or speed. Complete review exercises from Ch. 9 and 10 of Basic Coastal Navigation. Given a true course the students will be able to calculate the compass course and vice versa using the TVMDC, Add West Down formula.

COURSE: BASIC COASTAL NAVIGATION

TOPIC: Estimating Speed and Location

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: CT Frameworks: a) Properties of number systems are used to develop strategies for computation and estimation and judging the reasonableness of results. b) Proportional reasoning can be used to make predictions and describe relationships between variables. NCTM Standards: a) Judge the reasonableness of numerical computations and their results. b) Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
Estimation is necessary when plotting a course to prevent improper navigation	Is the time of departure or arrival reasonable? Is the bearing of the course line reasonable? Is the speed for arriving at each position reasonable?
Knowledge and Skills What students are expected to know and be able to do
Students will know… When time, distance, and speed for a course seems incorrect.	Students will be able to… Calculate the correct time, distance, and speed to alter their course accordingly.
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
Given a sample piloting worksheet for a day cruise, the students must find where estimation errors occurred.	Classwork on simulated estimation problems.
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: Use of a T-120 Teaching Chart with a previously plotted course to discuss estimation errors made by the navigator.

COURSE: BASIC COASTAL NAVIGATION

TOPIC: Calculating a Course

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: CT Frameworks: a) Geometric theorems and trigonometric relationships may be used to solve a variety of problems involving one-, two- and three- dimensional measurements. b) A wide variety of functions can be used to model real world situations. NCTM Standards: a) Analyze precision, accuracy, and approximate error in measurement situations.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
Measuring distance with dividers and bearing with a hand held compass must be precise in order to insure proper navigation. Calculating the boat’s distance from an object can be done by finding the object’s height on the chart and the angle of elevation to the top of the object from a hand held compass. Using a deviation table is necessary when converting from true course to compass course.	What are the different methods for calculating the distance from objects when on the water? Why is precision necessary when calculating a course to navigate?
Knowledge and Skills What students are expected to know and be able to do
Students will know… What the precision is when calculating distance and bearing.	Students will be able to… Measure distance on a chart with dividers and bearing with parallel rulers or 45-45-90 triangles. Measure distance on the water using trigonometry or 45-45-90 triangles and bearing using a hand held compass. Create a deviation table using charted objects.
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
On a boat, the students will measure distance using trigonometry or 45-45-90 triangles and create their own deviation table using the boat’s actual compass.	Have students answer review questions at the end of the chapter. Quizzes and assignments. Classwork on simulated distance, bearing, and deviation table problems.
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: Use a T-120 Teaching chart to measure distance with dividers and bearing with parallel rulers or 45-45-90 triangles. Students will solve sample trigonometry and similar triangle problems that simulate calculating distance on the water. Complete review exercises from Ch. 11 of Basic Coastal Navigation.