Sarah Slade - Michigan Technological University



Sarah Slade

Math and Navigation Teacher Institute

Lesson Plans

August 10, 2010

Lesson Plan #1: Real Life Application of Rates: Using Nautical Charts to Plan a Trip from Leland, Michigan, to North Manitou Island Loading Dock.

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Grade Level: 6th

Lesson Overview:

Rates have many real life applications, such as miles per hour, miles per gallon, cost per unit of weight, and calories per serving. Students in sixth grade are expected to solve applied problems involving rates such as those listed above. This activity is to be used after students complete Lesson 7-2 Rates, in the Glencoe Hill Mathematics Textbook. (It’s our math text for the sixth grade).

In this activity, students plan a boat trip from Leland to North Manitou Island. Their goal is to compute the travel time. They utilize charts to measure the distance in miles, they are given miles per hour.

Sources Consulted:

Brogdon, Captain Bill. Boat Navigation for the Rest of Us. International Marine/McGraw Hill. 2001.

Glencoe Mathematics Applications and Concepts Course 2. McGraw Hill Glencoe. 2006.

Materials Needed:

Glencoe Hill Mathematics Textbook listed above (1)

Lake Michigan Charts for Leland/North Manitou (one for every four students)

Square Leg Divider (for measuring distance on charts) (1 for every 4 students)

Calculator (each student)

Laptops with excel software (one per student)

New Vocabulary:

Rate: A rate is a ratio that compares two quantities with different kinds of units.

Unit rate: A unit rate occurs when a rate is simplified so that it has a denominator of 1 unit.

Focus Questions:

1. What formula is used to solve problems involving rate? ( distance = rate x time)

2. Given a speed of 8 knots, how long will it take to reach North Manitou Island?

3. Use excel and construct a spreadsheet and graph showing how long it will take to reach the Island based on various speeds (students make up the speeds). Explain why the ferry might be able to travel faster or have to travel slower (what are the variables).

Learning Objectives:

1. Students will learn how to read a nautical chart.

2. Students will learn how to utilize a square leg divider.

3. Students will calculate the distance from Leland Harbor to the North Manitou Landing Dock.

4. Students will calculate how long it takes to travel from Leland to North Manitou Island Landing Dock. (They will be given the speed of the ferry).

5. Students will create a spreadsheet and line graph on Excel, showing various travel times to the Island.

Michigan Sixth Grade GLCE’s:

A.PA.06.01 Solve applied problems involving rates including speed, e.g., if a car is going 50 mph, how far will it go in 3.5 hours?

N.FL.06.10 Add, subtract, multiply and divide positive rational numbers fluently.

N.FL.06.14 For applied situations, estimate the answers to calculations involving operations with rational numbers.

A.FO.06.06 Represent information given in words using algebraic expressions and equations.

Classroom Activity:

1. Review the concept of rate with the following short youtube video:

2. Introduce nautical charts by showing students the chart for Leland. Relate travel by land to travel on the water (distance is measured in nautical miles and speed is measured in knots).

3. Show the following video that details how to measure distance on a nautical chart:



4. Tell students they will be calculating the distance from Leland to North Manitou Island Landing Dock as well as the time it takes to travel there based on a given speed.

5. Students work in groups of three with a chart to calculate distance.

6. They compute the travel time using a speed of 9 knots.

7. Allow work time here for groups to complete this activity. Review as a class.

8. Students use laptops to construct a table and line graph showing how travel time varies according to speed. They are to choose various speeds, explaining why the ferry boat may have to travel at various rates. Students print tables/graphs.

9. Display work and share as a class.

10. Students finish the lesson by reflecting in their math foldable (their journal) as to how this lesson enhanced their understanding of rates.

Assessment:

1. Student grades are based on completion of the problems assigned (see focus questions above). They are expected to show the steps of problem solving.

2. Student grades are also based on completion of a table and line graph. Students are to print their tables and line graph.

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