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666666BOAT UNIT Essential Question:
How does the shape of a vessel affect its ability to carry weight through water?
Formal Assessment (s):
COW #8 Mystery Materials
COW #9 Float Your Boat
COW #10 Ferry Service
Unit 3
Division 1 MST 2008-2009
Description of Unit:
In the Boat unit, students design and float boats while investigating principles of fluid mechanics and dynamics. Math concepts include measurement, formula development and application, ratios and percents, scaling, spatial relations, and the Pythagorean Theorem. Student knowledge is conveyed and celebrated during classroom based presentations in an open-house format.Unit Objectives/Student Outcomes:
The density of a material relative to water determines whether it floats or sinks.
Archimedes Principle
The volume of a cargo ship impacts how much water it displaces, and, therefore, how much weight it can carry.
Engineering can improve the speed of a performance boat hull.
Drag is a friction force on a boat hull.
Understanding and applying the engineering design process
Multi-view drawings are key to the design process. Modeling can convey different ideas about a boat.
Boats can be important, even vital, parts of a society. Some boats may be a local wonder based on their appearance, strength, speed or historical or social impact.Approximate Length:
8 weeks
Math Teaching Questions of the Boat Building Unit
How do you isolating variables to solve for equations? (D=M/V and D*V=M)
How is density represented as the slope of a line?
What are the roles of variables within equations?
What is volume, mass, and surface area?
How do you represent 3-d objects with 2-d multi-view drawings?
How do you use proportional reasoning to scale to enlarge and shrink?
How do you find volume of regular and irregular figures?Technology:
Computer fans in a switched 9 volt circuit
Equipment:
Float tank
Basic handtools of carpentry: hammer, chisel, saw, sandpaper, and tape measure.
Foam cutter: Wonder cutter
Resources:
Aims Education Foundation: Floaters and Sinkers. Mass, Volume and Density
Tops Learning Systems: Floating and Sinking
Devens Fire Department rescue boat
USS Constitution
Hudson River Sloop Clearwater: Handy Sloopers Guide
MATH FRAMEWORKS
Number Sense and Operations
8.n.3 Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.
8.n.11 Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.
8.n.12 Select and use appropriate operationsaddition, subtraction, multiplication, division, and positive integer exponentsto solve problems with rational numbers (including negatives).
Patterns, Relations, and Algebra
8.p.1 Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding.
8.p.4 Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.
8.p.5 Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems.
8.p.6 Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b.
8.p.8 Explain and analyze how a change in one variable results in a change in another variable in functional relationships.
8.p.9 Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.
8.p.10 Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.
Geometry
8.g.4 Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems.
8.g.5 Use a straightedge, compass, or other tools to formulate and test conjectures, and to draw geometric figures.
8.g.7 Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.
8.g.8 Recognize and draw two-dimensional representations of three-dimensional objects, e.g., [nets] projections, and [perspective drawings].
Measurement
8.m.1 Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.
8.m.3 Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of [parallelograms, trapezoids], and circles. Given the formulas, determine the surface area and volume of [rectangular prisms], cylinders, and spheres. Use technology as appropriate.
8.m.4 Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement.
8.m.5 Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density.
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