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Content Supports - Activities and rich problems
Rainy Lake, aka Mirror Lake
Discipline
Mathematics
Grades
6, 7, 8
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Professional Commentary

Students use a topographical map featuring a body of water, such as a lake, pond, or river, to figure out how much the level of the water would rise after a one-inch rainfall the previous night. An extension of the problem and a discussion of the underlying mathematical ideas are included. This mathematically rich problem was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at The Ohio State University. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)


Common Core State Standards for Mathematics
Grade 6
Geometry
Solve real-world and mathematical problems involving area, surface area, and volume.
Grade 7
Geometry
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Ohio Mathematics Academic Content Standards (2001)
Measurement Standard
Benchmarks (8–10)
A.
Solve increasingly complex non-routine measurement problems and check for reasonableness of results.
C.
Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangles, quadrilaterals and composite shapes, and to find volume of prisms, cylinders, and pyramids.
E.
Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision.
Benchmarks (11–12)
C.
Estimate and compute areas and volume in increasingly complex problem situations.
Grade Level Indicators (Grade 9)
4.
Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures.
Grade Level Indicators (Grade 11)
4.
Calculate distances, areas, surface areas and volumes of composite three-dimensional objects to a specified number of significant digits.
5.
Solve real-world problems involving area, surface area, volume and density to a specified degree of precision.
Mathematical Processes Standard
Benchmarks (8–10)
A.
Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution.
B.
Apply mathematical knowledge and skills routinely in other content areas and practical situations.
Principles and Standards for School Mathematics
Geometry Standard
Use visualization, spatial reasoning, and geometric modeling to solve problems
Expectations (6–8)
use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume;
Measurement Standard
Apply appropriate techniques, tools, and formulas to determine measurements.
Expectations (6–8)
develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes;
solve problems involving scale factors, using ratio and proportion;
Expectations (9–12)
understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders;