Erving Lighthouse Grant What is MicroWorlds? First Steps Let's Dance Project Files Student Comments Massachusetts State Geometry Standards MicroWorlds Links Erving Elementary School   Massachusetts Curriculum Frameworks Geometry and Measurement Learning Standards Grades 5-8 Geometry - Grades 5-8 Learning Standards Students engage in problem solving, communicating, reasoning, and connecting to: identify, describe, compare, and classify geometric explore and describe the properties of points, lines, and planes. visualize and draw geometric figures. explore and describe transformations of geometric figures. represent and solve problems, using geometric models. apply geometric properties and relationships. develop and explain the concept of [[pi]]. develop and explain the concept of the Pythagorean theorem. Examples of Student Learning Students build shapes with toothpicks and 1 cm clay balls. They make geopanes by hanging the shapes on thread and dipping them into a mixture of water and soap. Beforehand, students predict what they think will happen and describe what does happen. This illustration of surface tension encourages discovery of the relationship of vertices, edges, and faces of 3-dimensional figures and an understanding of Euler's theorem. Students build a scale model of their school. They sketch elevations of the school building, estimate and measure the dimensions of the sides, determine the most cost-effective materials for construction of the model, and write a presentation describing their model. The model is displayed and the presentation is delivered to school and local communities. Students make Möbius strips to model a continuous one-sided surface. They write about what they observe and why they believe it is that way. Measurement - Grades 5-8 Learning Standards Students engage in problem solving, communicating, reasoning, and connecting to: select appropriate units and tools to measure to the degree of accuracy required in a particular situation. describe the meaning of perimeter, area, volume, angle measure, capacity, density, weight, and mass. develop and describe the concepts of rates and other derived and indirect measurements. develop and apply formulas and procedures for determining measures to solve problems. Examples of Student Learning Monuments found in Massachusetts provide the basis for exploration of indirect measurement and geometric constructions. At home, students peruse collections of post cards and photographs to find those with shadows cast by tourists and monuments. At school, groups of students cull the photographs and use them to derive the heights of different monuments. Students use measurement to construct clay and sand replicas of pyramids or obelisks are constructed and measured. Formulas are used to derive volume. A connection with art is reinforced with a trip to the Daniel Chester French house museum called Chesterwood in Great Barrington. It is a tribute to one of the most notable monument sculptors of our region. Students construct containers, explore surface area, and use popcorn to explore volume relationships. They sketch the container they believe to hold the most popcorn. They use surface area to find the most economical container to hold a specific volume. How It Looks in the Classroom To explore the constant relationship between the diameter of a circle and its circumference, a class of sixth graders form a straight line in a snowy field, with the teacher in the middle. As the line rotates around the teacher, a circle is formed by footprints in the snow. The class lines up around the circumference and predicts how many times their length will fit around the circle. By marking off start and finish points as the class "diameter" advances along the circumference, students discover that a little more than three diameters fill the circumference. They hypothesize whether this would be different for a larger or smaller class. Later in the art room, they test their ideas by using potato prints and units to measure the diameter and circumference of different size circles.