Pathways Project: Dream House Content Strand: Measurement Teacher: Terri Deja School: Buchanan Middle School Buchanan, MI Grade 6 Project Director: Jennifer Knudson 40 minutes Dream House: Students are architects designing a dream home for their client in this lesson from the Pathways curriculum. Pathways is composed of a series of design units based on the mathematics that used in real-world work settings. The focus for this lesson is on the concept of area, measuring the area of irregular figures, and is balanced by an open-ended question that includes area. The class first measured floor space and developed a definition of area in their own words to arrive at the mathematical definition of area. They moved into group work where they identified an irregular room in the blueprint for their dream home and solved for the area of the room recording their strategies along the way. Students assumed the role of carpet installers in their next challenge, and a visit from Mr. Scott, a local carpet installer, provided a model and insight into some of the fundamental mathematical concepts involved in laying carpet. The following day brought the class into the computer lab where they experimented with scale by enlarging one of the rooms in their dream home.
 Connected Mathematics Project : Designing Packages Content Strand: Measurement Teacher: Jim Mamer School: Rockway Middle School Springfield, OH Grade 7 Project Director: Yvonne Grant 40 minutes Designing Packages: Students learn about and experiment with surface area and volume in this lesson from the Connected Math Project. They begin by reviewing previously learned concepts of base, height, width, and length. As employees of the ABC Toy Company, their task is to design a package to house 24 blocks. They are supplied with 24 stacking cubes to explore the different ways the cubes can be put together and packaged. For each package built, they record the dimensions and determine surface area corresponding to that box. Students experience collecting data using manipulatives and devise creative solutions. The concepts of surface area and volume are repeated with each new investigation for each shape. Once students have finished, the class reviews and defines the different methods individual groups used to find surface area. The lesson culminates with the student discovery that as the smaller cubes are put together forming different rectangular shapes, if they are arranged to form a larger cube, the surface area is minimized.