This lesson is designed to get students to really think about how volume and area have practical applications.   The idea is to help the kids start to see the answer to the age old question: When am I going to use this in the real world?  The lesson introduces the concepts of perimeter, volume, circumference, angles, area, and surface area in a way that gets the kids working hands on.   The students must redesign the  cafeteria in a way that allows the cafeteria to operate more smoothly and the student flow to be more efficient.     The students must design a cafeteria which serves 450 students.   The cafeteria must include seating for all students, lunch lines, an entrance, and an exit.   All of these elements must be laid out in manner which promotes easy flow and minimizes congestion in the cafeteria.   This assignment achieves the same end result as the more traditional worksheets but allows the students to see the practical application and hopefully have a little more fun while they are doing it.      

NM-GEO. 9-12. 1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

NM-GEO. 9-12. 4: Use visualization, spatial reasoning, and geometric modeling to solve problems

NM-MEA. 9-12. 1: Understand measurable attributes of objects and the units, systems, and processes of measurement

NM-MEA. 9-12. 2: Apply appropriate techniques, tools, and formulas to determine measurements

NM-DATA. 9-12. 1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer.

NM-DATA. 9-12. 3: Develop and evaluate inferences and predictions that are based on data

NM-PROB. PK-12. 1: Build new mathematical knowledge through problem solving;    

NM-PROB. PK-12. 2: Solve problems that arise in mathematics and in other contexts;

NM-PROB. PK-12. 3: Apply and adapt a variety of appropriate strategies to solve problems;

• Students will be able to formulate and solve problems of area, perimeter, circumference, and volume.
• Students will be able to design a floor plan for a cafeteria which seats 450 students.  

• paper (for notes and design)
• assorted shapes (paper) to represent tables and counters
• poster board for blueprint

• surface area: the measure of how much exposed area an object has
• measurement: the act or process of measuring; a figure, extent, or amount obtained by measuring
• length: the longest dimension of an object
• area: the surface included within a set of lines
• perimeter: the boundary of a closed plane figure
• volume: the amount of space occupied by a three-dimensional object
• circumference: the perimeter of a circle
• angle: the figure formed by two lines extending from the same point

1.   Introduce the actual cafeteria measurements to the students.   Show the students the blue print as it currently exists.   2. Review the formulas for area, volume, circumference, perimeter, etc. 3.   Explain that the purpose is that they must use the data given to identify a more practical and efficient floor plan for the current cafeteria. 4. Arrange students in groups of no more than four students. 5.   Provide the students with the measurements and paper to begin designing. 6. Students analyze the efficiency of the current floor plan so that they can identify the problem.   The students should then discuss the problem with the teacher in a mini conference.   7.   Once the problem has been identified students work together to design a new layout.   They should be exploring new shapes, sketching the shapes out, and trying to identify any problems before they arise.   8.   Teacher pulls the students back together as a group once most students seem to have a new design idea.   Teacher redirects students to think about the original problem and then explains that students must now actually implement their design using the poster board and blueprints.   Students are only to be given one piece of poster board.   9.   Students create design. 10.   Students demonstrate design for the teacher. 11.   Students write a one to two paragraph short essay which discusses the successes and failures of their own design.   Students should address what they would have done differently in their new design.