The objectives are: 1) to increase spatial comprehension among third grade mathematics students; 2) to identify ways to divide a rectangular geoboard "cake" so that it can be fairly shared by two, three, four, or more students; and 3) to develop enhanced comprehension of basic mathematics concepts such as proportion, sets, and so forth.
Students will be provided with an introductory lesson on the "Cake Problem," a project in which a rectangular geoboard "cake" will be displayed. Students will be challenged to devise ways of dividing the cake so that it can be shared fairly by different numbers of people. Each student will have their own geoboard and will be asked to use a pencil and a ruler to divide the board by drawing lines to indicate divisions for two people, three people, four people, and so forth. Individualized hands-on activities of this type help students learn via manipulative activity how a single spatial plain can be subdivided into any number of equal parts.
Once students have completed a series of drawings and divisions, they will discuss the project and compare results. The teacher will have a template showing different division options using colored pencils to distinguish between each set of "pieces."
The students in this writer's third grade classroom who participated in the Cake Problem appeared to enjoy the activity and to grasp the basic concept of dividing a single item into parts of various sizes. The students were encouraged to consider ways of dividing other items into equal parts such as apples, a bunch of grapes, and a bag of M&M candies.
Using the Cake Problem to teach basic spatial relationships and to encourage grade three students' comprehension skill development is a low-cost strategy involving hands-on manipulative activity. The problem can be made as complex as one wishes or simplified to meet the developmental levels of any special needs children who might be in the inc...