Provide a metaview, lifting students into a wider view of the concept. Use another medium (not reading or writing) to connect students' personal knowing to the concept (i.e. visual arts, music, movement, metaphor, etc.) Involve learners in reflective production that blends the emotional and the cognitive.

Group boundary problem with boxes. Area paradox problem. Discuss.

Objective: To experiment with the concept of boundaries in a problem solving situation.

Activity: In groups of four, choose a secretary to record the problem solving process. Each group will receive a set of boxes (approximately 15 boxes) of varying shapes and sizes. 1. Ask the groups to arrange the boxes to cover the largest space possible. Share solutions with the groups. 2. Ask the groups to arrange the boxes to cover the smallest space possible. Share solutions with the groups. 3. Do area paradox problem. Give each student a sheet of centimeter paper. Cut an 8x8 square from one corner. Using an overhead transparency, show students where to cut their square into four pieces. Then ask students to work together to rearrange these four pieces into a rectangle. If they want, students may draw another 8x8 square and their new 13x5 rectangle on the remaining centimeter paper. Have students find the area of the square (64 sq. units) and then the area of the rectangle (65 sq. units). Ask questions such as 1) Are the areas correct? 2) Why or why not? 3) Is something wrong? 4) What basic property have we contradicted? (whole = sum of parts)

Assessment: Involvement and creativity in group activities.