I. Curricular Framework

Concept:

Boundaries

Essential Question:

Bridge:

Content:

Boundaries

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To focus thoughts on the concept of area.

Activity: Class will listen to song "Signs" recorded by Five Man Electric Band (a song concerning social boundaries). Ask students to discuss their reactions and feelings to the song. Ask students to think of a situation where they have been made to feel uncomfortable, unwanted, rejected, unacceptable, etc.

Assessment: Level of interest.

2. Attend: Attending to the Connection

Objective: To examine a personal experience.

Activity: Discuss the circumstances of their experiences.

Assessment: Level of participation and willingness to share.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

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.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To teach concepts of area and volume and their applications.

Activity: Teacher will give and/or derive area formulas and methods of solving different types of problems. Students will be made aware that they will need to find missing measurements before using the area formulas. They will need to recall many geometric facts learned earlier in the course.

Assessment: Quality of participation and level of student discussion and contributions.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To focus attention on the concepts of area and volume.

Activity: Students will work individually and in groups on computer activities (supposer or sketchpad software if available), group discovery activities, journal entries, and written test summaries to reinforce concepts. Tests and quizzes will follow.

Assessment: Level of participation in group work. Quality and accuracy of assessment activities.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To enhance student creativity and develop decision making process.

Activity: Students will be divided into groups of six. Each group must investigate a solid figure (prisms, pyramids, cones, cylinders, spheres) and prepare a presentation for the class. The presentation must include: 1) A creative representation which examines the solid and includes particular vocabulary and/or formulas, applications, etc. 2) A demonstration including instruction on drawing the solid formulas and their applications. 3) An assignment for the class due the next class period.

Assessment: Quality of discussion about connections between learned concepts and application to assignment.

7. Refine: Refining the Extension

Objective: To evaluate student progress and extend area/volume concepts.

Activity: Teach remaining sections of area/volume unit (except those topics which will be taught by student groups). Encourage students to share questions and thoughts about their projects with each other. Prepare students for their final presentation.

Assessment: Group interaction and excitement about the projects. Evidence that concepts learned during the teaching of the unit are being applied.

8. Perform: Creative Manifestation of Material Learned

Objective: To share their newly acquired knowledge.

Activity: Each group will present information on their solid and give class assignment. Each student will complete an individual and class evaluation.

Assessment: The level of enjoyment reached by the class during the presentation. Students will be evaluated on their method of presentation, meeting criteria, creativity, validity, and enthusiasm.

Assessment, Phase Five,Performance, Creative Use of Material Learned: