I. Curricular Framework

Concept:

Patterns

Essential Question:

What is the connection between factoring and real-life?

Bridge:

Problem-solving

Content:

Mathematical Factoring

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To help students understand the importance of patterns in life and everyday mathematics.

Activity: Students will be arranged in pairs or groups of four to view video. Ask students to write about their reactions/thoughts to the video. (Note: We created a seven minute video based on the work of artist M.C. Escher.)

Assessment: Quality of writing, participation and interest.

2. Attend: Attending to the Connection

Objective: To enhance student ability to discuss what they have seen, felt, and experienced. To arouse their curiosity for the material to be presented. To develop listening skills, group discussion techniques and opinion giving.

Activity: Students will discuss their thoughts with a partner. Students will share ideas with the class. Teacher will list thoughts, ideas, on board being mindful that there is not a right or wrong response to any of the things discussed. The role of the teacher is to encourage discussion and thought.

Assessment: Quality of discussion. Were the students engaged? How many ideas were generated?

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To integrate the previous experience and discussion into the concept of patterns. To experience the importance of finding a pattern as a solution to a problem. To experience a solution which involves "seeing" from a different viewpoint.

Activity: Students work in pairs to solve three puzzles. Envelopes containing puzzle pieces are identified on the outside as "circle," "square," and "horse." Each group of students is asked to take an envelope labeled "circle" and empty the pieces onto their desk. They are told to work together to find a way to arrange the pieces and form a circle. Teacher monitors student progress. After all or most pairs have computed the puzzle, the teacher can demonstrate the solution using pre-cut pieces on an overhead projector. Follow the same procedure for the "square" puzzle which is a tangram and then the "horse" puzzle. The horse puzzle is an ancient Chinese puzzle which involves placing two riders which are in the proper position on the horses. No flipping or overlapping is allowed. This puzzle involves being able to visualize the given pieces in several ways. Follow up discussion on what is important in working the puzzles, does looking for patterns help work the puzzles? Where have they seen or worked with patterns before (in math or elsewhere)? Examples: Art, English (Poetry), Chemistry, History ("History repeats itself"), Algebra II (patterns seen in multiplication unit just completed, in problem solving in math courses, geometry). Focus attention on the importance of patterns in life, jobs/careers where patterns are important--Electrician (circuit design), Fabric/wallpaper designs, Architect (building designs), Civil Engineer, Accountant, Music (Symphony), etc.

Assessment: Quality of discussion and participation. Creativity in finding solutions to puzzles. Quality of understanding of pattern concept in math and daily life.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To enhance knowledge of factoring and to understand factoring as a concept of pattern. To listen to lectures. To increase notetaking skills. To ask relevant questions. To write analytically.

Activity: Teacher will teach factoring: 1) Identify types. 2) Recognize patterns. 3) Understand concepts using "writing-to-learn" activities. Students will identify: 1) Common factors, 2) Difference of two squares, 3) Sum and difference of two cubes, 4) Perfect square trinomials, and 5) Grouping. Teacher will demonstrate patterns involved in all process.

Assessment: Students will identify and explain in writing the types of factoring and methods involved in factoring.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To allow students to practice concepts and reinforce learning.

Activity: Teacher generated worksheets, factor puzzles (steps to problems written on separate 3" x 5" cards which students in groups of four must arrange in order), MATHO (math bingo), more writing assignments designed for clarity of explanations, quizzes.

Assessment: Quality and accuracy of above

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To personalize unit material. To enhance student creativity.

Activity: The students are required to choose a project which will involve creating a pattern to be displayed on a poster, a t-shirt, or wall hanging. This step is the planning step. Teacher will provide a time line and completion date.

Assessment: Individual personalization plans.

7. Refine: Refining the Extension

Objective: To enable students to make the connection between mathematics and everyday applications. To enhance student's ability to plan a learning project. To enhance ability to find resource material. To refine skills.

Activity: Students hand in project plans including description of project, outline of progress, and 8" x 10" sketch of pattern. Teacher checks plans making revisions as necessary. Students continue review of unit material using worksheets, games, writing activities.

Assessment: Quality of plans. Unit test.

8. Perform: Creative Manifestation of Material Learned

Objective: To enhance students' ability to complete a project. To share projects with class and have classmates teach each other what they have learned about patterns.

Activity: Each student presents a project to the class. The students must explain how the pattern used was created and how the finished product was achieved. Teacher will display all projects in classroom.

Assessment: How well each project meets previously established criteria. Quality of presentations and sharing.

STUDENT EVALUATION OF 4MAT PROCESS I believe the 4MAT Method of teaching helps students understand by using a less structured, less strict way of teaching and learning. The old way taught that math was hard work and old and crotchety people loved it (don't ask me how I got that idea, but math teachers should have blue hair, arthritis and a metal edged ruler to swack knuckles with). Math is still hard, but the new way helps a lot.

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