I. Curricular Framework

Concept:

Patterns-wheel 2 of 7

Essential Question:

How has the study of patterns in your world led directly to the study of patterns in math?

Bridge:

Growth Patterns

Content:

Study of Exponential Forms

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To create an awareness of things that change in size.

Activity: Students brainstorm or cluster about things that have growth patterns, i.e.. things that expand or contract. Examples: interest on money is growth at a constant rate, Fibonacci's rabbits (from previous wheel), population growth, cells dividing in science class and the circles formed from dropping a stone into water. Depreciation on a car, the bounces of a ball dropped from high, or an echo as it fades out could be examples of growth decay or contraction.

Assessment: Student participation.

2. Attend: Attending to the Connection

Objective: To analyze and categorize the list of growth patterns.

Activity: Create a class list from the brainstorming or clustering. Students analyze and group the items according to size change: was the change an exponential growth (multiplied or divided by the same number each time) or a constant change caused by adding/subtracting the same amount each time?

Assessment: Participation in discussion.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To deepen the understanding of exponential growth.

Activity: Each student will fold a piece of paper in half repeatedly and observe the pattern of growth. The pattern could be growth if the students are counting the number of rectangles being formed or exponential decay or contraction if considering the size of each rectangle after each fold.

Assessment: Attentiveness to results of folding.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To define the use of exponents in our number system.

Activity: Teacher presents lessons on: Using positive and negative exponents to write powers of 10 in standard and exponential form. Finding products and quotients of power of 10. Writing base 10 numbers in other number bases. Writing number bases as base 10 numbers.

Assessment: Student notetaking and participation in class activities.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To reinforce understanding by practice.

Activity: Students practice skills using textbook exercises, worksheets, and quizzes.

Assessment: Quizzes and tests.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Activity: Go to patterns wheel 7

7. Refine: Refining the Extension

Activity: Go to patterns wheel 7

8. Perform: Creative Manifestation of Material Learned

Activity: Go to patterns wheel 7

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