Welcome to Unit 2.2 Circles in Squares!

The motivating CAHSEE question for this unit is the following:

The largest possible circle is to be cut from a 10-foot square board. What will be the approximate area, in square feet, of the remaining board (shaded region)? (A = Pi(r ²⁾ and Pi » 3.14)

• A. 20
• B. 30
• C. 50
• D. 80

As you progress through this unit, you will deepen your content knowledge on problem solving involving circles and develop instructional strategies that assist students in mastering these kinds of problems.

California Mathematics Content standards addressed in this question include:

Measurement and Geometry (7^th)
2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:

2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

Successful completion of Unit 2.1 The Cereal Box is a prerequisite to this unit.

In Unit 2.2 Circles in Squares, you will

• deepen your understanding of mathematical concepts in Algebra, including
  • calculations of changes in area when one geometric shape is cut out of another geometric shape
  • using formulas for finding the perimeter and area of basic two-dimensional figures
  • using formulas for common geometric shapes in order to solve a real-life, multi-step problem
• focus on several new instructional strategies, including
  • developmentally-appropriate instructional strategies such as cooperative learning and using manipulatives
  • engaging students in talking and writing mathematics
• complete activities for your Lesson Plan Project

• What you will see:
  • Each unit is organized around a highly-missed question from the CA High School Exit Examination
  • Each unit presents lessons taught by two middle school math teachers.
  • These teachers designed the lessons with input from our math experts, Dr. Marty Bonsangue and Dr. Harris Shultz.
  • Each Unit 2.2 has two strands--one on math content and one on instructional strategies.
• What you will do:
  • As you move through the unit, you will read text, view videoclips of classroom teaching, and respond to assessment questions.
  • You will submit your responses to the assessment questions as you move through the unit.
  • Once you submit a response, feedback from Drs. Bonsangue, Shultz, Ambrosetti, and Costa will "pop-up" for your viewing.
    • In addition, your Online Facilitator will be checking your responses for accuracy and completion.
  • At the end of each strand, you will be asked to post your reflection on the Discussion Board. You will also respond to a colleague's posting.
  • At the end of the unit, you will also be asked to reflect on the entire learning experience
  • At the end of each unit, you also complete part of an on-going lesson plan project. Our goal is to develop your ability to design, implement, and share effective lessons.

Unit 2.2 Circles in Squares should take approximately 10-15 hours, depending on your technology skills and knowledge of instructional strategies.  You may complete this unit on your own time, but each strand is expected to be completed by a specific deadline. This will allow your Online Facilitator to provide collective support and will facilitate your collaboration with your colleagues. It will also insure that you complete the unit by the course endpoint.