Overview

In this module you will see how two teachers take different approaches to solving the focus CAHSEE question. While their student populations are very different, both teachers achieve success by activating prior knowledge, acknowledging different learning styles, and having a keen awareness of their students' social needs.


The motivating CAHSEE release question for this module 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 module, you will deepen your content knowledge on problem solving involving areas 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 (7th)
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.

2.2 Estimate and compute the area of more complex or irregular two- or three-dimensional figures by breaking the figures down into more basic geometric objects.

Objectives

In Module 2.2 Perimeter and Area, 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