4. Use the diagram below to answer the question that follows.

Item #27: This item addresses a very important component of “Number Sense and Operations,” the Distributive Property. The problem is that it does so at the most trivial level, i.e., simply knowing enough about this property to recognize an instance of its use.

Alternative (a) (Open Response):
At the end of his “Math Concepts I” course, Mathematics Professor Richard Bisk, Worcester State College, poses the following problem to his students: “ Use the distributive property and the fact that 999 = 1000-1 to find 999 x 213. You must show correct work to receive credit. ”

In this example the examinee is asked to apply knowledge of the distributive property to demonstrate how the computational complexity of the problem can be simplified through its application.

Alternative (b) (Multiple Choice):
The following (released) MCAS item tests application of several properties and a misapplication of the associative property:

Item #41: This item addresses the “Geometry” strand. It is a multi-step problem that requires an understanding and application of multiple relationships of angles created by intersecting straight lines and within a triangle. It is of easy to moderate difficulty and adequately measures the competence of an elementary teacher candidate in this domain.

Alternative:
The following (released) MCAS multiple choice item tests adjacent angles and angles in right triangles within a real-world context:

Each of the two interior supports for part of a roof is perpendicular to a rafter, as shown below.

Item #42: This item also addresses the “Geometry” strand. It is a multi-step problem (converting measurements, multiplying and dividing) but at a simple level and within a simple context.

Alternative:
The following (released) MCAS open response item involves adding feet and inches together, along with determining perimeter and area of a complex figure:

A park has a rose garden with the dimensions shown below. A 36-inch-wide sidewalk surrounds the rose garden.