Assessment Plan - Week 6

Assessment Plan - Multiplying Fractions

This assessment plan is designed to serve as a final assessment for a lesson plan for multiplying fractions, a lesson subsequent to the Introduction to Fractions previously presented here.  The assessment activities are varied, and address the application of fractions to other fractions and the appropriate reduction of fractional equivalents.

Learning Outcome 1 - The student will demonstrate understanding of the subject matter within multiple contexts

Learning Outcome 2 - The student will create a word problem addressing at least 3 ways of fractionally dividing property between at least 4 different people.  The student will supply all the equations supporting the word problem.

Test Item Examples for Learning Outcome 1

Below are examples for each type of test item to be used in the assessment.  Ideally the test should be constructed of enough items to fill a single class period, perhaps with time left over for an extra credit item for early finishers.

Item 1 - Multiple Choice - Select the correct solution to the given equation from the 4 choices listed below it:

1/4 x 1/2 = ?

A. 1/6

B. 1/8

C. 2/6

D. 2/8

Item 2 - Fill In The Blank -  Solve the equation (Hint: Always remember to reduce fractions whenever possible):

1/4 x 2/3 = _________  

Item 3 - Matching Items - Draw lines between the equations and their correct solutions.  Include your calculations to support your choices. (Hint: Always remember to reduce fractions whenever possible):

2/3 x 3/4 2/5

1/2 x 3/8 1/2

3/4 x 1/6 3/16

3/5 x 2/3 1/8

Item 4 - Matrix Exercises - Draw a line in each matrix below to illustrate the indicated fractions:

*  *  *  *  *  * *  *  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  *

*  *  *  *  *  * *  *  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  *

*  *  *  *  *  * *  *  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  *

*  *  *  *  *  * *  *  *  *  *  *  *  * *  *  *  *  *  *  *  *  *  *

*  *  *  *  *  * *  *  *  *  *  *  *  *

         

   1/3 + 2/3 3/4 + 1/4 3/5 + 2/5

Item 5 - Matrix Creation - Create your own matrix, in the space below (different from any of the ones in item 4), that is divisible by 2, 3 and 4.  Draw lines in the matrix to illustrate a fractional division of your choice.  Include the equations for the number of items in the matrix as well as your fractional divisions.

Holistic Rubric

CATEGORY	4	3	2	1
Mechanics	The student provides correct equations for all of the test items.	The student provides correct equations for most of the test items.	The student provides correct equations for some of the test items.	The student provides correct equations for none of the test items.
Mathematical Concepts	The student\'s explanations show complete understanding of the mathematical concepts used to solve the problems.	The student\'s explanations show substantial understanding of the mathematical concepts used to solve the problems.	The student\'s explanations show some understanding of the mathematical concepts used to solve the problems.	The student\'s explanations show very limited or no understanding of the mathematical concepts used to solve the problems.
Diagrams and Sketches	Student\'s work with the matrix items is clearly diagrammed and fully correct.	Student\'s work with the matrix items is not always clearly diagrammed and is not fully correct.	Student\'s work with the matrix items is somewhat difficult to understand, but more than half the equations are correct.	Student\'s work with the matrix items is difficult to understand, with less than half of the equations stated correctly.
Completion	All test items are completed.	All but one of the test items are completed.	All but two of the test items are completed.	Several of the test items are not completed.

Testing Constraints 

Time - the assessment will be constructed so that it can be completed within a single classroom period.

Assistance from others - two of the test items include teacher hints reminding students to reduce fractions whenever possible

No other testing constraints are applicable.

Supporting My Assessment Choices - Week 3

When creating assessments it is important to make sure that they are valid and that they accurately support and reflect upon the learning outcome being assessed.  Kubiszyn and Borich (2010) provide a wealth of material when it comes to creating effective assessments.

The assessment activities recommended for my first two learning outcomes meet one of the authors' key criteria: applying "previously learned principles or procedures to novel situations" (p. 147).  Having the students reproduce the math from the work of others provides the opportunity for students to "use the principle or procedure with new information" (p. 147).

Fortunately, when it comes to testing for Learning Outcome 3, creating written tests for math lessons is far less demanding than those for other subjects.  As math problems generate concrete answers, it is relatively easy to avoid many of the pitfalls of written tests, including "too many correct responses" and "ambiguous lists" (p. 136).

The suggested essay question also meets the requirements as set forth by the authors, who state, "the well-constructed essay item…" calls for "the student to organize, integrate and synthesize knowledge… and to be original and innovative in problem solving" (p. 158).  Applying the skills learned with the objects used in the matrices to scenarios involving different quantities and objects provides the opportunity for just the kind of synthesis the authors call for.

Reference

Kubiszyn, T. & Borich, G.. (2010). Educational testing & measurement: Classroom application and practice (9th ed.). John Wiley & Sons, Inc: Hoboken, NJ.