The expected outcome for the module is that students will comprehend and retain the rules for simplifying calculations involving more than one arithmetic operations.
Included are activities to be used for the whole class, small groups or individual students. The instructor may choose one or any combination depending upon the needs of his students. The materials use basic arithmetic so that students can focus on order of operations and not be distracted by other concepts. This also makes them useful at any level. However, these materials can be easily modified by substituting problems from the student text for the course.
Following your introduction of the topic (see suggestions below), you may wish to administer the pre-test. The pre-test—which can also function as the post-test—has been designed so that:
students will have little problems with the arithmetic; (calculators should NOT be allowed since some will produce the correct result even when the student doesn't know how to work the problem.)
no answers produced will be fractions—even though the student works the problem incorrectly in ways that have been anticipated.
incorrect answers will point to specific errors; the key explains the error.
The key for the test includes the diagnostic information which can be used by the instructor and/or shared with students. The pre-test can be returned to online students along with the copy of the key with directions to re-work the incorrect answers. If the student is still unable to produce the correct results, the instructor will know that that student has completely missed the concept.
Introducing Students to the Topic
A different approach for presenting the topic may resonate with students previously unable to understand the topic. Opportunities will be available for those preferring groupwork as well as for those who find individual work more effective.
Order of Operations is a concept used when one encounters a problem where more than one arithmetic operation is required. This is a common occurence in mathematics courses from the most basic level through advanced math topics. Most formulas used in science and business also present this situation. Further, skilled trades often require that one perform appropriate calculations based on formulas. It will be to the benefit of the student to master this concept early in his mathematics study.
Here are some suggestions for conveying the signifance of the Order of Operations concept. What is an operation? It is something that one does. In mathematics this includes adding, subtracting, multiplying and dividing. What is meant by order of operations? Well, in real life there are many operations that require a specific order. For instance, which do you do first: open the door or walk through it? Can you think of other situations where order is important? In mathematics rules have been established so that everyone who works a given problem correctly gets the same result. Whether you realize it or not this topic is very important to you, not only in the study of mathematics, but in your life. It will be important to you that the finance manager at the auto dealership correctly applies the order of operations to the formula for calculating your car payment. You will also hope that the nurse giving you an injection has correctly calculated the dosage!
In-class (Group) Activities
The in-class activities in this module have suggested implementation strategies, but can certainly be altered by the experienced instructor to accommodate a specific group of learners. They are designed for group use rather than by individual students and would not be appropriate for self-paced study without adaptation, although they may be employed in a one-to-one tutoring situation.
These activities involve only positive whole numbers so that students can focus on the concept of order of operations. The instructor may wish to alter a particular activity to make it suitable for a particular level. For instance, the instructor may want to include negative numbers or perhaps fractions. This can be easily accomplished by using problems from the student text.
Each activity includes several suggestions for assessment.
Three individual activities are included here. Two of the activities are worksheets. The first includes two problems— worked incorrectly—and the student must correct the errors. The second asks students to insert symbols to produce a desired result. Three power points presentations are provided for self study.
Though these are provided as individual activities, they could certainly be used with pairs of students. They could also be used after a group activity to assess individual students.