## Instructor Guide

# Problem Design Features

## Randomized Values

The majority of *Physics LE* problems utilize randomization of the numerical values used in the problem. This assures that each student receives a unique version of the problem. Most problems have approximately 100 unique variations. This prevents plagiarism among students and makes it nearly impossible for students to search online for the answer to a particular problem variation.

## Intermediate Problem-Solving Steps

Intermediate problem-solving steps often appear in the question parts that make up a problem and are indicated with a "+" sign in the part header. Getting each part correct before moving on will help students obtain the correct final answer. The **Submit Answer** button appearing at the end of the problem can be used to submit any completed part of a multiple-part problem, uncompleted parts are ignored and only the completed part is submitted. As students develop their routine of solving *Physics LE* problems they should be sure to always submit the answer to each individual part before moving on.

Intermediate problem-solving steps are of the following types and point values:

1) Intermediate numerical values required to obtain the final answer (0.5 points)

2) Input of relevant equations or algebraic expressions (0.25 points)

3) Multiple-choice questions, using text or diagrams, checking for understanding and problem-solving approach (0.25 points)

The final answer is generally assigned a value of 1.0 point.

## Numerical Tolerance

The numerical tolerance used in the student answer for most numerical problems is set at ± 2%, however, this value does vary based on the specific problem. If the student's answer is within the numerical tolerance of the accepted answer it will be marked as correct. This value cannot be changed by the instructor as it is built into the individual problem. Experience shows that having one universal setting for numerical tolerance is not a good approach. A number of considerations come into play when deciding what numerical tolerance should be used for a particular problem.

## Significant Figures

The student answer will be checked for the correct number of significant figures following standard significant figures rules for mathematical operations. A student entering a correct numerical answer, but incorrect number of significant figures, is penalized 10% of the total possible points for the problem. This feature may not be turned off by the instructor.

Because problems contain randomized values, different sets of random numbers can produce answers with a varying number of significant figures when the rules for addition/subtraction are applied. This is of particular concern when multiple-step calculations are involved. For this reason, when a problem solution has multiple steps involving both multiplication/division and addition/subtraction, only the rules for multiplication/division will be employed by the grading system.

Flexibility is given by the grading system for answers not involving a decimal that happen to have a zero in the final significant figure position. For example, an answer of 150 m/s requiring three significant figures can be entered as 1.50 x 10^2 m/s or 150 m/s with no penalty. This approach is used to make sure all variations of a problem place the same requirements on a student, and not require certain students to enter their answer in scientific notation merely based on the random values used in the problem.

For problems involving multiple steps with a series of calculations, the student should carry at least one additional significant figure through all the intermediate calculations and then round the final answer to the proper number of significant figures. Students may find it convenient to input a series of calculations into their calculator and thereby automatically retain extra digits for intermediate calculations. The practice of not carrying at least one additional significant figure in multi-step calculations can create a compounding truncation/rounding error and cause the student answer to fall outside the tolerance limits of the accepted answer.

## Units

All numerical problems require students to enter a unit after the numerical value (with a few exceptions such as when entering a ratio). The unit can be typed immediately after the numerical value (with or without a space) in the same input field. If a student forgets to include the unit he/she will be prompted to enter it before the answer can be evaluated. Most units can be typed just as they normally appear in a textbook (e.g., kg, m, s, m/s, km/h, N). Units are case sensitive and students need to make sure to use the same uppercase/lowercase convention as used in a physics textbook.