Creating arithmetic questions

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Arithmetic questions enable you to assess users’ knowledge and comprehension of mathematics and number theory. Ensure each respondent receives a unique question by including set variables that randomly generate numbers within the problem.

Note As a best practice, we recommend that you create long answer (LA) question types for arithmetic problems that require users to demonstrate their calculations and show their work.

Create an arithmetic question

    1. Enter a Title. Enter a Points value. Select a difficulty level in the Difficulty drop-down list.
    2. Enter your arithmetic question in the Question Text field. Enclose variables with curly braces to generate random numbers.Example If you set variables x, y, and z with a Min 1 to Max 5 number range in 1-step increments, the question “You have {x} green marbles, {y} red marbles, and {z} blue marbles. How many marbles do you have in total?” will randomly generate a rational number (1, 2, 3, 4, 5) for {x}, {y}, and {z}.
    3. Click Add a File to upload an image to accompany your question. You can enter a description of the image in the Description field.
    4. Enter the solution’s Formula and enclose all variables in curly braces.Example The formula for the example question in Step 2 is {x}+{y}+{z}.The Formula field supports the following operations, functions, and constants:

Enumerations                Description

+, -, *, /, , ^                          Basic arithmetic operators

%                                           Modulo (remainder) operator

{x}^{y}                                 x to the power of y

abs({n})                              Absolute value of n

cos({n})                              Cosine of n (in radians)

sin({n})                               Sine of n (in radians)

sqr({n})                               Square root of n

tan({n})                              Tangent of n (in radians)

log({n})                               Log base 10 of n

ln({n})                                 Log base e of n

atan({n})                           Inverse tangent of n

sec({n})                              Secant of n

cosec({n})                        Cosecant of n

cotan({n})                        Cotangent of n

Factorial({n})                 Factorial of n, or (n!)

exp                                      The power of natural log (e)

pi                                          pi 3.14159 (accurate to 50 decimal places)

e                                            e 2.71828 (accurate to 50 decimal places)

5.   Select an Answer Precision from the drop-down list to define the number of acceptable decimal places. Select enforce precision if correct answers must contain a specific number of decimal places.

6.   Select and enter a tolerance level in the units +/- or percent +/- field to accept near-accurate, estimated, and rounded answers.

 Example:  A percent +/- tolerance of 3 would allow answers to be off by 3%. A units +/- tolerance of 0.5 would allow answers to be off by 0.5 units.

7.  Enter a unit type (mm, cm, grams, inches, etc.) in the Units field to assess if answers include correct units of measurement. Select a percentage from the Worth % of Points drop-down list to assign a weighted points value to the measurement unit.

8.  Set the Evaluation Options for your Units field:

      • Case Insensitive Auto-grading searches for a matching character pattern in the answer text with or without letter case correctness.
      • Case Sensitive Auto-grading searches for a matching character pattern in the answer text that must have letter case correctness.
      • Regular Expression Auto-grading uses meta-characters to search for one or more matching strings in the answer text’s character pattern. What you set as meta-character parameters helps determine letter case sensitivity. See Understanding regular expressions for more information.

9.  You can click Add Variable to create additional variables. To reduce the number of variables, click the corresponding Remove Entry icon.

10.  Enter a Name, a minimum value in Min, and a maximum value in Max for each variable. You can set the number of decimal places in the Decimal Places drop-down list.

11.  Enter a number in the Step field to set the system’s incrementing steps as it generates numbers from the range set by the Min and Max fields.Example If you create variable {x} with Min=100, Max=200 and Step=5, the system will only choose values for {x} that are increments of 5 above 100 (105, 110, 115, etc., up to 200) when generating numbers for your question.

12.  Now you can click Test beside your formula to test the formula. Click Done to continue editing your question.

13.  Provide comments and suggestions in the Question Hint and Question Feedback fields.

14.  Click Preview to view your question. Click Done to end the preview.

15.  Click Save to return to the main page, click Save and Copy to save and create another arithmetic question that retains the copied properties, or click Save and New to continue creating new arithmetic questions.


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