Create a randomized multiple-choice equation question

In this tutorial, you will create a randomized multiple-choice question in LearningLemur by generating different equations with variables and providing answer options based on common solving mistakes, so that, by the end, your question presents both the correct solution and typical student errors.

Before you begin

Prerequisites 

• You should be comfortable working with basic algebra.
• You should have completed Create a multiple-choice equation solving question.

Requirements

• A teacher account with permission to create questions in LearningLemur, accessed through learninglemur.com or your LMS.

Steps

Step 0 — Create a quiz

Why: LearningLemur organises all questions inside quizzes, so creating a quiz first provides the workspace where you will add and manage your questions.

1. Click on Create new quiz.
2. Enter the Quiz Title.
3. (Optional) Add a description to the quiz.
4. Click on Create.

Checkpoint: You should now see the quiz workspace with options to add questions.

Step 1 — Add a new question

Why: LearningLemur allows you to create questions either manually or with the help of AI. In this tutorial, we will create the question manually to understand how the editor works.

1. Inside the quiz, click Add question.
2. In the creation dialog, choose Manually.
3. Select the Multiple choice question.

This question type allows students to choose one answer from a list of options.

Checkpoint: You should see the Multiple choice question editor, including fields for the title, statement, and answers.

Step 2 — Write the question statement

Why: The statement explains the problem students must solve. It will use variables instead of fixed values.

1. Enter a Question title, for example: Solve a random equation.
2. In the Question statement, write the exercise text.

You can use the MathType editor to format the equation if needed, using mathematical notation.

Checkpoint: The question statement should display the variables inside the equation.

Step 3 — Define the random variables

Why: Random variables allow LearningLemur to generate a different version of the question each time.

1. Open Question settings.
2. Locate the Random variables section.
3. Add the following variables as random numbers:

These variables define the structure of the equation.

Checkpoint: The variables a, b, and x appear listed in the Random variables section.

Step 4 — Define the random expressions

Why: Random expressions allow you to compute values that depend on the generated variables, including both the equation itself and the answer options shown to students.

Complete the equation

1. In the Random variables panel, go to Add random expression.
2. Create the following expression:

This ensures that the equation always has a valid integer solution.

Define the answer values

1. Add the following expressions:

Explanation of the answer values

These expressions represent both the correct answer and common mistakes:

• sol → the correct solution.
• d1 → forgetting to subtract b
• d2 → forgetting to divide by a
• d3 → incorrect sign when moving terms.

Using random expressions ensures that all answer options are displayed as computed values instead of unevaluated expressions.

Checkpoint: The variables c, sol, d1, d2, and d3 appear under Random expressions.

Step 5 — Define the answer options

Why: Multiple-choice questions require a set of answer options, including one correct answer and plausible distractors.

When you create a Multiple Choice question, LearningLemur automatically provides one answer with a 100% score (the correct answer) and two answers with a 0% score (the incorrect answers).

1. In the Answers section, enter the correct answer in the option with 100% score: x = #sol
2. Enter the following incorrect answers in the remaining options:
   1. x = #d1
   2. x = #d2
3. Click Add answer to create a fourth option.
4. Enter x = #d3

Checkpoint: The answer list contains four options, with one assigned 100% and the others 0%, and the order is set to be randomized.

Step 6 — Add feedback for the incorrect answers

Why: Custom feedback helps students understand the mistake behind each distractor.

For each incorrect option, click Customized feedback for this answer and enter a message such as:

For x = #d1

For x = #d2

For x = #d3

• Check the sign when moving terms across the equation.

Checkpoint: Each incorrect option now has its own custom feedback message.

Step 7 — Preview the question

Why: Previewing allows you to test the question exactly as students will see it.

1. Click Preview question.
2. Observe the generated equation.
3. Use Select correct option, or calculate the result manually from the values shown.
4. Try incorrect options and review the feedback.
5. Click Regenerate question and compare the newly generated values with the previous ones.

Checkpoint: Each preview generates a different equation, and the correct answer and feedback behave as expected.

You're done

You have created a randomized multiple-choice question in LearningLemur. You learned how to:

• Generate equations using random variables.
• Define dynamic answer options.
• Create distractors based on common mistakes.
• Provide targeted feedback for each option.

Troubleshooting

The correct answer is marked as incorrect.
Check that:

• The variable c is defined as a * x + b
• The correct option uses #x

All options look similar or incorrect.
Check that:

• Each option uses a different expression
• Variables are referenced correctly (#a, #b, #c)

The same equation always appears.
Check that random variables are defined correctly and not fixed values.