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Writing math problems can be time consuming, particularly when it comes to properly formatting mathematical equations. TestDesigner.com offers the capability to create professional quality equations easily with our interactive math editor. With over 150 scientific and mathematical symbols to choose from, you can quickly generate equations ranging from basic exponents questions to the most complex calculus problems.
To format an equation, login to TestDesigner.com and begin creating a question. Click on the “Insert a Math Equation” button located above the question field. A box will open in which you can enter an equation while selecting from a wide variety of math symbols available under the headings on the right side of the box.
Once the item is complete, select “Insert Equation” and you will return to the question creation screen. Special math tags will appear around the problem in this view, but the finalized format will appear after saving the question or when viewing in it “Preview” mode.
A simple way to get started is by visiting our section on “How to Write Math Equations” and clicking on any of the sample formulas shown on the page. The selected equation will automatically populate in the sandbox at the top of the page. You can then copy-and-paste the coding for this equation into a question you create and edit numbers or mathematical notation to fit your needs.
When creating items, multiple equations can appear in both questions and answers as well as in science questions. View the following links for examples of individual problems and free worksheets created with our equation editing tool:
Sample Math Equations and Worksheets
Simplifying Monomial Expressions Worksheet
Multiplying Radicals Worksheets
Graphing Absolute Value Inequality Worksheet
Vertical Angles Worksheet
Logarithmic Equations Worksheet
Sample Science Equations and Worksheets
For information about including graphics with problems, read our post, “Using Math Images on TestDesigner.com.”
As educators, we expect our students to learn and apply math concepts using higher-order thinking skills that go beyond rote learning. With the adoption of the Common Core Math Standards, many of us must do just that, by focusing more in-depth on fewer math concepts. However, writing math problems that require higher-order strategies can be almost as difficult as solving them.
To get started, try writing a lower-level math problem then apply one or more of the following techniques:
Tips for Writing Higher-Order Math Problems
- Have students determine and extrapolate a mathematical process or pattern and apply it to an unfamiliar problem or scenario
- Ask students to identify and evaluate missing or incorrect information
- Challenge students to solve one problem using multiple methods
- Consider asking, “Given ____, what would happen if ____ changed?” questions
- Give an answer and a mathematical concept, have students write their own questions or equations that produce the given answer
- Ask students to justify their solutions or identify and justify the “best” or “most correct” solution from a selection of plausible choices
- Write problems that ask for connections between more than one set of information, this could include charts, tables, equations, graphics, and data sets
- Watch that answers for multiple-choice questions are logical and that the correct choice is not structurally different from the incorrect answers
- If you are having difficulty writing a problem, start by constructing questions that incorporate these higher-order key words and concepts: analyze, justify, explain, apply, interpret, compare, estimate, predict, prove, formulate, modify
Consider the Common Core Math Standard 7.G.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
A lower-order question for this standard could be:
What is the area of a circle with a radius of 5?
As presented, this question strictly tests student knowledge and application of the required formula. Instead, consider structuring the question using a “real-life” scenario that requires multiple steps to solve:
Official tournament play of Ringer marbles requires a circular game ring with a diameter of 10 feet. Alexis needs to construct multiple rings for a tournament using rope to mark the circumference of each ring. If she has 100 feet of rope, what is the maximum number of rings Alexis can make?
Finally, try constructing an open-response question that requires students analyze and evaluate the information in a non-routine manner:
Jackson explains to his classmate that doubling the circumference of a circle results in the doubling of the circle’s area. Is Jackson correct? Use the formulas for area and circumference to justify your answer.
This problem still satisfies skills posed in standard 7.G.4, however it now requires students not only demonstrate knowledge and application of the formulas, but also analyze the relationship between them.
Writing higher-order problems takes time, but ideally, the additional time will help students further develop the critical-thinking skills we strive to nurture as educators.
For more examples of higher-order math questions, view these questions created by TestDesigner.com members:
Read “How to Design a Good Test” and “Five Essential Thinking Skills to Teach in September” for more tips on creating meaningful questions and assessments.
Help Teaching is a service of Tribrio, Inc., a company focused on developing web-based solutions for education and training.
Help Teaching offers a powerful and easy to use online tool that can accommodate questions for any topic and any level of difficulty in a variety of formats: multiple choice, fill-in-the-blank, true or false, and open-ended questions. By leveraging the site’s free member-generated content, Pre-K through post-graduate educators can quickly and inexpensively create professional tests and worksheets. Help Teaching members can maintain their own database of questions and tests in a desired format that can be used year to year.