Writing Open Ended Questions

Ask students

We hear so much about integrating open ended questions in class but have you ever wondered
why?  What advantages are there to using open ended questions?  What is the best way to use them in class?

One great thing about open ended questions is there is not one correct answer.  Most textbooks are filled with problems designed to have only one possible solution. These problems are designed to be solved using a specific process.  Unfortunately, real life problems are not always as neatly solved as those in the textbooks.

In addition, these types of problems can be solved by students of different abilities with a differing level of knowledge.  These are perfect for differentiating the lessons to meet the needs of all students. These problems encourage student thinking and decision making. Textbook problems do not encourage students to develope their mathematical thinking.

The last thing these types of problems do is to help students develop their reasoning and communication abilities. The justification for the method chosen when working textbook problems is they use the method taught in the section. The reason for knowing the answer is it was in the back of the book.

The great thing about textbooks is they can provide problems which can be rewritten into open ended questions with a bit of adjustment.  First step is to start with the answer while throwing out the actual problem.  Instead of asking what 1/2 of 12 is, begin with the answer of 6.


Then create a question asking students to design a problem that gives produces that answer. So you could say 6 is a fraction of a number - what is that number and what is the fraction?

In addition there are a few other ways to create open ended questions for students.  One way is to ask students to compare and contrast numbers, shapes, graphs, probability, or measurements.  This requires more than something like 95 and 100 are different because one has 2 digits and the other has 3 digits.

Another way is to have students explain how something such as 5 is a factor of two numbers, what might be true for the two numbers? Or you could write a statement using soft words like almost or close such as two numbers multiplied together is almost 600?

Finally, have students make up sentences using numbers and mathematical words such as 8, 5, less, and. This allows for more than one answer.

If you have students who are not good at expressing their thoughts or using a more in depth explanation, these are some good ways to start students on their paths.  Let me know what you think, I would love to hear.