How to Create Higher-Order Thinking Questions for Math

Learn all about how to incorporate higher order thinking questions into you classroom to promote higher level thinking. A simple strategy to easily incoroporate these types of questions into your lesson plans. 

The Need For Better Math Problems

Many math teachers know they need to step up the quality of math problems in their classroom, but are not sure how to do it.  I was taught a great strategy to switch up my type of questioning and would like to share it with my fellow math teachers.   

The Problem

Teachers are often given math textbooks to teach from, and sadly, open-ended questions are not apart of the majority of math textbooks. However, changing common math problems into open-ended questions is very doable. Here is an idea that I have been taught that has encouraged higher level thinking in my math class.

The Solution

Take a common math problem and flip the question and the answer. Students can create questions with the given answer. Take the problem one step further by having them justify their answer either through writing or modeling (or both.)

Example 1

A common math question might be the following:  "Find the volume of a box with height 3 inches, width 5 inches and length 10 inches."  If you are familiar with Bloom's Taxonomy, a taxonomy of learning,  I would suggest this type of question falls into one of the lower levels. Students simply recall the algorithm and calculate the answer. 

While I do believe these types of questions have their place in a math classroom, they should be in the minority.  What if you instead changed the question to this, "Create a box that has a volume of 150 cubic inches." This question is now a critical thinking question that requires higher-order thinking skills. 

Example 2

Instead of, "Solve the following equation 3x + 2 = 11," flip around the question and say, "Create a two-step equation where the variable equals 3.  Write your equation in two different ways."

Example 3

"Find the mean of 12, 15, 18, 20 and 30."  Flip around the question and answer and ask, "What five numbers have a mean of 19 and a range of 18?  Justify your reasoning."  

Example 4

"Simplify the expressions 2(x + 1) + 4."   Change this problem to "Write three expressions that simplify to 2x + 6.  Prove that your expressions are all equivalent."

The Results

Flipping questions does take time, and sometimes it is "easier" to assign the basic problems.  Remember, however, that having students problem-solve and make sense of math will require less review and better retention.  I can assure you that doing so will definitely be worth your time.  

Also, one benefit of doing these type of questions, is there is often more than one correct answer. This can lead to great class discussions. 

Activities For You

If you want a head start on using reverse questioning in your classroom I have some great no-prep activities ready for you. Check out the following activities. 
Save This Article
Save these tips and ideas to your favorite classroom Pinterest board. Come back and reference them for ideas on how to taking create higher-order thinking questions for your math classroom.

How to create higher-order thinking questions for your math classroom


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