The Answer Is.....What Is The Question?

There is a joke I often heard my father crack when I asked him for help.  He always replied "The answer is 42" which it never was.  At least for the problems I was doing. When I stumbled across a image with "The answer is..... What is the question?", I realized I had another open ended question exercise I could use in class.

This activity  involves giving students the answer and letting them come up with the problem or question associated with it. The teacher provides the answer such as 42 while asking students to create a problem whose answer is 42.

One student might come up with 41 +1 or 43 - 1 while another might use 7 x 6 or 168/4.  There are as many possibilities as there are students.  This problem requires students to think about what problem yields this answer.  Someone might even come up with 4 x 10 + 2.

This type of activity is not restricted to only numbers, it could involve measurements such as the answer is 42 cubic feet.  The cubic feet immediately indicates a cube or rectangular prism with a volume of 42 cubic feet.  This means there are fewer possibilities but still quite a few ranging from 42 x 1 x 1 to 2 x 3 x 7.  This type of problems uses the measurement to provide context which students do not always pay attention to.  

Another type of problem could have an answer of x = 3 indicating the problem might be a one or two step equation or even one that has variables on both sides of the equation.  The context indicates it has to be an equation with at least one variable - x and when solved has a value of three such as x - 2 = 1 or 2x + 3 = 9 or 3x - 2 = 2x + 1.  

Then there is the answer of 1/2 pizza which might require the student to create a word problem to have this answer.  The problem might be that three boys purchased two pizzas which they ate 3/4th of the total pieces, how much is left?  or they might write, Dad brought home a pizza for dinner.  Out of 12 slices, we ate 6, how much was left?   Both problems can be answered with 1/2 a pizza.

The answer is..... what is the question? activity has students go beyond the usual procedural methods to using higher level thoughts to determine how they get to the answer.  Furthermore, the activity helps students to make mathematical decisions, while applying mathematics to new situations.  In addition, using this activity can help create a culture where students feel free to try different paths to get to the requested answer.  

It also provide automatic scaffolding because students use the type of math they are most comfortable with to come up with the question.  It also encourages students to feel successful because their question, as long as it gives the answer is correct and as they feel more confident they are likely to try and be willing to make mistakes.

Let me know what you think, I'd love to hear.  Have a great day.