Numberless Word Problems

The other day, I ran across the idea of using numberless word problems in class.  Most students when they see a number problem look for the numbers, apply one or more operations to it in the hopes they arrive at the correct answer.  A few understand that the material taught in the section is to be applied to the word problem but most haven't gotten the hang of it.  

Numberless word problems have a every thing a regular word problem has except for the amounts.  We know students automatically look for numbers rather than reading through the whole problem.  An example of a numberless word problem might be "I travelled ______ miles on a tank of gas.  I started with ______ gallons of gas, how many miles per gallon did I get?"

When the numbers are removed, students are forced to look at the meaning and context behind the problem. It helps develop mathematical reasoning.  They are forced to move away from the numbers and finding a solution to understanding exactly the problem itself.  It allows them to focus on context and the underlying structure of word problems.

In the past,   I've given students numbers and asked them to create their own word problem using the values and over half of the incoming freshmen wrote a one sentence problem such as two plus half of twelve is 15.  This indicates they had not yet learned how a word problem is put together instead they'd learned to focus on looking to create an equation to find the solution.

The great thing about giving students numberless word problems, is that you've removed all numbers so students can't "solve" the problem.  They have to slow down, read the problem itself to determine the context of the situation.  It gives them time to figure out how to go about finding a solution or a plan of action. 

Furthermore, by removing the numbers, students have an opportunity to notice that certain problems are similar to each other such as addition problems have them combining things  rather than treating each word problem as something you look for key words to tell them what to do with the numbers written down.  They have to really think about how they would solve it by creating a plan.  

In addition, many students hesitate to solve word problems that have fractions or large numbers or scientific numbers because they are uncomfortable working with them.  In situations like this, many students shut down and refuse to try but by removing the numbers, a limitation is removed and students are more willing to look at word problems because they cannot get a "wrong" answer.  

One way to utilize numberless word problems is to create a set of numberless word problems so students can sort them by operation.  This can easily be done in pairs or small groups where students talk about the phrasing to determine if the problem is asking for addition, multiplication, subtraction or division.  

A second way is to provide one problem to a small group of students and have them do a "What do you know about this problem?", "What do you need to know?" before answering questions such as "What is a possible answer to this problem?"  Then pass out a second problem which is the first problem with one piece of information added so students can answer "What changed in this problem?" "Does this piece of information change the problem?" if so "How?"  Then ask them the "What do you know and what do you need to know "questions before asking for possible solutions.  Finally, provide a third problem with all the information for students to solve independently before they work with a partner to prove their solution.

This way of teaching word problems can be used from Kindergarten to seniors in high school.  Perhaps by using numberless word problems, students will unlearn the idea they have to grab all the numbers, combine them in some manner to get the "right" answer.  Let me know what you think, I'd love to hear.  Have a great day.