What are numberless word problems and why are they useful? If I had to identify one consistent area of concern for parents seeking help for their children, it would definitely be word problems. While sometimes it is an issue of the reading level of the problem being higher than the child’s reading level, or the child not knowing how to do the math, even strong readers and mathematicians sometimes struggle with figuring out what the problem is asking. Many students see a word problem and want to immediately pull out the numbers and start computing. Often they will not analyze the problem, but just use whatever operation they have been learning most recently. Or they pull out a “key word” and decide that because the problem says “in all” they will add. This is a problem because today’s tests use much more complex problems, often with tricky wording.
There are several strategies for helping children build their confidence and ability in solving word problems. I have used several in the past, including having kids write their own word problems, teaching problem solving routines, acting out problems, and my oft repeated phrase “If in doubt, draw it out.” All of these help. But a strategy I had not heard of until recently, and now love for guided instruction, is using numberless word problems.
What Are Numberless Word Problems?
When I first heard of this idea I thought, “How can you have a word problem with no numbers?” The answer of course is that you do have numbers but you don’t start with them. You start by giving students a “math story” and have them think about the possibilities and ask questions. A basic example might be: “Some kids were eating cookies. Some of them were eating chocolate chip cookies.” (More specific examples for different grade levels are linked below.) Then you add the numbers in one at a time and add a relevant question. Alternatively, you can have each child input their own numbers and their own question/answer. Basically, this is a scaffolded approach to get kids thinking. It can be used very well as an extension of a Notice/Wonder math routine.
I loved this quote from Chase Orton at Undercover Calculus. “Students need to understand that data tells a story; it has contextual meaning that is both cohesive and incomplete.” Kristin Gray at Math Minds relates it to Common Core Standard of Mathematical Practice 1:
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.
Examples of Numberless Word Problems
Here are links to examples of numberless word problems at different grade levels:
- Kindergarten example from Math Minds
- 1st grade example from Undercover Calculus
- 1st grade example from Elementary Math Addict
- 2nd grade example from Undercover Calculus
- 3rd grade example from Undercover Calculus
- 3rd grade example from The Teaching Channe
- 4th/5th grade example from Teaching to the Beat of a Different Drummer
To Learn More
The most extensive resource I have found for numberless word problems comes from the creators of the strategy at Teaching to the Beat of a Different Drummer. At this site, run by Elementary Math Curriculum Coordinator of Round Rock ISD Brian Bushart, you can find an article about the inspiration for and origin of this strategy, problem banks of already written numberless word problems, instructions on writing your own numberless word problems, and even full examples of a class discussion of a numberless word problem. He has also now added a list of blog links with real teachers’ accounts of how this worked in their classroom.