Using Numberless Word Problems in the Upper Elementary Classroom

Do your students struggle with effectively solving word problems, even though they have shown proficiency with solving basic computation problems?  My students did until I decided to try a different approach: I ditched the mnemonic strategies and keyword tricks and focused on comprehension!  Yes, comprehension in math!  In order to be effective problem solvers, you students need to have strong computation AND comprehension skills.  Once I taught my students how to make sense of the context within word problems, they could put more effort on the computation(s) necessary to solve the word problems accurately.  What was my new approach to comprehension?  Numberless Word Problems. 

What are Numberless Word Problems?

Numberless word problems are exactly what you’d expect them to be: word problems without numbers (at least in the beginning)!  

Students are first presented with a word problem situation to make sense of, but it’s void of any numbers and questions.  Progressively, more information is added back into the problem until the question is finally revealed to students.

Here’s an example:

Example of a numberless word problem first read: Marcia purchased a new cell phone and set of ear buds with her birthday money. In this example, students are first presented with a brief context.
Students are first presented with a brief context.

why use Numberless Word Problems?

It’s important for students to comprehend what is going on in the problem.  Using numberless word problems will help increase your students’ understanding of the context within the word problem.  Once they understand the word problem’s context, it will not only help guide them to choose the correct operation(s) to use, but it will also help them check their answer for reasonableness.

For years I saw students fall apart with word problems, even though they demonstrated proficiency with the math concept embedded within. Why? For the most part, they were picking the numbers out of word problems and guessing on the operation to use based on the math unit we were in and/or operation keywords. While these strategies may have worked for them some of the time, they certainly didn’t when I presented them with a multi-step problem, a spiral review problem that involved a different operation than the one we were currently working on, or a problem that included an ambiguous keyword, such as “total”.

Once I started focusing my energy on comprehension by implementing numberless word problems in my classroom, I no longer saw these errors. Additionally, I found students were better able to check their answers for reasonableness when they understood the problem more clearly. No more irrational answers such as 3.5 buses or 0.5 kids! Instead, students were able to go back into the problems to determine that they needed to round their answer up to 4 buses to accommodate all students and that each kid received 0.5 pound of jelly beans when the bag was shared evenly.

Another benefit to using numberless word problems (and word problems in general) in your classroom? It’s an easy and authentic way to have students demonstrate the 8 Standards for Mathematical Practice! Make sense of problems and persevere in solving them (SMP #1)? Check! Reason abstractly and quantitatively (SMP #2)? Check! And so on…

how i use Them in my classroom

I first introduce numberless word problems at the beginning of the year during my “Launching Math” unit.  It’s important to start the year with a strong understanding of how to tackle word problems since students will be faced with them throughout the year.  Additionally, I use simpler numbers and operations so students can really focus on the comprehension piece without worrying too much about computing larger numbers.

After the initial introduction of numberless word problems at the beginning of the year, I spiral back throughout the year with them during math routine times, class lessons, small group time, and our intervention blocks.  You could certainly use numberless word problems anyway you see fit; this is just what has worked for me! 

Sample Numberless Word Problem progression

I present 1 numberless word problem at a time and use a “4 read” progression, as shown below. You can certainly condense or expand steps to best fit your classroom needs.

This is the first read of a numberless word problem. It reads: Some fifth graders and chaperones from Harrison Elementary School are going on a field trip to the Science Museum. They will be traveling by bus. This first read contains a context. It is void of numbers and a question.
The first read contains a context. It is void of numbers and a question.

First read prompts:
* What do you notice?
* What do you wonder?

This is the second read of a numberless word problem. It reads: 126 fifth graders and some chaperones from Harrison Elementary School are going on a field trip to the Science Museum. They will be traveling by bus. The second read contains some new information.
The second read contains some new information.

Second read prompts:
* What new information did you learn?
* What information do you still need?
* What are you still wondering?

This is the third read of a numberless word problem. It reads: 126 fifth graders and 18 chaperones from Harrison Elementary School are going on a field trip to the Science Museum. They will be traveling by bus. The third read contains additional information. For this example, not all information as been presented because it is a multi-step problem.
The third read contains additional information. For this example, not all information has been presented because it is a multi-step problem.

Third read prompts:
* What new information did you learn?
* What information do you still need?
* What are you still wondering?

This is the fourth read of a numberless word problem. It reads: 126 fifth graders and 18 chaperones from Harrison Elementary School are going on a field trip to the Science Museum. They will be traveling by bus. If each bus holds 48 people, how many buses will be needed to transport everyone to the science museum?
The final read contains the remaining necessary information and a question. For one-step problems, it will usually just be a question added.

Final read prompts:
* What steps do you need to take to answer the question?
* What operation(s) will you use? Why?
* What information will you need to use to answer the question?
* Check your answer for reasonableness. Does it make sense? How do you know?

free resource!

Are you interested in giving numberless word problems a try in your classroom? If so, I have put together a 50+ page resource to get you started! The resource includes an implementation guide, 6 sample problems in 4 different formats, and differentiation options, so you could easily use these in grades 4 and up. Click here to access the resource. If you’d like to have this free resource and more delivered to your inbox monthly, be sure to sign up for my newsletter here.