I recently asked my PD participants to share their biggest struggles around teaching number stories. Here are some of the challenges they shared:

• “They miss important details b/c they don’t slow down when reading.”
• “Comprehension … is the biggest problem.”
• “They’re great whole group and then it’s like they forgot everything we just did.”
• “…how to know which operation to use.”
• “They learned to be successful by picking out the patterns, picking out numbers, words, or key indicators…not slowing themselves down, not asking themselves questions, not making sense of them, looking for numbers and key words.”
• “Comprehension of the problem, they want to find the numbers and usually add or multiply.”

Their responses highlight common issues teachers have faced for years; kids don’t know how to make sense of math stories.

We’ve tried everything. We’ve been told keywords don’t work and not to use procedural strategies like CUBES. But no one told us what to replace them with. That’s why I created Structures of Equality. 

Along the way, I’ve found a few strategies that work well in conjunction with the structures. One of my favorites is incorporating numberless word problems. If you’re not using SoE yet, this can be a great entry point. And if you are, they make a perfect pair.

Today, we’ll talk about what numberless word problems are, why they work, and how you can get started using them in your classroom.

What is a numberless word problem?

Numberless word problems are exactly what they sound like, problems with the numbers removed. (I guess we can’t use the term “number stories” here!)

You remove the numbers from the story or replace them with alternative language such as some. You also remove the question so the focus remains on the context of the story and making sense of what’s happening.

In this example, students can quickly figure out they’re trying to find how many giraffes are in the zoo now. As you progress to multi-step problems or more complex story situations, removing the question stimulates rich discussion around what the problem could be asking.

What are the benefits of teaching numberless word problems?

Many students choose “plug and chug” strategy. They don’t read the problem, pick out the numbers, choose a random operation, and solve. They don’t slow down long enough to figure out what the problem is asking.

Numberless word problems force them to slow down and think about what is happening. They begin to understand that math is about reasoning, sense-making, and critical thinking. It’s more than arithmetic and calculations.

Removing the numbers makes problems less intimidating and encourages exploration of the situation. It’s also an effective strategy to help your kids develop a growth mindset.

How do you teach numberless word problems?

Similar to the way you implement SoE, you facilitate discussion by prompting students with questions based on the situation occurring in the story. Then you progressively introduce the numbers and a question into the context. 

Brian Bushart has a bank of numberless word problems on his site that he’s already broken down into a progression. He includes questions you can pose along the way. I’m going to walk you through what instruction of one of his problems could look and sound like.

First Read

I love this question Brian suggests:

• What are you picturing in your mind when you read these sentences?

From the start, we are asking kids to visualize what’s happening in the story. The next questions you could pose are:

• What do you know about the amount of comic books they both have? (If the idea of more or fewer doesn’t come up, you can prompt with: Who has more comic books? Who has fewer?)
• What is the thing we’re counting or comparing?

The 2nd question comes directly from the Compare question stems on my website.

At this point, your students will already know that we’re comparing two unique sets. 

Second Read

Notice the gradual introduction of a number into the problem. Because we only know one value, your students won’t have the option of trying to solve before they have comprehension of the story.

Brian suggests another question to progress the discussion.

• What changed? What did we learn from this new information?

I’d also pose the following:

• In our first read, we noticed Andrew has fewer comic books than Sahar. That means Sahar has more. If Sahar has 24 comic books, what must be true about the amount Andrew has?
• What are some possible amounts of comic books Andrew could have?

Third Read

You’ll now introduce the second value.

Questions to pose:

• What changed? What did we learn from this new information? (Brian’s question)
• What is the math main idea?
• Which structure would we use to represent this situation? (This is a question you would pose if your students are already familiar with SoE. If they’re not, you could ask: How could we draw a model to represent this situation?)
• What questions could we ask about this situation? (Brian’s question)

Understanding the math main idea is a critical component of teaching kids reading comprehension in math. If this idea is new to you, you can explore it here.

Fourth Read

It’s finally time to reveal the question!

To move the discussion along, ask:

• What is this question asking us? (Brian’s question)

If your students have created a Compare structure using sentence strips or by drawing it, here are additional questions you can ask:

• Where is the line of equality? What does that tell us?
• Earlier you said Andrew has fewer comic books which means Sahar has more. Point to Sahar’s more.

📹 To see this in action, check out “Compare Structure of Equality With Fewer” on my YouTube channel.

After this rich discussion, your students will comprehend what the problem is asking. They’ll know exactly what to do with the numbers and can use the strategies they have to find a solution.

Conclusion

Numberless word problems, especially when partnered with SoE, help your students slow down and focus on the context of a number story. This improves reading comprehension which alleviates the common challenges we mentioned earlier. 

Your students will have the confidence to tackle number stories. Instead of rushing through and focusing on getting an answer, they’ll have the strategies to internalize what’s happening and strategically figure out how to solve what the question is asking.

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