1. What are they?

What is a Numberless Word Problem?

Simply put, a Numberless Word Problem is a word problem where all the numbers have been removed.

Regular word problem

Derek has 5 toy cars. Hector has 3 more toy cars than Derek. How many toy cars do the two friends have altogether?

Numberless Word Problem

Derek has some toy cars. Hector has more toy cars than Derek. How many toy cars do the two friends have altogether?

Why remove the numbers?

Research has shown that when students are presented a word problem they often demonstrate a “compulsion to calculate.” What this means is that they ignore the context of the problem. Instead, they pluck out numbers and perform some kind of calculation with them. They might:

• add all the numbers together because that’s the easiest thing to do,
• choose the operation that matches the one being studied in the current math unit, or
• base their decision on some “key word” in the problem that they associate with a specific operation.

Is it any wonder that this often leads to incorrect answers?

If there are no numbers, then what do students do?

Good question! Removing the numbers allows the teacher to invite students into a conversation:

• What is going on in the problem? What can you picture in your mind?
• What do we know about the quantities and relationships in the problem even though there are no numbers?
• What is the question asking us to find out?

Consider our earlier problem:

Derek has some toy cars. Hector has more toy cars than Derek. How many toy cars do the two friends have altogether?

Here’s what students can uncover through conversation:

• There are two friends, Derek and Hector.
• Each friend has some toy cars.
• Hector has more toy cars than Derek.
• We need to find out the total number of toy cars the two friends have.

After bringing these ideas to the surface, students are set up for greater success solving the problem. They are able to make sense of the quantities, relationships, and question before the numbers are finally introduced.

Is it really that easy?

Taking the numbers out is easy, but that’s just the first step. There are other important pedagogical moves to consider as you plan and implement Numberless Word Problems. Next, let’s take a look at a Numberless Word Problem in action to see how taking the numbers out fundamentally changes the way students engage with word problems.