Which One Doesn’t Belong? (WODB) is an instructional routine that helps teachers create a classroom culture of inquiry, exploration, and collaboration, making math more engaging and meaningful for students.
The basic structure is simple – you present four of something and then ask students which one is different from the others.
One of the first times I used Which One Doesn’t Belong was about 10 years ago.
Because it was a new routine, we did the first one together as a “think aloud” so students could be clear on how the routine worked. I shared the four numbers below and asked students which one didn’t belong.
Before you read what my students said, how would you answer the question, Which One Doesn’t Belong?
As we talked though it, interesting things started to come out immediately. One student said, “I know 3 and 27 are both part of the three times table, and I know 31 isn’t, but I’m not sure about the 123. I don’t think it is.” Another student asked how she knew the 31 was not “part of the three times table” and she said, “Because I know that 30 is, because it goes 27, 30, 33, so it skips the 31”. Then another student had some memory of a divisibility rule for 3 (add up all the digits and see if it’s a multiple of 3) and we tried it with some numbers we knew were multiples of 3 and then we tried it on the 123. Then someone suggested we check and divided 123 by 3 to see if it came out evenly. All of that reasoning and calculation, just to make an observation about one of the numbers (the 31). I made sure to offer “3 is the only single digit number” and “123 is the only three digit number” as potential answers to help less confident students realize that any differences they saw were acceptable.
Once they all seemed clear on what to do, I put another four numbers up on the board and asked them to come up with one quality that made each number different/unique compared to the other three.
Here’s the first one I gave students to work on their own:
The way I set up the activity was to draw the square pictured above on the board and have students copy it in their notebook and write the differences around it. Then as we went over it one number at a time, I had a few volunteers share what they observed. One math practice that came up immediately was the use of precision in explaining mathematical ideas. With me as the note-taker, I was able to encourage students to clarify their statements by asking other students to say it in their own words. When someone else understood something different from what they meant, we worked together to make the statement more precise. The next time I do this activity I think I will have the students come up and write their observations themselves.
Here are the reasons and rationale my students came up with:
The first thing that attracted me to the exercise was the way students at all different levels could approach the problem. There are so many different and correct ways to describe what makes each number unique that every student was engaged. As I walked around and looked at students filling the margins with calculations & observations and talking to their neighbors, I saw how effectively this activity could develop student fluency and comfort with numbers. I liked the approach of the student who said, “If you divide 16 by 2 it is the only one without a remainder”. They didn’t look at it and say “16 is the only even number”, but they were just playing around with the numbers and were curious as to what would happen if they divided each of them by 2. Then, with their observation up on the board, we talked about it a bit and connected it to the idea of even numbers.
Along similar lines, sharing observations was a great opportunity to introduce some vocabulary. In the board work above you can see that for 43, one student observed “No number can be multiplied by itself to get 43”. Which was a nice place to introduce “perfect squares“, which many of them recognized but did not know the words for.
Here’s the second WODB they worked on:
And here’s what students came up with:
We didn’t get to as many different observations for the second one, in part because it was second, but also because we had such a rich conversation about the first number we discussed. I started with the 17 and one student said, “It is the only one you can’t multiply anything to get”. We spent some time unpacking that (clarifying what he meant; coming up with the two numbers that can be multiplied to get 17 are 1 and 17; testing to be sure that was not true of the other numbers). Students were curious about this strange phenomenon of a number that “you can’t multiply anything to get.” I asked if anyone knew the name for that kind of number. No one did, so I was able to say, “there Is a word for the type of number you’ve been talking about. They are called. prime numbers. It is nice to introduce vocabulary word after students have already defined it and have spent some time unpacking.
After we finished up, I asked students to reflect on the activity and they all said or agreed with some version of the statements “It was interesting”, “It was challenging but not too hard” and “You really had to think about the numbers in different ways”.
A few of them asked where they could find more puzzles like these and I gave them the website to explore on their own. Several said they would try it out with their kids and report back on how it goes.
There are some very good resources for finding pre-made examples of WODB that you can use with your students.
- There is a WODB Generator on Polypad that uses fraction circles, prime factor circles, dice, dots, equations, rectangular prisms, and more. Just click on the Generate!button to produce a new WODB.
Here are a few examples:
2. WODB – Which One Doesn’t Belong is a collection of WODB created by other math teachers. The collection is divided into three categories: Number, Shapes, and Graphs. The WODB that I did with my students and described above were all from the NUMBERS collection.
Here are a few examples from their SHAPES and GRAPHS collections:
After many years, I have really come to appreciate like the WODB routine.
It encourages critical thinking: WODB tasks ask students to analyze a set of four items (shapes, numbers, graphs, equations, etc.) and decide which one doesn’t belong. There are multiple correct answers, depending on the reasoning. This openness encourages students to think critically, justify their reasoning, and consider multiple perspectives.
It promotes mathematical discussion: By design, WODB invites discussion and debate. Students must explain their reasoning and listen to others, building their ability to communicate mathematical ideas. Teachers can facilitate rich conversations that draw out students’ ways of thinking.
It is accessible to all learners: The routine is low-floor, high-ceiling. Every student can participate by identifying visible differences. Students can find subtle, complex, and creative reasons why something doesn’t belong.
It reveals student thinking: Teachers gain insight into students’ understanding of concepts and vocabulary.
It supports diverse learning goals: You can use WODB with just about any math topic you are teaching. You can use WODB at the beginning of a unit to see what students know, and draw out vocabulary. You can use WODB as a formative assessment during a unit or as a summative assessment after a unit. You can use it to give students the opportunity to use new concepts they are learning. You can use it to make connections between materials students have already learned and new concepts.
It builds reasoning and justification skills: Explaining why something doesn’t belong requires students to use evidence and logical reasoning. These skills are critical not only in math but in other content areas as well.
It is inclusive and engaging: The routine values multiple approaches and solutions, creating a classroom environment where all contributions are valid and valued. This builds students’ confidence and conveys that math is more about just getting the right answer or following a memorized procedure.
It is super easy to implement: WODB is a flexible and quick routine that requires minimal preparation. You can create their own tasks or use pre-made examples.
