Barbara Soots, Washington OSPI OER Project, Washington OSPI Mathematics Department
Material Type:
Teaching/Learning Strategy
Preschool, Lower Primary, Upper Primary, Middle School, High School
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  • Washington Office of Superintendent of Public Instruction
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    Education Standards

    MPIR - Which One Doesn't Belong

    MPIR - Which One Doesn't Belong


    Which One Desn't Belong is one of many Mathematically Productive Instructional Routines (MPIR). They are short (10ish minutes), daily exercises aimed at building number sense. This is one of six different MPIR covered in the Mathematically Productive Instructional Routines collection from the Washington Office of Public Instruction and the Washington Association of Educational Service Districts.

    Why Which One Doesn't Belong?

    Which One Doesn’t Belong (WODB) gives students the opportunity to explain their thinking and justify their reasoning. Each WODB set is designed to be interpreted in a variety of different ways, and because all answers are correct, students naturally shift their focus to justifications that spark deep mathematical thinking and discussion. WODB promotes a respectful learning community by creating a culture of valuing students as thinkers, reasoners, listeners, justifiers, and doers of mathematics.

    WODB activities can be used to support a variety of computation strategies at all grade levels and topics. The graphics can be topic/lesson specific or more broad and open-ended. This routine creates avenues for students to use mathematical vocabulary. WODB can be used in a variety of contexts or subjects encouraging mathematical thinking across broad curriculum.


    Mathematical Practices:

    The specific task used may expand the Mathematical Practice possibilities, but in general, this routine will encourage students to use:

    SMP 2: Reason abstractly and quantitatively

    SMP 3: Construct viable arguments and critique the reasoning of others

    SMP 6: Attend to precision

    What is Which One Doesn't Belong?

    Students are presented with four numbers, shapes, visual images, data sets or graphs and asked to share their reasoning as to Which One Doesn't Belong and why. In this routine there are no wrong answers, as long as the student can justify their choice. The focus of this routine is not on the answer, but on students being able to communicate their reasoning and justify their choice.

    WODB can be used to introduce a new concept or to continue developing mathematical ideas. It is a quick routine can be done regularly to explore any concept in math. This is an accessible routine for all students to develop reasoning and communication skills using mathematical language. It can be used as a lesson starter or at any time within a lesson.

    How Do I Implement Which One Doesn't Belong?

    Students are presented with 4 different, yet similar images (numbers, graphs, pictures, etc.) on a 2 x 2 grid. The prompt to students is "Which one doesn't belong?". Students take a few minutes of think time to decide on their answer and their reasoning. Students then turn and talk to a partner and take turns sharing their thinking.  The teacher then facilitates a whole class discussion, where students take turns sharing which of the four items they believe does not belong and also justify why their choice is valid. For older students encourage them to articulate a rule that the other images follow that the 4th image does not.

    A more detailed outline can be found in the Which One Doesn't Belong Process & Resources handout.

    Additional Resources


    • Process and Resources sheet



    • Which One Doesn't Belong? A Shapes Book, by Christopher Danielson
    • Which One Doesn't Belong? A Shapes Book Teacher's Guide, by Christopher Danielson

    Other Resources

    • Which One Doesn’t Belong? Shapes Posters, by Christopher Danielson

    Mathematically Productive Instructional Routines Menu

    Which One Doesn't Belong is one of many Mathematically Productive Instructional Routines (MPIR). Click on one of the images below to see other examples:

    clothesline    teacher and students          boy thinking
                   Clothesline                              My Favorite kNOw                        Notice and Wonder

    number talk in math class     students discussing math          shapes
               Number Talks                                Ten Minute Talk                          Which One Doesn't Belong

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