EXPLORATION

By Bethany Neel

In the routine Same but Different, developed by Looney Math, students are presented with two images, numbers, or expressions and asked to explain how the two are the same AND how they are different. The focus is on finding connections as well as what makes them distinct from one another. Teachers provide wait time, foster discussion, and record students' responses so that students notice mathematically important similarities and differences for each image. Prompts are carefully designed to highlight an attribute, connection, relationship, or misconception.

This routine works well with any topic or grade level. It provides an entry point for all students, as everyone can see something that is the same or something that is different between two images. Sometimes what students bring out isn't what is expected or even mathematical, but we can value their thinking and contributions.

This geometry example allows students to consider the attributes of these two figures. What do you notice that is the same about these two figures? What do you notice that is different? What might your students notice? What might be the instructional goal of a teacher displaying these particular images?

Maybe someone would notice that both figures are black, made of straight lines, have no holes or gaps, have five sides, and are pentagons. They might also notice that they are labeled with different letters, or that Shape t has five sides of equal length, but the sides of Shape E have different lengths.

These images were adapted from Teaching Student-Centered Mathematics Grades K-2, Third Edition, Activity 16.2, Page 368. They were designed to help students see that pentagons need not have equal sides and can look very different from one another. Maybe you thought of another instructional goal for these images.

Things to consider as you implement the routine:

• How will you ensure that students have individual think time before they discuss their ideas?
• How will you encourage respectful, productive discussion between students?
• How will you record student responses? For example, a T-Chart labeled with Same and Different is one option.

Here is a recording of my 3rd-grade students' thinking when I used this routine at the beginning of our fractions unit.

My students noticed many of the things I expected, but this discussion also uncovered some misconceptions about squares and rectangles that I was able to address briefly during the routine and then later in another lesson.

Resources for Implementing the Routine:

When choosing or creating a prompt, consider what features or mathematical ideas you want students to attend to and what images would encourage focus on those. These resources can help you get started:

• Looney Math has a well-curated library of prompts on a variety of topics and other resources such as a student recording sheet and journaling prompts.
• KCM slide deck with sample tasks to get you started.
• Math Learning Center Web Apps and Polypad by Amplify are great tools for creating your own prompts.

Final Thoughts:

Same but Different is a rich classroom routine that will help your students think critically about the connections and distinctions between two images, numbers, or expressions. Encourage students to continue to come up with ways the two things are the same and different. Anticipate what your students might notice, but be ready for some original thinking that you might not have expected!