What are Comparing Routines?

By engaging in Comparing Routines, students develop the need for precise mathematical language, refine their reasoning skills, and work to verbally justify their decisions.

Students also use mathematical vocabulary, and by identifying similar and different characteristics, build a deeper understanding of the relationships between mathematical objects.

More Information

Along with the K-12 Math Task Collection which includes several Comparison Prompts linked to SK outcomes, you can also check out the Comparing Routines below.

Which One Doesn't Belong?

Which One Doesn't Belong? is a structure where students answer this question given four mathematical objects (shapes, numbers, graphs, etc.). There are many different correct answers and justifications for choosing which one doesn't belong. In fact, there is a justification for each of the four objects!

You can use this in a Four Corners activity or as a Number Talk style prompt to get students thinking and reasoning. You can even ask students to make their own WODB.

PD via Twitter: @WODBMath, @marybourassa, @Trianglemancsd, #wodb

Same or Different

Same or Different can be used within a Number Talk where students have time to think, then share characteristics with a partner, small group, or the class. The teacher moves the conversation along and prompts students to fully explain their thinking, and make connections.

PD via Twitter: #samediffmath

Would You Rather?

Would You Rather? is a comparison routine where students choose a path and justify it. This is a strategy that helps to build students' ability to use their intuition and estimation skills, as well as their ability to provide a clear mathematical argument or proof for their choices.

The options are presented as engaging images. For example, the images include food options, subscription plans, rates of time or money, unit conversions, etc.

PD via Twitter: #WYRmath, @Jstevens009

Attribute Train

To play Attribute Train, you need a bunch of stuff -- can be math manipulatives, items you find around the class, or even images mixed up on a smartboard (of random objects, math manips, graphs, functions, etc.)

Pick one item. Then, students look at the rest of the objects, and select one that has something in common with the first, and place it in the line. They explain the commonality and continue building the train in this fashion.

Once finished, consider going back and asking students to review the characteristics that were in common between each pair of items.

Desmos Polygraph Activities

Desmos Polygraph activities allow students to ask each other questions based on groups of characteristics to identify the mathematical object their partner has selected. Polygraph is similar to the board game "Guess Who?"

Desmos Polygraph allows students to transfer their informal language to formal mathematical vocabulary when discussing the attributes of Shapes, Angles, Translations, Functions, Domain and Range, and more.

The teacher dashboard allows the teacher to view and snapshot the questions students are asking to draw attention to key questions and help consolidate the learning after the actvitiy.

To make your own Desmos Polygraph, sign in, click Custom, and then select "New Polygraph" at the top right corner.

PD via Twitter: @Desmos