Making Meaning in Math: Making Arguments

Conceptual understanding and critical thinking are necessary, but sometimes difficult goals for students to achieve with a given topic. Access to skills through repeated practice is more easily demonstrated and assessed. However, retention and expansion of those skills is dependent upon understanding the math principles they are based on.

One way to support students with skill practice, conceptual development, and discourse is through making mathematical arguments about patterns. When students have to identify patterns and make connections, they are using higher order thinking to rationalize how numbers, equations, shapes, operations, or other math topics are alike. 

When given the opportunity to make a claim or argument about the patterns they notice, they have to justify their thinking first to themselves and then to an audience. These kinds of exercises are great for promoting rich mathematical thinking and classroom discussions.

Making Multiple Arguments

Try this activity for making arguments about factors and multiples in your classroom (grades 4-6). 

Making Arguments: Shapes and Properties

You can also try this activity for making arguments about two-dimensional shapes (grades 1-3).