Modeling Functions

During the November 6th Genius Hour, we reviewed a variety of instructional practices that help build conceptual understanding. The following samples aligned to linear functions were provided.

The "Build This!" activity is the brilliant work of Nat Banting from his Relation Stations post over on his {Musing Mathematically} blog. The link was shared by Kathryn Freed during a recent #alg1chat on Twitter. Students view three patterns and determine what all three patterns have in common...a starting point and a constant change. Then students are asked to create a pattern of their own. Finally students rotated stations to investigate the models created by their classmates and build a table of values to model the pattern. The extension outlined in the blog post involves students using their record sheet to write equations for each pattern the following day. Starting with a concrete model of color tiles and eventually expanding to the abstract algebraic equation is powerful.

Nat mentioned in the #alg1chat that he has reversed the activity to provide students an equation and ask for the model. The possibilities are endless! You could have each team build two patterns with the same starting point...one with a constant change and one with a varying change to emphasize linear and nonlinear patterns. You could also add graphing to the table of values record sheet to make further connections.

Create a Model

The next activity is adapted from the Modeling with a Linear Function task on the Illustrative Mathematics website. (On a complete side note...we simply must chat about the word "task" and its use in today's math classroom. Care to define that one for me?) The activity poses a linear function and proceeds to outline a variety of models...some describe the linear function while others do not. However, the descriptions that do not match the linear function are common misconceptions. When structured as a Takeoff... Touchdown..., this activity is an engaging way to get students to differentiate between concept and misconceptions.

Differentiate Common Misconceptions

The following prompt (which would be a fabulous RoundTable...or, better yet, use three additional functions to create a Simultaneous RoundTable) is an adaptation of a released open response item from the Arkansas Department of Education. The original function was quadratic and the table didn't contain the same rational values. This prompt integrates prior knowledge of transformations and operations with rational numbers with the current knowledge of linear functions.

Integrate Prior Knowledge
All of these instructional practices help students build conceptual understanding and/or make connections between content. And that is the key to success in math...whether that's today, the next unit, the standardized test, or next year's math class.

These activities highlight Common Core State Standards 8.F.A.3 and 8.F.B.4 that are included in MATH-8 and Accelerated Algebra 1.