Grades 9-12 Algebra 2 – Rational Functions


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Content Standard

HSA-CED.A.2 Create equations that describe and relationships

HSF-IF.C.7 Analyze functions using different representations

HSF-IF.C.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations and showing end behavior

HSF-BF.B.3 Building new functions from existing functions

Standards for Mathematical Practice

MP 1 Make sense of problems and persevere in solving them.

MP 2 Reason abstractly and quantitatively

MP 4 Model with mathematics

MP 5 Use appropriate tools strategically


This lesson titled “Rational Functions” from Illuminations-NCTM has students work on rational functions within the context of different carnival games. Students are asked to construct graphs and model these graphs using rational functions. Students are asked to use intuition to construct these graphs. Students are then required to transition to rational functions more generally, as well as provide explanations about how different components of the rational function affect the graph. ¬†Questions are provided for the teacher to use for formative assessment, and assessment materials are provided.


Some of the cautions to consider are the lack of differentiation provided. While there are questions provided with activities to function as extension materials, there is limited support to scaffold the material for struggling learners. The assessments provided do not include rubrics or sample student work. This lesson also requires additional support for English language learners. A multitude of materials is also necessary for some of the classroom activities.


This lesson attends to the rigor of the Common Core, rooting the activity within a real-world context and asking students to be metacognitive during the process. There is a clear focus of the material on the content, asking students to move beyond just the equation and graph. Students are also examining the function is multiple representations. This lesson also provides a detailed outline and instructional support for the teacher.