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Students will use the structure of a visual pattern that is growing in two dimensions to calculate the area of a subsequent figure. Attention should be paid to the connection between area and quadratic functions.

Students analyze different representations of quadratic functions to determine what characteristics of quadratic functions are true for every quadratic function, and then extend their understanding to analyze polynomial functions.

Use the structure of a set, including the color, of growing sequences to make matches to corresponding quadratic functions.

This Core Resource focuses on how we can distinguish quadratic functions from linear and exponential functions based on their properties when represented as sequences, tables, graphs, and using rate of change to find intervals of a function that are increasing, decreasing, positive, negative, and symmetry of a function (if any).    

After this unit, how prepared are your students for the end-of-course Regents examination?  The end of unit assessment is designed to surface how students understand the mathematics in the unit.  It includes spiralled multiple choice and constructed response questions, comparable to those on the end-of-course Regents examination.  A rich task, that allows for multiple entry points and authentic assessment of student learning, may be available for some units and can be included as part of the end of unit assessment.  All elements of the end of unit assessment are aligned to the NYS Mathematics Learning Standards and PARCC Model Frameworks prioritization. 

During this week students create and study different representations of quadratic functions in order to make connections between the different representations.

Connect the elements of standard and vertex form to the graphs and tables of quadratic functions by recognizing the key characteristics in both forms.

Students will connect a graph of a parabola with a written description of its axis and number of roots. 

Use the structure of a set of graphs of parabolas and a set of quadratic equations to make connections related to the direction the graph opens and the y-intercept of the graph.

Make connections between the operations used to model how a figure changes in a pattern to predict future values.

This goal of this lesson is for students in making connections between the standard form of a quadratic function (where a = 1) and the graph or table of that function.

The objective is for students to be able to create a visual representation, from the sequence of numbers, that shows the correspondence between the function given and the numbers produced by that function.