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In Algebra 1, students demonstrate fluency by creating, comparing, analyzing, solving, providing multiple representations, and identifying the structures of exponential & quadratic functions building on the understanding of linear functions from grade 8 to apply linear, quadratic and exponential models to data and unfamiliar problems.
The Story of Alg. 1 - Unit 7: Applying Functions
(Up to 29 days)
In Unit 2, students were introduced to the three main functions of exploration in Algebra 1, and they studied each of them individually more in depth (with comparison to the others) in Units 3, 4 & 5. The primary purpose of this unit is to now apply what they have learned to model, interpret and solve problems without being told in advance what type of growth they are encountering. As such, essential standards such as F-LE.1 (red) & A-REI.7 (purple) can be reengaged here along with the rest of the F-LE supporting standards for added depth. The focus of the unit is applying functions; therefore, the emphasis should be on students Creating & Using Equations (A-CED) to model & solve problems or stated another way, generating Explicit & Recursive Functions from a Context (F-BF.2). Along the way, students might Rearrange Formulas, Graph Functions (F-IF.7), see Solution Sets on a Curve (A-REI.10), and perform Operations on Functions (F-BF.1). In addition, Comparing Two Functions (F-IF.9) directly supports Graphing & Solving Two Functions (A-REI.11) and vice versa. The purpose of this unit is to have students determine the type of relationship exhibited and assign a function to it; therefore, constructing, interpreting and comparing linear, quadratic, and exponential models to solve problems (F-LE) directly supports the goal of this unit; so these supporting standards could be embedded in first instruction or explored on their own afterwards. The secondary purpose of this unit is to build new functions from existing functions. This can be extended, time permitting, to the supporting standard of F-IF.7b - "Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions" comparing and contrasting the new functions to ones studied in this course. F-IF.7b is repeated in Algebra 2 so this might be the last instructional piece explored to provide depth, time permitting.
Unit 7 Notes
Unit 7 is a chance to examine other functions & build new functions from existing functions. Knowledge obtained from units 2-7 is applied as students construct & compare linear, quadratic, & exponential models and solve problems (F-LE.A). Students essentially compare all three types of growth as they observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically (F-LE.3) bringing back all three functions as interleaved practice.
Vocabulary, Tools & Developmental Notes from SBAC
Tasks for this target will require students to create equations and inequalities in one variable to solve problems. Other tasks will require students to create and graph equations in two variables to represent relationships between quantities.
Tasks for this target will ask students to graph functions (linear, quadratic... exponential... ) by hand or using technology and compare properties of two functions represented in different ways. Some tasks will focus on understanding equivalent forms that can be used to explain properties of functions and may be associated with Algebra Target H.
Tasks for this target will require students to write a function (recursive or explicit, as well as translate between the two forms) to describe a relationship between two quantities.
Tasks for this target will require students to interpret a line or curve as a solution set of an equation in two variables, including tasks that tap student understanding of points beyond the displayed portion of a graph as part of the solution set. Some of these tasks should explicitly focus on non-integer solutions (e.g., give three points on the graph of y = 7x + 2 that have x-values between 1 and 2).
Other tasks for this target will require students to approximate solutions to systems of equations represented graphically, including linear... exponential... (often paired with Target L - Interpret functions that arise in applications in terms of the context).
F.LE.A Construct and compare linear, quadratic, and exponential models and solve problems. (Claim 4)
F.LE.A Construct and compare linear, quadratic, and exponential models and solve problems. (Claim 4)
F-LE.A is assessed in Claim 4.
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