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.
Frequently Asked Questions
What is the primary purpose of this unit?
Students were introduced to the three main functions of exploration in Algebra 1 in Unit 2, and they studied each of them in Units 3, 4 & 5. The 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, F-LE.1 (red) & A-REI.7 (purple) can be reengaged here along with the rest of the F-LE supporting standards.
What is the secondary purpose of this unit?
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 they have studied in this course.
Do I have to re-teach F-LE.1 & A-REI.7?
The short answer is no. They are included here in case they were skipped due to time constraints in their perspective units. Both standards involve comparing two different types of growth; therefore, they could be embedded in A-REI.11 Graphing & Solving Two Functions. The key is for students to come up with each of the functions they are graphing and solving and see the differences in the rate of change or growth in each. This could culminate in the supporting standard of F-LE.3 where students compare and contrast the growth of all three - linear, exponential & quadratic - to see that exponential growth eventually exceeds them all.
What about the connecting standards in this unit?
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.
Developmental Notes
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-BF.B is assessed in Claim 3.
Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.
CLAIM 2: Problem solving, which of course builds on a foundation of knowledge and procedural proficiency, sits at the core of doing mathematics. Proficiency at problem solving requires students to choose to use concepts and procedures from across the content domains and check their work using alternative methods. As problem solving skills develop, a student’s understanding of and access to mathematical concepts becomes more deeply established.
CLAIM 3: This claim refers to a recurring theme in the CCSSM content and practice standards: the ability to construct and present a clear, logical, convincing argument. For older students this may take the form of a rigorous deductive proof based on clearly stated axioms. For younger students this will involve more informal justifications. Assessment tasks that address this claim will typically present a claim or a proposed solution to a problem and will ask students to provide, for example, a justification, and explanation, or counter-example. (Math Content Specifications, p.63). Communicating mathematical reasoning is not just a requirement of the Standards for Mathematical Practice—it is also a recurrent theme in the Standards for Mathematical Content. For example, many content standards call for students to explain, justify, or illustrate.
CLAIM 4: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.
CLAIM 2:
CLAIM 3:
CLAIM 4:
For information on what is required in this unit, check out the assessment tab!