Notes & FAQs

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

Why are other functions included in this unit?

Much of the standards are written with comparison & contrast in mind. Quadratics should be compared and contrasted with linear growth just as exponential growth was compared to linear in Unit 4. The idea is spelled out specifically in A-REI.7, linear & quadratic systems. F-LE.3, comparing all three types of growth to one another has been saved for Functions 2 (Unit 7); however, F-IF.9, comparing two functions, opens the door for the comparison of quadratics to other functions including exponentials. This further reengagement of linear functions here supports the need move on and not camp out in the linear functions unit, Unit 3.

What about algebra tiles?

Arithmetic operations on polynomials including area models with & without algebra tiles for multiplying & factoring are a major focus of the unit and are necessary components for developing fluency with quadratic functions (A-REI.4 & A-APR.1). Tiles can be introduced through polynomial addition & subtraction (A-APR.1) to build procedural proficiency from conceptual understanding.

Developmental Notes

Notes for A-CED.A

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.

A-CED.A Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for F-IF.C

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.

F-IF.C Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for A-REI.D

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).

A-REI.D Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for F-BF.A

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.

F-BF.A Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for A-APR.A.1

Tasks for this target will require students to add, subtract, and multiply polynomials.

A-APR.A.1 Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for A-REI.B

Tasks for this target will require students to solve linear equations and inequalities in one variable and solve quadratic equations in one variable. Tasks asking students to choose the appropriate method will contribute evidence to Claim 2 and 4.

A-REI.B Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for A-REI.7 (Claims 2, 3 & 4)

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.

A-REI.7 Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

CLAIM 2:

CLAIM 3:

CLAIM 4:

For information on what is required in this unit, check out the assessment tab!

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