The following evidence outcomes apply throughout Algebra 1, focusing on the families of linear, exponential, and quadratic functions.

The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.

Students Can (Evidence Outcomes):

HS.N-Q.A. Quantities: Reason quantitatively and use units to solve problems.

• Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. (CCSS: HS.N-Q.A.1)

• Define appropriate quantities for the purpose of descriptive modeling. (CCSS: HS.N-Q.A.2)

• Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. (CCSS: HS.N-Q.A.3)

HS.A-SSE.A. Seeing Structure in Expressions: Interpret the structure of expressions.

• Interpret expressions that represent a quantity in terms of its context.⭑ (CCSS: HS.A-SSE.A.1)

  • Interpret parts of an expression, such as terms, factors, and coefficients. (CCSS: HS.A-SSE.A.1.a)

  • Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)n as the product of P and a factor not depending on P. (CCSS: HS.A-SSE.A.1.b)

• Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). (CCSS: HS.A-SSE.A.2)

HS.A-CED.A. Creating Equations: Create equations that describe numbers or relationships.⭑ 

• Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and exponential functions. (CCSS: HS.A-CED.A.1)

• Create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales. (CCSS: HS.A-CED.A.2) 

• Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. (CCSS: HS.A-CED.A.3)

HS.A-REI.A. Reasoning with Equations & Inequalities: Understand solving equations as a process of reasoning and explain the reasoning.

• Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (CCSS: HS.A-REI.A.1)

HS.A-REI.D. Reasoning with Equations & Inequalities: Represent and solve equations and inequalities graphically. 

• Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). (CCSS: HS.A-REI.D.10)

• Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, and exponential functions. (CCSS: HS.A-REI.D.11)

HS.F-IF.A. Interpreting Functions: Understand the concept of a function and use function notation.

• Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (CCSS: HS.F-IF.A.2)

HS.F-IF.B. Interpreting Functions: Interpret functions that arise in applications in terms of the context.

• For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (CCSS: HS.F-IF.B.4)

• Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.⭑ (CCSS: HS.F-IF.B.5)

• Calculate and interpret the average rate of change, presented symbolically or as a table, of a function over a specified interval. Estimate the rate of change from a graph.⭑ (CCSS: HS.F-IF.B.6)

HS.F-IF.C. Interpreting Functions: Analyze functions using different representations. 

• Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. (CCSS: HS.F-IF.C.9) 

HS.F-BF.A. Building Functions: Build a function that models a relationship between two quantities. 

• Write a function that describes a relationship between two quantities.⭑ (CCSS: HS.F-BF.A.1)

  • Determine an explicit expression, a recursive process, or steps for calculation from a context. (CCSS: HS.F-BF.A.1.a)

HS.F-BF.B. Building Functions: Build new functions from existing functions. 

• Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k both positive and negative; find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. (CCSS: HS.F-BF.B.3)

HS.S-ID.B. Interpreting Categorical & Quantitative Data: Summarize, represent, and interpret data on two categorical and quantitative variables. 

• Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (CCSS: HS.S-ID.B.6) 

  • Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. (CCSS: HS.S-ID.B.6.a)

A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.