# Algebra I

Algebra I is organized around the families of functions, with special emphasis on linear and quadratic functions. Students will learn to represent them in multiple ways as verbal descriptions, equations, tables, and graphs. These functions will be applied and used to model real-world situations in order to solve arising problems. Students will also learn data analysis and apply geometric properties in the algebraic realm.

**Credits:** 1.0 (0.5 per semester)

**Estimated Completion Time:** 2 semesters/18-36 weeks

**State Course Number:** 115810

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- A1.NQ.A.1 Explain how the meaning of rational exponents extends from the

properties of integer exponents. (N.RN.1) - A1.NQ.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Limit to rational exponents with a numerator of 1. (N.RN.2)
- A1.NQ.B.3 Use units of measure as a way to understand and solve problems involving quantities.
- Identify, label and use appropriate units of measure within a

Problem. - Convert units and rates.
- Use units within problems.
- Choose and interpret the scale and the origin in graphs and data displays. (N.Q.1)

- Identify, label and use appropriate units of measure within a
- A1.NQ.B.4 Define and use appropriate quantities for representing a given context or problem (N.Q.2)
- A1.NQ.B.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. (N.Q.3)
- A1.SSE.A.1 Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions. (A.SSE.1)
- A1.SSE.A.2 Analyze the structure of polynomials to create equivalent expressions or equations. (A.SSE.2)
- A1.SSE.A.3 Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.
- Find the zeros of a quadratic function by rewriting it in factored form.
- Find the maximum or minimum value of a quadratic function by completing the square. (A.SSE.3)

- A1.CED.A.1 Create equations and inequalities in one variable and use them to model and/or solve problems. (A.CED.1 & REI.B.3)
- A1.CED.A.2 Create and graph linear, quadratic and exponential equations in two variables. (A.CED.2)
- A1.CED.A.3 Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context (A.CED.3)
- A1.CED.A.4 Solve literal equations and formulas for a specified variable that highlights a quantity of interest. (A.CED.4)
- A1.REI.A.1 Explain how each step taken when solving an equation or inequality in one variable creates an equivalent equation or inequality that has the same solution(s) as the original. (A.REI.1)
- A1.REI.A.2 Solve problems involving quadratic equations.
- Use the method of completing the square to create an equivalent quadratic equation.
- Derive the quadratic formula.
- Analyze different methods of solving quadratic equations. (A.REI.4)

- A1.REI.B.3 Solve a system of linear equations algebraically and/or graphically. (A.REI.6)
- A1.REI.B.4 Solve a system consisting of a linear equation and a quadratic equation algebraically and/or graphically. (A.REI.7)
- A1.REI.B.5 Justify that the technique of linear combination produces an equivalent system of equations. (A.REI.5)
- A1.REI.C.6 Explain that the graph of an equation in two variables is the set

of all its solutions plotted in the Cartesian coordinate plane. (A.REI.10 and 11) - A1.REI.C.7 Graph the solution to a linear inequality in two variables. (A.REI.12)
- A1.REI.C.8 Solve problems involving a system of linear inequalities. Β (A.REI.12)
- A1.APR.A.1 Add, subtract and multiply polynomials, and understand that polynomials follow the same general rules of arithmetic and are closed under these operations. (APR.A.1)
- A1.APR.A.2 Divide polynomials by monomials.
- A1.IF.A.1 Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range.
- Represent a function using function notation.
- Understand that the graph of a function labeled π is the set of all ordered pairs (π₯, y) that satisfy the equation π¦=f (π₯). (IF.A.1)

- A1.IF.A.2 Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (IF.A.2)
- A1.IF.B.3 Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities. (IF.B.4)
- A1.IF.B.4 Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (IF.B.5)
- A1.IF.B.5 Determine the average rate of change of a function over a specified interval and interpret the meaning. (IF.B.6)
- A1.IF.B.6 Interpret the parameters of a linear or exponential function in terms of the context (LE.B.5)
- A1.IF.C.7 Graph functions expressed symbolically and identify and interpret key features of the graph. (IF.C.7)
- A1.IF.C.8 Translate between different but equivalent forms of a function to reveal and explain properties of the function and interpret these in terms of a context. (IF.C.8)
- A1.IF.C.9 Compare the properties of two functions given different representations. (IF.C.9)
- A1.BF.A.1 Analyze the effect of translations and scale changes on functions. (BF.B.3)
- A1.LQE.A.1 Distinguish between situations that can be modeled with linear or exponential functions.
- Determine that linear functions change by equal differences over equal intervals.
- Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval. (LE.A.1)

- A1.LQE.A.2 Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. (LE.A.3)
- A1.LQE.A.3 Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables. (LE.A.2 &BF.A.1)
- A1.LQE.B.4 Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms. (BF.A.2)
- A1.LQE.B.5 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers. (IF.A.3)
- A1.LQE.B.6 Find the terms of sequences given an explicit or recursive formula.
- A1.DS.A.1 Analyze and interpret graphical displays of data.(ID.A.1)
- A1.DS.A.2 Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. (ID.A.2)
- A1.DS.A.3 Interpret differences in shape, center and spreads in the context of the data sets, accounting for possible effects of outliers (ID.A.3)
- A1.DS.A.4 Summarize data in two-way frequency tables.
- Interpret relative frequencies in the context of the data.
- Recognize possible associations and trends in the data. (ID.B.5)

- A1.DS.A.5 Construct a scatter plot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship.
- Construct a linear function to model bivariate data

represented on a scatter plot that minimizes residuals. - Construct an exponential function to model bivariate data

represented on a scatter plot that minimizes residuals. (ID.B.6)

- Construct a linear function to model bivariate data
- A1.DS.A.6 Interpret the slope (rate of change) and the y-intercept (constant term) of a linear model in the context of the data.(ID.C.7)
- A1.DS.A.7 Determine and interpret the correlation coefficient for a linear association. (ID.C.8)
- A1.DS.A.8 Distinguish between correlation and causation. (ID.C.9)