Algebra 1

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Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. A1.A-SSE.A.1.a

Use the structure of an expression to identify ways to rewrite it. For example, see 𝑥𝑥4 − 𝑦𝑦4 as (𝑥𝑥2)2 − (𝑦𝑦2)2, thus recognizing it as a difference of squares that can be factored as (𝑥𝑥2− 𝑦𝑦2)(𝑥𝑥2+ 𝑦𝑦2).A1.A-SSE.A.2

Choose and produce an equivalent form of an expression or equation to reveal and explain properties of the quantity represented by the expression. ★ (A1 and A2)A1.A-SSE.B.3

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A1.A-CED.A.1

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.A1.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.A1.A-CED.A.3

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law 𝑉𝑉 = 𝐼𝐼𝐼𝐼 to highlight resistance 𝑅𝑅.A1.A-CED.A.4

Explain each step-in solving equations 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. (A1 and A2)A1.A-REI.A.1

Solve rational and radical equations in one variable and give examples showing how extraneous solutions may arise. (A1 and A2)A1.A-REI.A.2

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.A1.A-REI.B.3

Solve quadratic equations in one variable. (A1 and A2)A1.A-REI.B.4

Explain how the strategy of elimination results in finding solution(s) to a system of equations.A1.A-REI.C.5

Solve systems of linear equations exactly and approximately. For example, with graphs, focusing on pairs of linear equations in two variables.A1.A-REI.C.6

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. (A1 and A2)A1.A-REI.C.7

Understand 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). (A1 and A2)A1.A-REI.D.10

Explain why the solution(s) of a system of equations are the point(s) of intersection(s) on a coordinate plane. Find the solutions approximately. For example, using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝑓𝑓(𝑥𝑥) and/or 𝑔𝑔(𝑥𝑥) are quadratic, exponential, rational, absolute value functions, polynomial, exponential, and logarithmic functions. ★ (A1 and A2)A1.A-REI.D.11

Graph and interpret (with the use of technology) the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. (A1 and A2)A1.A-REI.D.12

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝑓𝑓 is a function and 𝑥𝑥 is an element of its domain, then 𝑓𝑓(𝑥𝑥) denotes the output of 𝑓𝑓 corresponding to the input 𝑥𝑥. The graph of 𝑓𝑓 is the graph of the equation 𝑦𝑦 = 𝑓𝑓(𝑥𝑥).A1.F-IF.A.1

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.A1.F-IF.A.2

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by 𝑓𝑓(0) = 𝑓𝑓(1) = 1, 𝑓𝑓(𝑛𝑛 + 1) = 𝑓𝑓(𝑛𝑛) + 𝑓𝑓(𝑛𝑛 − 1)for 𝑛𝑛 ≥ 1. A1.F-IF.A.3

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 given a verbal description of the relationship. Key features may include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximum and minimum; and symmetries. ★ (A1 and A2)A1.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.A1.F-IF.B.5

Calculate and interpret the average rate of change of a nonlinear function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. ★ (A1 and A2)A1.F-IF.B.6

Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.A1.F-IF.C.7

Note: b, c, and d, exist and can be found in A2.

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. For example, use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. (A1 and A2)A1.F-IF.C.8

Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context.A1.F-BF.A.1a

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Note: Interpret arithmetic sequences as linear functions and geometric sequences as exponential functions. ★ (A1 and A2)A1.F-BF.A.22

Identify the effect on linear and quadratic graphs of replacing 𝑓𝑓(𝑥𝑥) by 𝑓𝑓(𝑥𝑥) + 𝑘𝑘 , 𝑘𝑘𝑘𝑘(𝑥𝑥), 𝑓𝑓(𝑘𝑘𝑘𝑘), and 𝑓𝑓(𝑥𝑥 + 𝑘𝑘) for specific values of 𝑘𝑘 (both positive and negative); find the value of 𝑘𝑘 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.A1.F-BF.B.3

Distinguish between situations that can be modeled with linear functions and with exponential functions. A1.F-LE.A.1

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (A1 and A2)A1.F-LE.A.2

Use graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.A1.F-LE.A.3

Interpret the parameters in a linear or exponential function in terms of a context. (A1 and A2)A1.F-LE.B.5

Represent data with plots on the real number line (dot plots, histograms, and box plots) in a modeling context. ★ A1.S-ID.A.1

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. ★A1.S-ID.A.2

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). ★A1.S-ID.A.3

Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. ★A1.S-ID.B.5

Represent data on two quantitative variables on a scatter plot and describe how the variables are related. ★A1.S-ID.B.6

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. ★A1.S-ID.C.7

Compute (using technology) and interpret the correlation coefficient of a linear fit. ★A1.S-ID.C.8

Distinguish between correlation and causation. ★A1.S-ID.C.9