8A: Grade 8 Accelerated

Grade 8 Accelerated

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Algebra I content is compressed into the accelerated track: linear and quadratic equations, polynomial operations, systems, and exponential models, alongside a full functions strand covering domain, range, representations, and transformations. Statistical inference, regression, and probability are included, and the Pythagorean theorem anchors the geometry work.

8A.1Explain how the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for an additional notation for radicals in terms of rational exponents. [Algebra I with Probability, 1]8A.10Explain why extraneous solutions to an equation involving absolute values may arise and how to check to be sure that a candidate solution satisfies an equation. [Algebra I with Probability, 8]8A.11Select an appropriate method to solve a quadratic equation in one variable.8A.12Select an appropriate method to solve a system of two linear equations in two variables.8A.13Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions. [Algebra I with Probability, 11]8A.14Create equations in two or more variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 12]8A.15Represent constraints by equations and/or inequalities, and solve systems of equations and/or inequalities, interpreting solutions as viable or nonviable options in a modeling context. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 13]8A.16Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. [Grade 8, 13, edited for added content]8A.17Given a relation defined by an equation in two variables, identify the graph of the relation as the set of all its solutions plotted in the coordinate plane. [Algebra I with Probability, 14]8A.18Compare and contrast relations and functions represented by equations, graphs, or tables that show related values; determine whether a relation is a function. Identify that a function f is a special kind of relation defined by the equation y = f(x). [Algebra I with Probability, 16]8A.19Combine different types of standard functions to write, evaluate, and interpret functions in context. Limit to linear, quadratic, exponential, and absolute value functions.8A.2Rewrite expressions involving radicals and rational exponents using the properties of exponents. [Algebra I with Probability, 2]8A.20Explain 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).8A.21Graph 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, using technology where appropriate. [Algebra I with Probability, 20]8A.22Solve systems consisting of linear and/or quadratic equations in two variables graphically, using technology where appropriate. [Algebra I with Probability, 18]8A.23Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Include linear, quadratic, exponential, absolute value, and linear piecewise. [Algebra I with Probability, 21, edited]8A.24Define sequences as functions, including recursive definitions, whose domain is a subset of the integers.8A.25Identify the effect on the graph of replacing f (x) by f (x) + k, k·f (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 explain the effects on the graph, using technology as appropriate. Extend from linear to quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 23, edited]8A.26Distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions.8A.27Construct 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). [Algebra I with Probability, 25]8A.28Use graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. [Algebra I with Probability, 26]8A.29Interpret the parameters of functions in terms of a context. Extend from linear functions, written in the form mx + b, to exponential functions, written in the form ab^x. [Algebra I with Probability, 27]8A.3Define the imaginary number i such that i^2 = -1. [Algebra I with Probability, 3]8A.30For 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. Note: Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries; and end behavior. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and general piecewise functions. [Algebra I with Probability, 28]8A.31Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Limit to linear, quadratic, exponential, and absolute value functions. [Algebra I with Probability, 29]8A.32Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.8A.33Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 31]8A.34Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, describing patterns in terms of positive, negative, or no association, linear and non-linear association, clustering, and outliers. [Grade 8, 18]8A.35Given a scatter plot that suggests a linear association, informally draw a line to fit the data, and assess the model fit by judging the closeness of the data points to the line. [Grade 8, 19]8A.36Use a linear model of a real-world situation to solve problems and make predictions.8A.37Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects, using relative frequencies calculated for rows or columns to describe possible associations between the two variables. [Grade 8, 21]8A.38Distinguish between quantitative and categorical data and between the techniques that may be used for analyzing data of these two types. [Algebra I with Probability, 34]8A.39Analyze the possible association between two categorical variables.8A.4Interpret linear, quadratic, and exponential expressions in terms of a context by viewing one or more of their parts as a single entity. [Algebra I with Probability, 4]8A.40Generate a two-way categorical table in order to find and evaluate solutions to real-world problems.8A.41Use mathematical and statistical reasoning with bivariate categorical data in order to draw conclusions and assess risk. [Algebra I with Probability, 32]8A.42Design and carry out an investigation to determine whether there appears to be an association between two categorical variables, and write a persuasive argument based on the results of the investigation. [Algebra I with Probability, 33]8A.43Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). [Algebra I with Probability, 37]8A.44Explain whether two events, A and B, are independent, using two-way tables or tree diagrams. [Algebra I with Probability, 38]8A.45Compute the conditional probability of event A given event B, using two-way tables or tree diagrams. [Algebra I with Probability, 39]8A.46Recognize and describe the concepts of conditional probability and independence in everyday situations and explain them using everyday language. [Algebra I with Probability, 40]8A.47Explain why the conditional probability of A given B is the fraction of B's outcomes that also belong to A, and interpret the answer in context. [Algebra I with Probability, 41]8A.48Informally justify the Pythagorean Theorem and its converse. [Grade 8, 26]8A.49Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane. [Grade 8, 27]8A.5Use the structure of an expression to identify ways to rewrite it. [Algebra I with Probability, 5]8A.50Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications. [Grade 8, 28]8A.6Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.8A.7Add, subtract, and multiply polynomials, showing that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication. [Algebra I with Probability, 7]8A.8Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph. [Grade 8, 17]8A.9Solve systems of two linear equations in two variables by graphing and substitution.
Example Problems
Simplify:
Factor completely:
In 16 years, Ben will be 3 times as old as he is right now.
How old is he right now?
Solve for x.
Use the equation:


Complete the missing value in the solution to the equation:
Goblins

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