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STANDARDS

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US-AL

Math

Alabama Math

Grade 8 Accelerated: Algebra and Functions

Expressions can be rewritten in equivalent forms by using algebraic properties, including properties of addition, multiplication, and exponentiation, to make different characteristics or features visible.

8A.4

Not covered
Interpret 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]
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8A.5

Not covered
Use the structure of an expression to identify ways to rewrite it. [Algebra I with Probability, 5]
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8A.6

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

8A.6.a

Not covered
Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.
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8A.6.b

Not covered
Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.
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8A.6.c

Not covered
Use the properties of exponents to transform expressions for exponential functions. [Algebra I with Probability, 6]
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8A.7

Not covered
Add, 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]
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8A.8

Fully covered
Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph. [Grade 8, 17]

Analyze and solve linear equations and systems of two linear equations.

8A.9

Solve systems of two linear equations in two variables by graphing and substitution.

8A.9.a

Fully covered
Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.

8A.9.b

Fully covered
Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems. [Grade 8, 12]

Finding solutions to an equation, inequality, or system of equations or inequalities requires the checking of candidate solutions, whether generated analytically or graphically, to ensure that solutions are found and that those found are not extraneous.

8A.10

Not covered
Explain 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]
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The structure of an equation or inequality (including, but not limited to, one-variable linear and quadratic equations, inequalities, and systems of linear equations in two variables) can be purposefully analyzed (with and without technology) to determine an efficient strategy to find a solution, if one exists, and then to justify the solution.

8A.11

Select an appropriate method to solve a quadratic equation in one variable.

8A.11.a

Not covered
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Explain how the quadratic formula is derived from this form.
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8A.11.b

Partially covered
Solve quadratic equations by inspection (such as x^2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real. [Algebra I with Probability, 9]

8A.12

Select an appropriate method to solve a system of two linear equations in two variables.

8A.12.a

Not covered
Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.
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8A.12.b

Partially covered
Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods. [Algebra I with Probability, 10]

Expressions, equations, and inequalities can be used to analyze and make predictions, both within mathematics and as mathematics is applied in different contexts – in particular, contexts that arise in relation to linear, quadratic, and exponential situations.

8A.13

Partially covered
Create 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.14

Partially covered
Create 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.15

Partially covered
Represent 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]

Functions shift the emphasis from a point-by-point relationship between two variables (input/output) to considering an entire set of ordered pairs (where each first element is paired with exactly one second element) as an entity with its own features and characteristics.

8A.16

Define 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.16.a

Not covered
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [Grade 8, 14, edited for added content]
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8A.16.b

Not covered
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Limit to linear, quadratic, exponential, and absolute value functions. [Algebra I with Probability, 15]
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8A.17

Mostly covered
Given 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.18

Mostly covered
Compare 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.19

Combine different types of standard functions to write, evaluate, and interpret functions in context. Limit to linear, quadratic, exponential, and absolute value functions.

8A.19.a

Not covered
Use arithmetic operations to combine different types of standard functions to write and evaluate functions.
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8A.19.b

Not covered
Use function composition to combine different types of standard functions to write and evaluate functions. [Algebra I with Probability, 17]
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Graphs can be used to obtain exact or approximate solutions of equations, inequalities, and systems of equations and inequalities – including systems of linear equations in two variables and systems of linear and quadratic equations (given or obtained by using technology).

8A.20

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).

8A.20.a

Not covered
Find the approximate solutions of an equation graphically, using tables of values, or finding successive approximations, using technology where appropriate. [Algebra I with Probability, 19] Note: Include cases where f(x) is linear, quadratic, exponential, or absolute value functions and g(x) is constant or linear.
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8A.21

Not covered
Graph 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]
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8A.22

Mostly covered
Solve systems consisting of linear and/or quadratic equations in two variables graphically, using technology where appropriate. [Algebra I with Probability, 18]

Functions can be described by using a variety of representations: mapping diagrams, function notation (e.g., f(x) = x^2), recursive definitions, tables, and graphs.

8A.23

Compare 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.23.a

Fully covered
Distinguish between linear and non-linear functions. [Grade 8, 15a]

8A.24

Define sequences as functions, including recursive definitions, whose domain is a subset of the integers.

8A.24.a

Not covered
Write explicit and recursive formulas for arithmetic and geometric sequences and connect them to linear and exponential functions. [Algebra I with Probability, 22]
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Functions that are members of the same family have distinguishing attributes (structure) common to all functions within that family.

8A.25

Not covered
Identify 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]
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8A.26

Distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions.

8A.26.a

Fully covered
Show that linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals.

8A.26.b

Not covered
Define linear functions to represent situations in which one quantity changes at a constant rate per unit interval relative to another.
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8A.26.c

Not covered
Define exponential functions to represent situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. [Algebra I with Probability, 24]
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8A.27

Partially covered
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). [Algebra I with Probability, 25]

8A.28

Fully covered
Use graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. [Algebra I with Probability, 26]

8A.29

Partially covered
Interpret 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]

Functions can be represented graphically and key features of the graphs, including zeros, intercepts, and, when relevant, rate of change and maximum/minimum values, can be associated with and interpreted in terms of the equivalent symbolic representation.

8A.30

Partially covered
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. 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.31

Mostly covered
Calculate 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.32

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

8A.32.a

Partially covered
Graph linear and quadratic functions and show intercepts, maxima, and minima.

8A.32.b

Not covered
Graph piecewise-defined functions, including step functions and absolute value functions.
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8A.32.c

Partially covered
Graph exponential functions, showing intercepts and end behavior. [Algebra I with Probability, 30]

Functions model a wide variety of real situations and can help students understand the processes of making and changing assumptions, assigning variables, and finding solutions to contextual problems.

8A.33

Not covered
Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 31]
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