Algebra I foundations

Add and Subtract Polynomials

I can add and subtract polynomials by combining like terms and keeping signs accurate.

Analyze Model Assumptions and Limitations

I can analyze a model's assumptions and limitations and decide whether a prediction is reasonable in context.

Choose Among Linear, Exponential, and Quadratic Models

I can choose whether a situation is best modeled by a linear, exponential, or quadratic rule and justify the choice with evidence.

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Compare Distributions

I can compare two distributions by describing differences in center, spread, and consistency with numerical evidence.

Compare Linear and Exponential Change

I can compare linear and exponential change in tables, graphs, and contexts.

Complete an Algebra I Modeling Investigation

I can use data to choose a model, test the fit, and write a justified conclusion with units and a realistic limitation.

Connect Factors and Zeros

I can connect a factored polynomial to its zeros by setting each factor equal to zero.

Distinguish Correlation from Causation

I can tell when two variables are correlated and when there is enough context evidence to claim one variable likely causes the other.

Factor Out Greatest Common Factors

I can factor a polynomial by pulling out the greatest common factor from every term.

Factor Simple Trinomials

I can factor a trinomial of the form x^2 + bx + c by finding integers whose product is c and whose sum is b.

Fit Linear Models

I can fit a linear model to data and interpret the meaning of the slope and intercept in context.

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Graph Linear Functions

I can graph linear functions from equations and connect the graph to slope and intercept.

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Graph Quadratic Functions

I can graph quadratic functions by identifying a vertex, axis of symmetry, and matching points.

Identify Arithmetic Sequences

I can identify arithmetic sequences by checking for a constant difference between consecutive terms.

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Identify Geometric Sequences

I can identify geometric sequences by checking for a constant ratio between consecutive terms.

Interpret Correlation and Residuals

I can interpret the direction and strength of correlation and explain what a residual says about one data point and a linear model.

Interpret Quadratic Functions

I can interpret quadratic functions, zeros, and the vertex.

Interpret Quadratic Models

I can interpret what a quadratic model says about a real situation by reading values, intercepts, and the highest or lowest point in context.

Interpret Rate of Change

I can interpret rate of change from graphs, tables, equations, and short contexts.

Model and Interpret Systems

I can model a real situation with a system of linear equations and interpret the solution in context.

Model Constraints with Equations and Inequalities

I can model exact totals and real-world constraints with equations or inequalities and explain why the symbol, variable, and units match the context.

Model Data with Linear Functions

I can model data with linear functions and decide whether a linear rule fits the pattern.

Model Growth and Decay

I can model exponential growth and decay in real-world contexts.

Multiply Polynomials

I can multiply polynomials by distributing each factor completely.

Recognize and Compare Exponential Functions

I can recognize exponential patterns and compare them with linear growth.

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Recognize Exponential Relationships

I can recognize exponential relationships in tables, graphs, and short contexts.

Recognize Quadratic Patterns

I can recognize when a table, graph, or sequence shows quadratic growth instead of linear growth.

Represent Linear Functions in Context

I can represent linear functions and interpret slope and intercept in context.

Review Exponent Properties

I can simplify expressions with like bases by using exponent rules and repeated-factor reasoning.

Simplify Algebraic Expressions

I can simplify algebraic expressions by combining like terms, distributing correctly, and checking equivalence.

Solve Absolute-Value Equations and Inequalities

I can solve absolute-value equations and inequalities by thinking about distance from a center and deciding whether solutions stay within or outside a boundary.

Solve Compound Inequalities

I can solve compound inequalities, graph the solution correctly, and explain whether the word and means overlap or the word or means either branch.

Solve Multi-Step Linear Equations

I can solve multi-step linear equations by simplifying each side, isolating the variable, and checking the solution in the original equation.

Solve Quadratics by Factoring

I can solve quadratic equations by factoring, setting each factor equal to zero, and checking both solutions in the original equation.

Solve Quadratics Using Square Roots

I can solve quadratic equations by isolating a squared expression, using positive and negative square roots when needed, and checking every solution in the original equation.

Solve Systems by Elimination

I can solve a system of two linear equations by elimination and explain why combining equations can remove one variable.

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Solve Systems by Graphing

I can solve a system of two linear equations by graphing and explain what the intersection means in context.

Solve Systems by Substitution

I can solve a system of two linear equations by substitution and explain why replacing an equal quantity keeps the system balanced.

Solve Systems of Inequalities

I can solve a system of two linear inequalities by graphing and interpret the overlapping region as the set of solutions.

Solve Systems of Linear Equations in Context

I can solve and interpret systems of linear equations in contextual problems.

Solving linear equations in one variable

I can solve a linear equation in one variable and justify each step.

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Summarize One Variable Data

I can summarize one-variable data by describing center, spread, shape, and any unusual values.

Transform Linear Functions

I can describe and graph transformations of linear functions by changing slope and intercept.

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Transform Parabolas

I can describe and graph how parabolas shift, reflect, and stretch from the parent function y = x^2.

Write Equations of Lines

I can write equations of lines from graphs, tables, points, and short situations.

Write Explicit and Recursive Arithmetic Rules

I can write both explicit and recursive rules for arithmetic sequences using the first term and common difference.

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Write Explicit and Recursive Geometric Rules

I can write both explicit and recursive rules for geometric sequences using the first term and common ratio.

Write Exponential Functions

I can write exponential functions from tables, graphs, and short contexts.