Select quantities and use units as a way to: i) interpret and guide the solution of multi-step problems; ii) choose and interpret units consistently in formulas; and iii) choose and interpret the scale and the origin in graphs and data displays.

Choose a level of accuracy appropriate to limitations on measurement and context when reporting quantities.

Interpret expressions that represent a quantity in terms of its context.

Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.

Interpret expressions by viewing one or more of their parts as a single entity.
e.g., interpret P(1+r)ⁿ as the product of P and a factor not depending on P.  This standard is a fluency recommendation for Algebra I.  Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in factoring, completing the square, and other mindful algebraic calculations.

Recognize and use the structure of an expression to identify ways to rewrite it.
Algebra I expressions are limited to numerical and polynomial expressions in one variable.  Use factoring techniques such as factoring out a greatest common factor, factoring the difference of two perfect squares, factoring trinomials of the form ax²+bx+c with a lead coefficient of 1, or a combination of methods to factor completely. Factoring will not involve factoring by grouping and factoring the sum and difference of cubes.

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

Use the properties of exponents to rewrite exponential  expressions.  Exponential expressions will include those with integer exponents, as well as those whose exponents are linear expressions. Any linear term in those expressions will have an integer coefficient. Rational exponents are an expectation for Algebra II.

Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.

Create equations and inequalities in one variable to represent a real-world context.

Create equations and linear inequalities in two variables to represent a real-world context.
• This is strictly the development of the model (equation/inequality).
• Limit equations to linear, quadratic, and exponentials of the form f(x)=a(b)^x where a>0 and b>0 (b≠1).

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.

Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
e.g., Rearrange Ohm’s law V = IR to highlight resistance R.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Algebra I tasks do not involve solving compound inequalities.

Solve quadratic equations in one variable.

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. Understand that the quadratic formula is a derivative of this process.
When utilizing the method of completing the square, the quadratic's leading coefficient will be 1 and the coefficient of the linear term will be limited to even (after the possible factoring out of a GCF). Students in Algebra I should be able to complete the square in which manipulating the given quadratic equation yields an integer value for q.

Solve quadratic equations by:
i) inspection (An example for inspection would be x²=49, where a student should know that the solutions would include 7 and -7), ii) taking square roots, iii) factoring, iv) completing the square, v) the quadratic formula (When utilizing the quadratic formula, there are no coefficient limits), and vi) graphing (The discriminant is a sufficient way to recognize when the process yields no real solutions).  Recognize when the process yields no real solutions.  Solutions may include simplifying radicals or writing solutions in simplest radical form.

Solve systems of linear equations in two variables both algebraically and graphically. Algebraic methods include both elimination and substitution.

Solve a system, with rational solutions, consisting of a linear equation and a quadratic equation (parabolas only) in two variables algebraically and graphically.

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

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.
Graphing linear equations is a fluency recommendation for Algebra I.  Students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope.  Such fluency can support them in solving less routine mathematical problems involving linearity; as well as modeling linear phenomena (including modeling using systems of linear inequalities in two variables).

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 f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y=f(x).
Domain and range can be expressed using inequalities, set builder, verbal description, and interval notations for functions of subsets of real numbers to the real numbers.

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Recognize that a sequence is a function whose domain is a subset of the integers.
 • Sequences (arithmetic and geometric) will be written explicitly and only in subscript notation.
 • Work with geometric sequences may involve an exponential equation/formula of the form a_n=ar^n-1, where a is the first term and r is the common ratio.

For a function that models a relationship between two quantities:
i) interpret key features of graphs and tables in terms of the quantities; and
ii) sketch graphs showing key features given a verbal description of the relationship.
Algebra I key features include the following: intercepts; zeros. intervals where the function is increasing, decreasing, positive, or negative; maxima, minima; and symmetries.  Tasks have a real-world context and are limited to the following functions: linear, quadratic, square root, piece-wise defined (including step and absolute value), and exponential functions of the form f(x)=a(b)^x where a>0 and b>0 (b≠1).

Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.

Calculate and interpret the average rate of change of a function over a specified interval. 
• Functions may be presented by function notation, a table of values, or graphically.
• Algebra I tasks have a real-world context and are limited to the following functions: linear, quadratic, square root, piece-wise defined (including step and absolute value), and exponential functions of the form f(x)=a(b)^x where a>0 and b>0 (b≠1).

Write a function in different but equivalent forms to reveal and explain different properties of the function.

For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.
Algebraic processes include but not limited to factoring, completing the square, use of the quadratic formula, and the use of the axis of symmetry.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Algebra I tasks are limited to the following functions: linear, quadratic, square root, piecewise defined (including step and absolute value), and exponential functions of the for f(x)=a(b)^x where a>0 and b>0 (b≠1).

Write a function that describes a relationship between two quantities.

Determine a function from context.  Define a sequence explicitly or steps for calculation from a context.
• Algebra I tasks are limited to linear, quadratic and exponential functions of the form f(x)=a(b)^x where a>0 and b>0 (b≠1).
• Work with geometric sequences may involve an exponential equation/formula of the form a_n=ar^n-1, where a is the first term and r is the common ratio.
• Sequences will be written explicitly and only in subscript notation.

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

Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.
e.g., A flower grows two inches per day.

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.
e.g., A flower doubles in size after each day.

Construct a linear or exponential function symbolically given:
i)   a graph;
ii)  a description of the relationship;
iii) two input-output pairs (include reading these from a table).
Tasks are limited to constructing linear and exponential functions in simple context (not multi-step).

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Interpret the parameters in a linear or exponential function in terms of a context.
Tasks have a real-world context.  Exponential functions are limited to those with domains in the integers and are of the form f(x)=a(b)^x where a>0 and b>0 (b≠1).

Represent data with plots on the real number line (dot plots, histograms, and box plots).

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, sample standard deviation) of two or more different data sets.
Values in the given data sets will represent samples of larger populations. The calculation of standard deviation will be based on the sample standard deviation formula s=√(Σ(x-x)² /(n-1)).  The sample standard deviation calculation will be used to make a statement about the population standard deviation from which the sample was drawn.

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

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.

Represent bivariate data on a scatter plot, and describe how the variables’ values are related.
It’s important to keep in mind that the data must be linked to the same “subjects,” not just two unrelated quantitative variables; being careful not to assume a relationship between the actual variables (correlation/causation issue).

Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.
Algebra I emphasis is on linear models and includes the regression capabilities of the calculator.

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.