Algebra I

Essential Standards

The Algebra I courses at the High School provide a detailed study of the essential algebraic strands outlined in the Common Core Learning Standards. The topics include operations with polynomials, rational and irrational numbers, and functions -- including linear, absolute value, quadratic, cubic, radical, exponential, basic rational, piecewise and step. Students enhance their understanding of functions and relations and explore linear inequalities, and systems of equations with two variables both algebraically and graphically. Critical connections between principles defining algebraic models are made with the graphs that they produce. Arithmetic and geometric sequences are developed in relation to linear and exponential models. Uni-variate data is analyzed through the construction of dotplots, boxplots and histograms while associations are investigated through two-way tables and the comparison between marginal and conditional frequencies. Bivariate data is explored through a deep understanding of regression analysis. The High School Algebra I courses are leveled (Modified, Regular, and Honors) in order to differentiate student academic needs, but at their core all levels will be founded on the following essential standards:

Numbers & Quantity

  • N-Q.1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Algebra

  • A-SSE.1.a. Interpret expressions that represent a quantity in terms of its context: Interpret parts of an expression, such as terms, factors, and coefficients.
  • A-SSE.2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
  • A-SSE.3.a. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression: Factor a quadratic expression to reveal the zeros of the function it defines.
  • A-SSE.3.b. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • A-APR.1. Add, subtract, and multiply polynomials.
  • A-APR.7. Add, subtract, multiply, and divide rational expressions.
  • A-CED.1. 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.
  • A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A-CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
  • A-REI.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
  • A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • A-REI.4.a. 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. Derive the quadratic formula from this form.
  • A-REI.4.b. Solve quadratic equations in one variable: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.
  • A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
  • A-REI.7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
  • A-REI.11. 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); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, and exponential functions.

Functions

  • F-IF.1. 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).
  • F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • F-IF.8.a. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function: 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.
  • F-IF.8.b. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function: Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
  • F-BF.1.a. Write a function that describes a relationship between two quantities: Determine an explicit expression, a recursive process, or steps for calculation from a context.
  • F-LE.2. 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).

Geometry

  • G-GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Statistics & Probability

  • S-ID.1. Represent data with plots on the real number line (dot plots, histograms, and boxplots).
  • S-ID.2. 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.
  • S-ID.3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • S-ID.5. 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.
  • S-ID.6.a. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
  • S-ID.6.c. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related: Fit a linear function for a scatter plot that suggests a linear association.
  • S-ID.7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
  • S-ID.8. Compute (using technology) and interpret the correlation coefficient of a linear fit.
  • S-ID.9. Distinguish between correlation and causation.