SBG Common Core Algebra 1 Pacing Chart

Algebra I Pacing Chart
Common Core Standards

Priority Standards in Bold- Priorities are things we will keep coming back to over and over throughout the year and are assessed on ACT.

Quarter 1

A.REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
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.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.REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method
• N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
• N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Interpret expressions that represent a quantity in terms of its context.
Interpret parts of an expression, such as terms, factors, and coefficients.
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

• 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.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
• S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean, and spread of two or more different data sets.

Quarter 2

Functions and Graphs
• 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.4 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries
• F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms
• 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)
• S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
o a. 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 and exponential models.
o b. Informally assess the fit of a function by plotting and analyzing residuals.
o c. 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.
• F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
• F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
o a. Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.
o b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
o c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
o a. Graph linear, exponential, and quadratic functions and show rate of change, intercepts, maxima, and minima.
• 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.

Quarter 3

Systems of Equations
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.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
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.REI.12 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.

Rational Exponents
N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
• N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
• N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Quarter 4

Polynomials and Factoring
A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
o a. Factor a quadratic expression to reveal the zeros of the function it defines.
• 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)

Quadratic Functions
• F.IF.8 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.
• 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.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
• A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
• A.REI.4 Solve quadratic equations in one variable.
o b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

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