**Algebra I Pacing Chart**

**Common Core Standards**

**2010-2011**

**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**

**Equations/Inequalities**•

**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.

**Statistics**• 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.

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**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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