Plank- Common Core Algebra 1 Curriculum Map Month Unit(s) Learning Targets Vocab Book/ Assessment Links rational irrational integer prime composite inequality perfect squares square root absolute value UNIT 1 Pearson Algebra 1 Chapter 1 PARCC PT 7, 21, 23 PAARC PA 12, 16 ACT 39, 41 (*Standards) August Unit 1: Mathematician Makeover (N.Q.1, N.Q.2, N.Q.3, N.RN.3) A copy of the standards (by unit) have been attached at the end of this document for reading purposes. Unit 2: Expressions, Equations, & Inequalities (A.CED.1, A.CED.4, A.REI.1, A.REI.3, A.SSE.1, A.SSE.2) I can classify numbers. (rational, irrational, integers) I can interpret mathematical symbols appropriately. (inequality symbols, squares, square roots, exponents, absolute value, fractions) I can compare size and magnitude of numbers using a number line. I can use order of operations to simplify numeric expressions. I can use scientific notation to represent extremely large and small quantities. I can solve real-world questions involving scientific notation. I can use the properties of exponents to simplify numerical expressions. I can calculate unit conversions. I can choose a level of precision / accuracy that is appropriate when reporting quantities. I can determine the limitations of different measurement tools. I can classify an expression as numeric or algebraic. I can identify terms, factors, and coefficients. I can simplify algebraic expressions. (adding, subtracting, multiplication w/ distributive property, division) I can translate algebraic expressions. I can evaluate expressions. (Connection to Real World Formulas) scientific notation unit conversion precision expression variable term factor coefficient like terms distributive property translate evaluate UNIT 2 Pearson Algebra 1 Chapters 2 & 3 PARCC PT PAARC PA 8 ACT 5, 7, 21, 24, 30, 35, 61, 65, 71, 85, 97, 90 September October Unit 3: Introduction to Functions (F.IF.1, F.IF.2, F.IF.4, F.IF.5, F.IF.7, F.IF.9, A.REI.10, F.IF.3, F.BF.2, F.BF.3, F.LE.5) November I can solve equations. (1-step, 2-step, variables on both sides, proportions, absolute value, literal, & other multi-step equations) I can explain the process of solving an equation and justify the solution. I can solve inequalities. I can graph the solution to an inequality on a number line. I can create one-variable equations and inequalities that can be solved to model a real-world situation. I can solve inequalities. I can graph the solution to an inequality on a number line. I can create one-variable equations and inequalities that can be solved to model a real-world situation. I can identify functions. (algebraic equations, graphs, tables, maps) I can use function notation to evaluate functions for different inputs. I can graph a function by creating a table of points. I can identify characteristics of functions. (domain & range) I can relate the domain of a function to its graph. (real-world situations.) I can use technology to graph functions and identify key features. (domain, range) I can compare characteristics of functions written in different ways. (equations, graphs, tables, maps) I can identify function families. (linear, quadratic, exponential, absolute value) I understand how changing the parameters of a function will cause shifts up, down, left, right, and in steepness/spread. I recognize that sequences are functions. (arithmetic, geometric, Fibonacci) I can write arithmetic and geometric sequences using solve proportion identity proportion justify compound inequality function vertical-line test function notation f(x) domain range intercepts (x and y) linear nonlinear quadratic exponential absolute value parameter function family parent function sequence arithmetic sequence geometric sequence Fibonacci sequence UNIT 3 Pearson Algebra 1 Chapter 4 PARCC PT 4, 10, 15, 29 PAARC PA 5 ACT 8, 15, 17, 18, 40, 44, 67, 68 formulas. Unit 4: Linear Functions (F.IF.6, A.CED.2, A.REI.3, F.BF.1, F.BF.4, S.ID.6,7,8, & 9 December COMPREHENSIVE FINAL EXAM January Unit 5: Systems of Equations and Inequalities (A.CED.2, A.CED.3, A.REI.5,6, & 7, A.REI.11 &12 I can identify relationships in data by using best fit lines from scatterplots. I can identify types of correlation. (positive, negative, no correlation) I can distinguish between correlation and causation. I can compute and interpret the correlation coefficient of a linear fit using technology. I can determine the slope and y-intercept of a set of linear data. (by hand and with technology) I can create equations to model relationships between two variables. (focus on slope-intercept form, y=mx + b) I can solve linear equations to make accurate predictions. I can calculate the rate of change (slope) over specified time intervals. I can determine slope and y-intercept from given the context of real-world situations. I can find the inverse of a linear function. correlation causation correlation coefficient slope y-intercept parallel slope-intercept form interval arithmetic sequence UNIT 4 Pearson Algebra 1 Chapter 5 PARCC PT 18 PAARC PA 2, 7, 10 ACT 8, 15, 17, 18, 40, 44, 67, 68, 79 inverse Review of Fall Learning Targets I can create equations with 2 or more variables to model relationships. (slope-intercept form, standard form, I can solve systems of equations by making a table. I can solve a system of equations by graphing. (focus on using technology) I can solve systems of equations algebraically using the elimination method. I can graph linear inequalities. I can solve systems of inequalities by graphing and shading. I can interpret the solution of a system of equations or inequalities. system of equations intersection infinite solutions no solution elimination UNIT 5 Pearson Algebra 1 Chapter 6 PARCC PT 19, 25, 33 PAARC PA 3 ACT 6, 10, 16, 19, 20, 34, 59, 83, 86, 91 Unit 6: Exponential Functions (A.CED.2, F.BF.1, F.LE.1, F.LE.2, S.ID.6, F.IF.7.e, F.IF.8.b) February Unit 7: Polynomials & Quadratic Functions (A.APR.1, F.IF.8, A.CED.2, A.REI.4, F.IF.4, A.SSE.3, F.BF.1, F.IF.7, F.IF.9) I understand that a quantity increasing exponentially will always surpass a quantity increasing in a linear manner. I can classify polynomials by the number of terms and degree. I can add and subtract polynomials. I can multiply polynomials (distributive property, FOIL method) I can divide polynomials. (by a monomial) I can factor polynomials using the GCF. I can factor trinomials. March April FUNCTIONS REVIEW I can identify exponential functions. (tables, graphs, & equations) I can create an equation to model exponential data. (y= a• bx) I can solve exponential equations. (e.g. 2x + 5 = 13) I can distinguish between linear and exponential functions. I can factor polynomials completely. I can identify quadratic functions. (equations, tables, graphs) I can identify characteristics of quadratic functions (domain, range, maximum, minimum, axis of symmetry, intercepts, periods of increase/decrease) by hand an using technology. I can factor a quadratic equation to reveal its zeros. I can solve quadratic equations. (quadratic formula) Students must be able to identify equations, tables, and graphs as being linear, exponential, or quadratic functions. exponential geometric sequence log Ln monomial binomial trinomial constant linear quadratic distributive property FOIL method factor vertex minimum maximum axis of symmetry domain range discriminant UNIT 6 Pearson Algebra 1 Chapter 7 PARCC PT 20, 24, 30 PAARC PA 9 ACT 1, 3, 26, 43, 58 UNIT 7 Pearson Algebra 1 Chapters 8 & 9 PARCC PT 3, 6, 12, 13, 14, 17, 22, 27, 31, 32, 35 PAARC PA 1, 4, 6, 13 ACT 2, 9, 14, 22, 25, 28, 36, 37, 38, 42, 46, 49, 51, 53, 69, 72, 75, 77, 80, 81 Given 1 of the 3 forms (equation, table, or graph) students need to be able to create the other 2 forms. Unit 8: Statistics & Probability (S.ID.1, S.ID.2, S.ID.3, S.ID.5) I can represent data with real plots on the number line. (histogram, box plots) I can use stats to compare the shape, center, and spread for two or more different data sets. I understand how outliers affect shape, center, and spread of data sets. I can summarize data in two-way frequency tables and interpret the data in context. histogram mean median mode lower quartile upper quartile percentile minimum maximum range “two-way frequency table” histogram UNIT 8 Pearson Algebra 1 Chapter 12 PARCC PT 28 PAARC PA ACT 27, 48, 74, 76 box-and-whisker plot May I can explain the meaning of rational exponents. Unit 9: I can use the properties of exponents to rewrite radical Radical expressions. Expressions (N.RN.1, N.RN.2) *Comprehensive Review of Yearly Learning Targets Final rational exponents radical expressions UNIT 9 Pearson Algebra 1 Chapters 10 & 11 PARCC PT PAARC PA ACT 31, 47, 73 Literacy Standards Incorporated Within Algebra 1 Content: RSL4. Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics. RSL7. Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g. in an equation) into words. RSL8. Assess the extent to which the reasoning and evidence in a text support the author’s claim or a recommendation for solving a scientific or technical problem. Algebra 1 Curriculum Map: Standards by Unit Unit 1- Mathematician Makeover 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. 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. Unit 2- Expressions, Equations, & Inequalities 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.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.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. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A.SSE.1 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). Unit 3- Introduction to 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.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. (Interpret functions that arise in applications in terms of the 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; end behavior; and periodicity.* 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.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.* a- Graph linear and quadratic functions and show intercepts, maxima, and minima. e- Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 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. 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.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. 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). F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. Unit 4- Linear Functions F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 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.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. F.BF.1 Write a function that describes a relationship between two quantities. F.BF.4 Find inverse functions. S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 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. Unit 5- Systems of Equations & Inequalities 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.3 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. A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 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. 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 halfplanes. Unit 6- 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. F.BF.1 Write a function that describes a relationship between two quantities. F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. 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. F.IF.7.e Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F.IF.8.b 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. Unit 7- Polynomials & Quadratic Functions 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. F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. *8.a – 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. 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.4 Solve quadratic equations in one variable. 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; end behavior; and periodicity.* A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*.a – Factor a quadratic expression to reveal the zeros of the function it defines. F.BF.1 Write a function that describes a relationship between two quantities. 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.*.a – Graph linear and quadratic functions and show intercepts, maxima, and minima. 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. Unit 8- Statistics & Probability 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 (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. Unit 9- Radical Expressions 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.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.