COMMON CORE ALGEBRA 1 CURRICULUM MAP

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1 September - How do number properties assist in computation? - When are algebraic and numeric expressions used? - Why do we need a specific order of operations? - Why do we use variables? - How do we translate verbal expressions into mathematics? - How is thinking algebraically different from thinking arithmetically? Real Numbers and Polynomials Lesson 1: Order of Operations (1 day) Lesson 2: Operations on Fractions (1 day) Lesson 3: Properties of Real Numbers / The Real Number System / Rational or Irrational (2 days) Lesson 4: Working with Variable Expressions (3 days) Lesson 5: Properties of Exponents (3 days) Lesson 6: Scientific notation (1 day) Lesson 7: Adding and Subtracting Polynomials (1 day) {M1, L6} Lesson 8: Multiplying Monomials / Polynomials (1 day) Lesson 9: Distributive Property / Area Models (1 day) {M1, L6} Lesson 10: Dividing a polynomial by a monomial (1 day) N.RN.1, 2 Extend the properties of exponents to rational exponents. N.RN.3 Use properties of rational and irrational numbers. A.SSE.1a, 1b, 2 Interpret the structure of expressions. A.APR.1 Perform arithmetic operations on polynomials. A.APR.A.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. Marshmallow Challenge Polyahtzee October - What is meant by equality? - How do we choose the best model to represent a situation? - How do we use real-world data to write linear equations? - How do we use algebra to make decisions? - How do we use inequalities to make comparisons? - How does solving a linear equation compare to solving a linear inequality? - How does explaining my process help me better understand the solution to a problem? - How do I know if a result is reasonable? Linear Equations, Inequalities and Problems in Context Lesson 1: Solving one and two step equations (1 day) Lesson 2: Solving linear equations with fractions (1 day) Lesson 3: Solving proportions (1 day) Lesson 4: Ratio and proportion word problems (2 days) Lesson 5: Set, Interval Notation/ Number Line (1 day) {M1, L11} Lesson 6: One, Zero, or Infinitely many solutions (1 day) Lesson 7: Solving inequalities (3 days) {M1, L14/15/16} Lesson 8: Word Problems (3 days) Lesson 9: Literal Equations (2 days) {E1, L19} Lesson 10: Equations w/ domain restrictions (2 days) {E1, L18} A. SSE.1a, 1b, 2 Interpret the structure of expressions. A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A.CED.A.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. A.CED.A.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 Understand solving equations as a process of reasoning and explain the reasoning. A.REI.A.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.A.3, 4 Solve equations and inequalities in one variable A.REI.10, 11, 12 Represent and solve equations and inequalities graphically. Literal Equations Memory

2 November - Why do we differentiate between relations and function? - How do functions express relationships? - What types of relationships can be represented graphically? - What is function notation? Functions Lesson 1: Introduction to Functions (3 days) Lesson 2: Domain and Range (2 days) Lesson 3: Graphing Linear Equations (3 days) {E1, L20} Lesson 4: Piecewise Functions (2 days) Lesson 5: Graphing Stories (2 days) F.IF.1, 2, 3 Understand the concept of a function and use function notation. F.IF.4, 5, 6 Interpret functions that arise in applications in terms of a context. F.IF.7, 8, 9 Analyze functions using different representations. F.BF.1 Write a function that describes a relationship between two quantities. Piecewise Graphing Stories Mini Project November- December - What is a system? - How does a system support real world problem solving? - How do we determine the most efficient method to solve a system? Systems of Equations and Inequalities Lesson 1: Solving and graphing linear equations (4 days) Lesson 2: Word Problems / Situations (3 days) Lesson 3: Solving and graphing systems of inequalities (4 days) Lesson 4: Linear Programming (2 days) A.SSE.1a, 1b, 2 Interpret the structure of expressions. A.CED.A.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. A.REI.5, 6, 7 Solve systems of equations. A.REI.10, 11, 12 Represent and solve equations and inequalities graphically. Bacon, Egg, Cheese Exploration Clothing Manufacturing Task Bryce Canyon Task Don t Sink the Boat January (10 days) - How can pattern recognition help solve problems? - How can we determine and analyze the relationships among numerical patterns? Sequences Lesson 1: Arithmetic Sequences (4 days) Lesson 2: Geometric Sequences (4 days) F.BF.1 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). Tower Task Mirror Task January- February (25 days) - Why do we factor polynomials? - How do we choose the best factoring method for a given polynomial? - How does the graph of a function relate to its equation? - When is it appropriate to complete the square or use the Quadratic Equations and Factoring Lesson 1: Factoring Polynomials (6 days) Lesson 2: Solving Quadratic Equations (3 days) MIDTERM Lesson 3: Key Features of Quadratics (3 days) Lesson 4: Graphing Quadratics (4 days) Lesson 5: Completing the Square (4 days) Lesson 6: Quadratic Formula (1 day) Lesson 7: Discriminant (1 day) A.ASSE.1a, 1b, 2 Interpret the structure of expressions. A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines. A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. A.APR.B Understand the relationship between zeros and factors of polynomials. A.APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function Quadratic Roots Discovery Hidden Body Task

3 quadratic formula? defined by the polynomial. A.REI.4a, 4b Solve quadratic equations in one variable. F.IF.7, 8, 9 Analyze functions using different representations. F.IF.7 Graph linear and quadratic functions and show intercepts, maxima, and minima. F.IF.8 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. March - How does solving/graphing an absolute value function compare to solving/graphing a linear function? Transformations Lesson 1: Absolute Value Function (3 days) Lesson 2: Transformations of Functions (8 days) F.IF.7, 8, 9 Analyze functions using different representations. F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). F.BF.3 Build new functions from existing functions. 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. Transformations Lab using Desmos 1 & 2 Gallery Walk

4 March- April (25 days) - Why is data collected and analyzed? - How can we predict outcomes based on data? - How do charts and graphs help us make decisions? - How does standard deviation address dispersion? Statistics Lesson 1: Measures of Central Tendency (1 day) Lesson 2: Scatterplots (1 day) Lesson 3: Histograms, Box Whisker, Dot Plots (5 days) Lesson 4: IQR and Outliers (2 days) Lesson 5: Two-way Tables (2 days) Lesson 6: Standard Deviation (2 days) Lesson 7: Line of Best Fit / Residuals (3 days) Lesson 8: Regression Analysis (5 days) HSS.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). HSS.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. HSS.ID.3 accounting for possible effects of extreme data points (outliers). HSS.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. HSS.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. HSS.ID.6AFit 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. HSS.ID.6B Informally assess the fit of a function by plotting and analyzing residuals. HSS.ID.6C Fit a linear function for a scatter plot that suggests a linear association. HSS.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. HSS.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. What is Fair?

5 May - How are verbal and algebraic models and formulas used to represent real life situations? - Why do quantities have nonlinear relationships? What s the significance if they do? - How do we compare linear growth to exponential growth? - How can exponential functions be used to model real-life situations? Exponential Functions and Geometric Sequences Lesson 1: Graphing Exponential Functions (3 days) Lesson 2: Word Problems (3 days) Lesson 3: Solving Exponential Equations (2 days) Lesson 4: Exponentials v. Geometric Sequences (2 days) Lesson 5: Exponential or Linear? (3 days) A.ASSE.1a, 1b, 2 Interpret the structure of expressions. A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. relationships between quantities; graph equations on coordinate axes with F.IF.8 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.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. 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). F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. Shrinking Dollar Zombie Attack

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