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2 | Common Core Curriculum Mapping CC Algebra 12/3/2014 Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8 .Look for and express regularity in repeated reasoning. | |||||||||||||||||||||||||

3 | Vocabulary: domain, input value, range, parabola, y-intercept, absolute value, function, maximum, minimum, x-intercept, line of symmetry, graph, output value, equation, xy-table, quadratic function | |||||||||||||||||||||||||

4 | Learning Outcome: I will work with my study team to solve function puzzles, investigate growth patterns and quadratic functions and their graphs. Target Goals: 1.1.1) Multiple representations of linear functions. 1.1.2 A) Collecting and analyzing data with tables. B) Introduction to proportional, inversely proportional and exponential data. 1.1.3) Describing parabolas | |||||||||||||||||||||||||

5 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

6 | 1 week | 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.7e - Graph exponential functions and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 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. 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-IF.7a - Graph linear and quadratic functions and show intercepts, maxima, and minima. | How can I work with my team to figure it out? How does it grow? What do I know about parabola? | 1.1.1-1.1.3 | ||||||||||||||||||||||

7 | Learning Outcome: I will work with my study team to clarify nonlinear functions and their graphs, investigate functions, function notation, domain and range. Target Goals: 1.2.1) Describe a graph for y=√x. 1.2.2) Graph and describe cube root and absolute value relations. 1.2.3) Describe input/output relations and introduction of domain and range. 1.2.4) Determination of functions from graph and table. 1.2.5) Describe the domain and range by examining a graph or equation. | |||||||||||||||||||||||||

8 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

9 | 2 weeks | 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. F-IF.7b - Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value 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.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. 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). | How can I describe a graph? What is the difference? What is the function? Can I predict the output? What can go in?/What can come out? | 1.2.1-1.2.5 | ||||||||||||||||||||||

10 | Mathematical Practices for Unit:1,2,4,5,6 | |||||||||||||||||||||||||

11 | Summary (Timeframe): 3 weeks | |||||||||||||||||||||||||

12 | ||||||||||||||||||||||||||

13 | Vocabulary: graph, linear equation, function, y=mx + b, variable, y-intercept, zero slope, piecewise function, parameter, unit rate, slope, x-intercept, coefficient | |||||||||||||||||||||||||

14 | Learning Outcome: I will work with my study team to find connections between starting value and growth rates with y-intercepts and slopes. We will also study lines that point upward, downward, and lines that are horizontal and vertical. Target Goals: 2.1.1) Seeing growth in linear representations. 2.1.2) Introduction to slope. 2.1.3) Build understanding about positive, negative and zero slope. 2.1.4A) Formalize y=mx + b. 2.1.4B) Find slope when given two points. 2.1.4C) Investigate the slope of vertical lines. | |||||||||||||||||||||||||

15 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

16 | Week 3-4 | F-IF.7a - Graph linear and quadratic functions and show intercepts, maxima, and minima. F-LE.1a - Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 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.5 - Interpret the parameters in a linear or exponential function 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. A-SSE.1a - Interpret parts of an expression, such as terms, factors, and coefficients. A-SSE.1b - Interpret complicated expressions by viewing one or more of their parts as a single entity. 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-BF.1a - Determine an explicit expression, a recursive process, or steps for calculation from a context. | How does is grow? How can I measure steepness? How steep is it? What information determines a line? | 2.1.1-2.1.4 | ||||||||||||||||||||||

17 | Learning Outcome: I will work with my team to investigate situations where slope represents speed in real life situations. Target Goals:2.2.1) Slope in Motion. 2.2.2)Rate of Change. 2.2.3) Equations of Lines in Situations. | |||||||||||||||||||||||||

18 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

19 | Week 5-6 | 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-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 sowing key features given a verbal description of the relationship. F-IF.7a - Graph linear and quadratic functions and show intercepts, maxima, and minima. F-BF.7a - Determine an explicit expression, a recursive process, or steps for calculation from a context. F-LE.1b - Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. F-LE.2 - Contruct 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.5 - Interpret the parameters in a linear or exponential function in terms of a context. 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. 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. F-IF.7b - Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. F-IF.9 - Compare properties of two functions each represented in a different way (algebraically, numerically intables, or by verbal descriptions). F-BF.1a - Determine an explicit expression, a recursive process, or steps for calculation from a context.. | What is the equation of the line? What can rate of change represent? How can I use y=mx + b? | 2.2.1-2.2.3 | ||||||||||||||||||||||

20 | Learning Outcome: I will work with my team to develop an algebraic method for finding the equation of a line when given two points on the line. Target Goals:2.3.1) Finding an equation given the slope and a point. 2.3.2)Finding the equation of a line through two points | |||||||||||||||||||||||||

21 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

22 | Week 7 | N-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. 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-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. F-IF.7a - Graph linear and quadratic functions and show intercepts, maxima, and minima. F-BF.1a - Determine an explicit expression, a recursive process, or steps for calculation from a context. F-LE.1b - Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 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.5 - Interpret the parameters in a linear or exponential function in terms of a context. 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). | 2.3.1-2.3.2 | |||||||||||||||||||||||

23 | Mathematical Practices for Unit:1,3,4,5,6,8 | |||||||||||||||||||||||||

24 | ||||||||||||||||||||||||||

25 | Vocabulary: area, polynomial, equation, closed set, solve, binomial, exponent, terms, expression, integers, product, sum, standard form, distributive property, dimensions, algebra tiles, solution, evaluate, base | |||||||||||||||||||||||||

26 | Learning Outcome: I will work with my team to simplify exponential expressions by using the number 1. Target Goals: 3.1.1) Simplifying exponential expressions 3.1.2) Zero and negative exponents | |||||||||||||||||||||||||

27 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

28 | Week 8 | A-SSE.3c. - Use the properties of exponents to transform expressions for exponential functions. | How can I rewrite it? How can I rewrite it with zero or negative exponents? | 3.1.1-3.1.2 | ||||||||||||||||||||||

29 | Learning Outcome: I will work with my team to develop equations using algebra tiles. We will also use algebra tiles to develop products of binomials and other polynomials. Target Goals: 3.2.1) Equations and Algebra tiles. 3.2.2) Exploring an area model. 3.2.3) Multiplying binomials and the distributive property. 3.2.4) Using generic rectangle to multiply. | |||||||||||||||||||||||||

30 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

31 | Week 9-10 | 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-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. A-REI.3 - Solve linear equations and inequalities in one variable, including equations with coeffcients represented by letters. A-SSE.3a - Factor a quadratic expression to reveal the zeros of the function it defines. | How can I represent an equation? What can I do with rectangles? How can I write a product? How can I generalize the process? | 3.2.1-3.2.4 | ||||||||||||||||||||||

32 | Learning Outcome: I will work with my study team to solve one variable equations containing products and absolute value. We will also learn how to solve multivariable equations for one variable. Target Goals: 3.3.1) Solving equations with multiplication and absolute value. 3.3.2) Working with multi-variable equations. 3.3.3) Summary of solving equations. | |||||||||||||||||||||||||

33 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

34 | Week 11 | 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.1a - Interpret parts of an expression, such as terms, factors, and coefficients. 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-CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. | What if an equation has a product? How can I can it to y=mx + b form? What kind of equation can I solve now? | 3.3.1-3.3.3 | ||||||||||||||||||||||

35 | Mathematical Practices for Unit: 1, 4,6,7,8 | |||||||||||||||||||||||||

36 | Summary (Timeframe): | |||||||||||||||||||||||||

37 | ||||||||||||||||||||||||||

38 | Vocabulary: equation, standard form, coincide, y=mx + b, substitution method, elimination method, graph, mathematical sentence, parallel, solution, system of equations. | |||||||||||||||||||||||||

39 | Learning Outcome: I will work with my team to write and solve mathematical sentences to solve situational word problems. Target Goals: 4.1.1) Solving word problems by writing equations. 4.1.2) Solving word problems using one or two equations. | |||||||||||||||||||||||||

40 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

41 | Week 12 | N-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. A-SSE.1b - Interpret complicated expressions by viewing one or more of their parts as a single entity A-CED.1 - Create equations and inequalities in one variable and use them to solve problems. A-REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. F-LE.1b - Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. A-CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | How can I use variable to solve problems? How many equations do I need? | 4.1.1-4.1.2 | ||||||||||||||||||||||

42 | Learning Outcome: I will develop methods to solve systems of equations in different forms. You will learn what it means for a system to have no solutions or infinite solutions. You will also find ways to know which solving method is most efficient and accurate. Target Goals: 4.2.1) Solving Systems of equations using substitution. 4.2.2) Making Connections: Systems, Solutions and Graphs. 4.2.3) Solving Systems using elimination. 4.2.5) Choosing a strategy for solving the system. | |||||||||||||||||||||||||

43 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

44 | Week 13-14 | A-REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. N-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. 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.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-REI.6 - Solve systems of linear equations exactly and approximately focusing on pairs of linear equations in two variables. | How can I solve the system? How does a graph show a solution? Can I solve without substituting? How can I eliminate a variable? What is the best method? | 4.2.1-4.2.5 | ||||||||||||||||||||||

45 | Learning Outcome: My study team and I will make important connections between solving equations, multiple representations, and systems of equations. Target Goals: 4.3.1) Putting it all together. | |||||||||||||||||||||||||

46 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

47 | Week 14 | 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. A-CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | What can I do now? | 4.3.1 | ||||||||||||||||||||||

48 | Mathematical Practices for Unit: 1, 2, 4, 7 | |||||||||||||||||||||||||

49 | Summary (Timeframe): | |||||||||||||||||||||||||

50 | ||||||||||||||||||||||||||

51 | Vocabulary: arithmetic sequence, linear equation, geometric sequence, multiplier, sequence, recursive sequence, sequence generator, exponential function, y-intercept, term, term number, common ratio, initial value, domain, common difference | |||||||||||||||||||||||||

52 | Learning Outcome: My team and I will use tables, graphs, and equations to represent the growth. Target Goals: 5.1.1) Representing exponential growth. 5.1.2) Rebounding Rates. 5.1.3) The bouncing ball and exponential decay. | |||||||||||||||||||||||||

53 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

54 | Week 15 | N-Q.2 - Define appropiate quantities for the purpose of descriptive modeling. F-IF.7e - Graph exponential functions, showing intercepts and end behavior. F-LE.1c - Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. | How does the pattern grow? How high will it bounce? What is the pattern? | 5.1.1-5.1.3 | ||||||||||||||||||||||

55 | Learning Outcome: We will do an investigation where you categorize several sequences.We will create multiple representations of arithmetic sequences, including equations for sequences that depend on previous terms. Target Goals: 5.2.1) Generating and investigating sequences. 5.2.2) Generalizing arithmetic sequences. 5.2.3) Recursive sequences. | |||||||||||||||||||||||||

56 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

57 | Week 16 | 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). F-IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | How can I describe a sequence? How do arithmetic sequences work? How else can I write the equation? | 5.2.1-5.2.3 | ||||||||||||||||||||||

58 | Learning Outcome: I will compare the growth of various sequences and recognize growth by multiplication and growth by addition. Then I will create multiple representations of geometric sequences and compare sequences to functions. Target Goals: 5.3.1) Patterns of growth in tables and graphs. 5.3.2) Using multipliers to solve problems. 5.3.3) Comparing Sequences to functions. | |||||||||||||||||||||||||

59 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

60 | Week 17-18 | 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. F-LE.1a - Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 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.1c - Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 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-IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | What is the rate of change? How can I use a multiplier? Is it a function? | 5.3.1-5.3.3 | ||||||||||||||||||||||

61 | Mathematical Practices for Unit: 1, 2, 3, 7,8 | |||||||||||||||||||||||||

62 | Summary (Timeframe): | |||||||||||||||||||||||||

63 | ||||||||||||||||||||||||||

64 | Vocabulary: residual plot, slope, correlation coefficient, random scatter, line of best fit, lower bound, outlier, extrapolation, predictions, upper bound | |||||||||||||||||||||||||

65 | Learning Outcome: Our study team will be describing a dependent relationship, called the association, between two numerical variables. We will use scatterplots of data to create lines and curves that model the data and then use those models to make predictions. Target Goals: 6.1.1) Line of best fit. 6.1.2) Residuals. 6.1.3) Upper and lower bounds. 6.1.4) Least Square Regression Line. | |||||||||||||||||||||||||

66 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

67 | Week 19-20 | 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. S-ID.6a - 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.6c - 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. N-Q.3 - Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | How can I make predictions? How close is the model? What are the bounds of my prediction? How can we agree on a line of best fit? | 6.1.1-6.1.4 | ||||||||||||||||||||||

68 | Learning Outcome: Our teams will mathematically describe the form, direction, strength, and outliers of an association. Target Goals: 6.2.1) Residual plots. 6.2.2) Correlations. 6.2.3) Studies and cause and effect. 6.2.4) Interpreting correlation in context. 6.2.5) Curved Best-fit models | |||||||||||||||||||||||||

69 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

70 | Week 21-23 | 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. S-ID.6a - Fit a function to the data; use functions fitted to data to solve problems in the context of the data. S-ID.8 - Compute (using technology) and interpret the correlation coefficient of a linear fit. S-ID.6b - Informally assess the fit of a function by plotting and analyzing residuals. S-ID.9 - Distinguish between correlation and causation. | When is my model appropriate? How can I measure my linear fit? Why can’t studies determine cause and effect? What does the correlation mean? What if a line doesn’t fit the data? | 6.2.1-6.2.5 | ||||||||||||||||||||||

71 | Mathematical Practices for Unit: 1, 2, 3, 4, 5, 6, 7, 8 | |||||||||||||||||||||||||

72 | Summary (Timeframe): | |||||||||||||||||||||||||

73 | ||||||||||||||||||||||||||

74 | Vocabulary: appreciation, exponential function, multiplier, step function, exponents, asymptote, half-life, parameter, compound interest, depreciation, initial value, roots, fractional exponents | |||||||||||||||||||||||||

75 | Learning Outcome: Our teams will investigate a family of exponential functions. We will recognize exponential growth when given situations, tables, graphs, or equations, and you will make connections between these representations. You We will also extend your knowledge of exponents and their properties and learn how to use these properties, along with the algebra skills you already possess, to solve exponential equations. We will be introduced to step functions. At the end of the section, we will get to apply exponential functions to real-life situations involving growth and decay. Target Goals: 7.1.1) Investigating y = bx. 7.1.2) Multiple representations of exponential functions 7.1.3) More applications of exponential growth 7.1.4) Exponential decay 7.1.5) Graphs and equations 7.1.6) Completing the Multiple Representation Web. | |||||||||||||||||||||||||

76 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

77 | Week 24-25 | 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. F-IF.7e - Graph exponential functions, showing intercepts and end behavior. A-CED.1 - Create equations and inequalities in one variable and use them to solve problems. 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-IF.8b - Use the properties of exponents to interpret expressions for exponential functions. F-LE.1a - Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. F-LE.1c - Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 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.5 - Interpret the parameters in a linear or exponential function in terms of a context. F-IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. F-IF.7b - Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 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. F-IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). A-SSE.1b - Interpret complicated expressions by viewing one or more of their parts as a single entity. A-SSE.3c - Use the properties of exponents to transform expressions for exponential functions. | What do exponential graphs look like? What is the connection? How does it grow? What if it does not grow? What are the connections between graphs and equations? What is the connection? (Graphs, tables, equations, situations) | 7.1.1-7.1.6 | ||||||||||||||||||||||

78 | Learning Outcome: Our study teams will find exponential equations that fit given data. In doing so, you will learn about fractional exponents. Target Goals: 7.2.1) Curve fitting and fractional exponents. 7.2.2) More Curve fitting. 7.2.3) Solving systems of exponential functions graphically. | |||||||||||||||||||||||||

79 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

80 | Week 26 | 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. N-RN.2 - Rewrite expressions involving radicals and rational exponents using the properties of exponents. F-IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. F-IF.7e - Graph exponential functions, showing intercepts and end behavior. F-BF.1a - 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). 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). N-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. F-LE.1c - Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. | How can I find the equation? How can I use exponential functions? | 7.2.1-7.2.3 | ||||||||||||||||||||||

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82 | Vocabulary: binomial, graph, product, roots, zero, sum, vertex, y-intercept, factored form, factor, quadratic equation, solution, graphing form, symmetry, x-intercept, zero product property, completing the square, generic rectangle, parabola, standard form, difference of squares, perfect square trinomials | |||||||||||||||||||||||||

83 | Learning Outcome: Our study teams will develop a method to change a quadratic equation written as a sum into its product form (also called its factored form). Then you will learn shortcuts for factoring some quadratics. Target Goals: 8.1.1) Introduction to factoring quadratic expressions. 8.1.2) Factoring with generic rectangles. 8.1.3) Factoring with special cases. 8.1.4) Factoring completely. 8.1.5) Factoring shortcuts. | |||||||||||||||||||||||||

84 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

85 | Week 27-28 | A-SSE.3a - 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. | How can I find the product? Is there a shortcut? How can I factor this? Can it still be factored? Are there more shortcuts? | 8.1.1-8.1.5 | ||||||||||||||||||||||

86 | Learning Outcome: We will find ways to generate each representation of a quadratic function (rule, graph, table, and situation) from each of the others. We will also develop a method to find the x-intercepts of a parabola using the Zero Product Property. Then we will see another way to write the equation of a parabola, called graphing form, and use square roots to find the x-intercepts. Finally we will “complete the square” to change between standard form and graphing form of a quadratic function. Target Goals: 8.2.1) Multiple representations for quadratic functions. 8.2.2) Zero product property 8.2.3) More ways to find x-intercept. 8.2.4) Completing the quadratic web. 8.2.5) Completing the square | |||||||||||||||||||||||||

87 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

88 | Week 29-30 | 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. A-SSE.3a - Factor a quadratic expression to reveal the zeros of the function it defines. 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-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. F-IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. F-IF.7a - Graph linear and quadratic functions and show intercepts, maxima, and minima. F-IF.8a - 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.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). F-BF.1a - Determine an explicit expression, a recursive process, or steps for calculation from a context. A-REI.4b - 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. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. A-SSE.1b - Interpret complicated expressions by viewing one or more of their parts as a single entity. A-SSE.3b - Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. A-REI.4a - 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. | What is the connection? How are quadratic rules and graphs connected? How else can I find the roots? What is the connection? How can I write it in graphing form? | 8.2.1-8.2.5 | ||||||||||||||||||||||

89 | Mathematical Practices for Unit: 1, 2, 3, 4, 6, 7, 8 | |||||||||||||||||||||||||

90 | Summary (Timeframe): | |||||||||||||||||||||||||

91 | ||||||||||||||||||||||||||

92 | Vocabulary: Zero Product Property, Boundary Point, Coordinates, Quadratic Equation, Graph, Inequality, Completing the Square, Region, Quadratic Formula, System of Inequalities, Standard Form, Factor, Number Line, Solution, Boundary Line or Curve | |||||||||||||||||||||||||

93 | Learning Outcome: 9.1 – I will solve quadratic equations using the Quadratic Formula. Target Goals: 9.1.1 A – Expand skills using the Zero Product Property to solve quadratic equations B – Develop the method of completing the square to solve equations 9.1.2 A – Use the Quadratic Formula to solve quadratic equations 9.1.3 A – Continue to solve quadratic equations, including those that are not in standard form, have only one solution, or no real solution 9.1.4 A – Practice solving using multiple approaches by deciding which method to try first for different types of quadratic equations B – Use graphs and tables to help estimate a solution or verify an algebraic one | |||||||||||||||||||||||||

94 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

95 | Week 31 (4 days) | A-CED.1 - Create equations and inequalities in one variable, including ones with absolute value, and use them to solve problems. 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-IF.8a - 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-REI.4a - 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.4b - 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. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. A-SSE.3b - Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. | What else can I solve? What if it’s not factorable? What if the equation is not in standard form? Which method should I use? | 9.1.1-9.1.4 | ||||||||||||||||||||||

96 | Learning Outcome: 9.2 – I will solve linear inequalities and apply this understanding to solving applications. Target Goals: 9.2.1A – Solve linear inequalities with one variable 9.2.1B – Represent solutions to linear inequalities on a number line 9.2.2A – Find a boundary point for linear, one-variable inequalities 9.2.2B – Test a value in a linear, one-variable inequality 9.2.2C – Apply inequalities | |||||||||||||||||||||||||

97 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment | |||||||||||||||||||||

98 | Week 32 (2 days) | A-CED.1 - Create equations and inequalities in one variable and use them to solve problems. A-REI.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. N-Q.2 - Define appropriate quantities for the purpose of descriptive modeling. | What if the quantities are not equal? How can I use inequalities? | 9.2.1-9.2.2 | ||||||||||||||||||||||

99 | Learning Outcome: 9.3 – I will represent solutions to one-variable inequalities on a number line, and study how to represent the solutions of two-variable inequalities on anxy-graph. Target Goals: 9.3.1 A – Graph linear inequalities with two variables 9.3.2 A – Graph linear and nonlinear inequalities with two variables B – Use the graph of a two-variable, linear inequality to solve a word problem | |||||||||||||||||||||||||

100 | Time Frame | Common Core Concepts & Skills | Teaching Points/Essential Questions | Practice Lessons | Assessment |

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