Bridge to Algebra II Standards for Mathematical Practice


 Melvin Robbins
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1 Bridge to Algebra II Standards for Mathematical Practice The Standards for Mathematical Practices are to be interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. Students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. Students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument explain what it is. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. High school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. High school they have learned to examine claims and make explicit use of definitions. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate result August 2016 Page 1 of 10
2 Bridge to Algebra II Curriculum Map QUARTER 1 ARKANSAS MATHEMATICS STANDARDS ESSENTIAL QUESTIONS OBJECTIVES I can RF.2.BTAII.4 Rewrite expressions involving radicals and rational exponents using the properties of exponents RF.2.BTAII.2 Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior. RF.2.BTAII.3 Explain how extending the properties of integer exponents to rational exponents provide an alternative notation for radicals. FM.3.BTAII.17 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers FR.1.BTAII.1 Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity. use order of operations agreement. solve problems using rational numbers. apply the properties of exponents to simplify algebraic expressions. apply the properties of exponents to simplify expressions with integer and rational exponents. write expressions with rational exponents as radical expressions. apply the properties of exponents to simplify algebraic expressions with integers and rational exponents. write terms and use the formula of an arithmetic sequence. explain recursive patterns under the domain of integers. evaluate algebraic expressions. August 2016 Page 2 of 10
3 ARKANSAS MATHEMATICS STANDARDS ESSENTIAL QUESTIONS OBJECTIVES I can FM.3.BTAII.1 Create equations and inequalities in one variable and use them to solve problems. Note: Including but not limited to equations arising from: o Linear functions o Quadratic functions o Exponential functions o Absolute value functions FR.1.BTAII.6 Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters. FM.3.BTAII.2 Create equations in two or more variables to represent relationships between quantities Graph equations, in two variables, on a coordinate plane. RT.2.BTAII.8 Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically. RF.2.BTAII.5 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any polynomial function. FM.3.BTAII.7 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.* solve linear equations and inequalities. apply linear equations to a real world context. evaluate and solve linear equations and inequalities. graph systems of equations in two or more variables. solve a system of linear equations algebraically and graphically to find a point of intersection. evaluate graphs and tables and interpret real world situations. calculate and interpret the average rate of change of a function. August 2016 Page 3 of 10
4 QUARTER 2 ARKANSAS MATHEMATICS STANDARDS ESSENTIAL QUESTIONS OBJECTIVES I can RF.2.BTAII.1 Explain why the xcoordinates 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 by using technology to graph the functions making tables of values Finding successive approximations include cases (but not limited to) where f(x) and/or g(x) are o Linear o Polynomial o Absolute value o Exponential FM.3.BTAII.12 Identify the effect on the graph of replacing ff(xx) bbbb ff(xx) + kk, kk ff(xx), ff(kkkk), and ff(xx + kk) for specific values of kk (kk, a constant both positive and negative); Find the value of kk given the graphs of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without technology. Include recognizing even and odd functions from their graphs and algebraic representations for them. FM.3.BTAII.6 Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes. FR.1.BTA.8 In terms of a context, interpret the parameters (rates of growth or decay, domain and range restrictions where applicable, etc.) in a function. explain that a point of intersection on a graph of a system of equations represents the solution to both equations. identify the effects on a graph for specific values of k. identify odd and even functions. identify how the domain of a function is represented in its graph. identify any values for which the function may approach but does not reach and interpret its meaning in terms of the context. August 2016 Page 4 of 10
5 ARKANSAS MATHEMATICS STANDARDS ESSENTIAL QUESTIONS OBJECTIVES I can FM.3.BTAII.8 Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior. FM.3.BTAII.5 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. FR.1.BTAII.7 Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination. FM.3.BTAII.3 Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or realworld context. graph functions and explain key features with and without technology. graph exponential functions and explain the key components and end behavior with and without technology. graph square root, cube root, and piece wise functions and explain the key components with and without technology. interpret key features of two or more functions. solve systems of equations in a variety of methods. solve systems of inequalities in a variety of methods. August 2016 Page 5 of 10
6 ARKANSAS MATHEMATICS STANDARDS ESSENTIAL QUESTIONS OBJECTIVES I can FM.3.BTAII.16 Solve linear inequalities and systems of linear inequalities in two variables by graphing. FM.3.BTAII.19 Construct linear and exponential equations, including arithmetic and geometric sequences, given a graph, a description of a relationship or two inputoutput pairs (include reading these from a table). understand that the solutions to a system of inequalities in two variables are the points that lie in the intersection on the corresponding half plane. construct a linear and exponential function given a graph, verbal description, and table. August 2016 Page 6 of 10
7 QUARTER 3 ARKANSAS MATHEMATICS STANDARDS ESSENTIAL QUESTIONS OBJECTIVES I can FM.3.BTAII.4 Rearrange literal equations using the properties of equality FM.3.BTAII.20 Use the properties of exponents to transform expressions for exponential functions FR.1.BTAII.3 Add, subtract, and multiply polynomials Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication FR.1.BTAII.4 Use various methods to factor quadratic polynomials; understand the relationship between the factored form of a quadratic polynomial and the zeros of a function FR.1.BTAII.5 Identify zeros of polynomials (linear, quadratic) when suitable factorizations are available Use the zeros to construct a rough graph of the function defined by the polynomial. RF.2.BTAII.6 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Note: Students should be able to identify and use various forms of a quadratic expression to solve problems. o Standard Form: aaxx 2 + bbxx + cc o Factored Form: aa(xx rr 1 )(xx rr 2 ) o Vertex Form: aa (xx h ) + kk solve formulas for a specific variable. use properties of exponents to transform expressions for exponential functions. add, subtract, and multiply polynomials. factor trinomials. understand the relationship between the factored form and standard form of quadratic polynomials. find and graph the zeros of a quadratic function with and without technology. solve higher degree polynomial equations. identify zeros of polynomials by factoring. use the zeros to construct a rough graph of the function. factor an expression and find the zeros of the function. complete the square for a quadratic function. find the minimum and maximum value of a function. August 2016 Page 7 of 10
8 ARKANSAS MATHEMATICS STANDARDS ESSENTIAL QUESTIONS OBJECTIVES I can RF.2.BTAII.7 Solve quadratic equations in one variable. 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. Solve quadratic equations (as appropriate to the initial form of the equation) by: o Inspection of a graph o Taking square roots o Completing the square o Using the quadratic formula o Factoring FR.1.BTAII.2 Use the structure of an expression to identify ways to rewrite it. FM.3.BTAII.9 Write expressions for functions in different but equivalent forms to reveal key features of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values (vertex), and symmetry of the graph, and interpret these in terms of a context. Note: Connection to A.SSE.B.3b FM.3BTAII.10 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). solve quadratic equations by completing the square. solve quadratic equations by the quadratic formula. derive the quadratic formula. recognize the types of roots from a quadratic equation including real and complex roots. choose factoring as a method to understand the structure of an expression. find the zeros of a quadratic function. find the extreme values, axis of symmetry and vertex of quadratic and exponential function in context. compare the properties of two functions when they are represented different ways, for instance comparing graphs to tables or to equations. August 2016 Page 8 of 10
9 QUARTER 4 ARKANSAS MATHEMATICS STANDARDS ESSENTIAL QUESTIONS OBJECTIVES I can FM.3.BTAII.11 Write a function that describes a relationship between two quantities. From a context, determine an explicit expression, a recursive process, or steps for calculation. FM.3.BTAIII.13 Solve an equation of the form yy = ff(xx) for a simple function f that has an inverse and write an expression for the inverse. FM.3.BTAII.15 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities FM.3.BTAII.18 Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another SP.4.BTAII.1 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 determine an explicit expression and a recursive process for a function from context. combine functions using arithmetic operations. discover and give examples of exponential growth and decay. graph and recognize inverses of relations and functions. find inverses of functions. report measured quantities in a way that is reasonable for the tool used to make the measurement. report calculated quantities using the same level of accuracy as used in a problem statement. differentiate between characteristics of linear and exponential function. discover real world applications of exponential growth and decay. find measures of central tendency and measures of measures of variation for statistical data. examine the effects of outliers on statistical data. August 2016 Page 9 of 10
10 ARKANSAS MATHEMATICS STANDARDS ESSENTIAL QUESTIONS OBJECTIVES I can SP.4.BTAII.2 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. SP.4.BTAII.3 Compute (using technology) and interpret the correlation coefficient of a linear fit. FM.3.BTAII.14 Define appropriate quantities for the purpose of descriptive modeling (I.E., Use units appropriate to the problem being solved.) compute probabilities with permutations and combinations. justify the probability that an event will not occur. justify the probability of one event or a second event occurring. compute probabilities of one event and a second event occurring. compute conditional probabilities. find measures of central tendency and measures of measures of variation for statistical data. examine the effects of outliers on statistical data. identify the variables or quantities of significance from the data provided. identify or choose the appropriate unit of measure for each variable or quantity. August 2016 Page 10 of 10
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