Survey

Document related concepts

Quartic function wikipedia, lookup

Elementary algebra wikipedia, lookup

System of polynomial equations wikipedia, lookup

Quadratic form wikipedia, lookup

Linear algebra wikipedia, lookup

Quadratic equation wikipedia, lookup

History of algebra wikipedia, lookup

Transcript

ALGEBRA 1 Scope and Sequence 2012-13 Unit 1: Expressions and Solving Equations Day Standard 1 A.SSE.1a A.SSE.1b A.SSE.2 ● ● ● ● ● ● Parts of an expression Combining like terms Associative Property Commutative Property Distributive Property Review: Order of Operations Algebraic Expressions Terms Coefficients Factor Variables Simplify Evaluate Associative Property Communicative Property Distributive Property 2 A.REI.1 A.REI.3 ● ● ● ● ● Solving one-step equations Solving two-step equations Solving multistep equations Solving verbal equations Verifying Solutions Algebraic Equation Inverse Operations 3 A.REI.3 ● ● Graphing one variable inequalities Solving one variable inequalities Inequality Greater Than Less Than Greater than or equal to Less Than or not equal to Equal to Not Equal to 4 A.CED.4 ● Literal Equations Formula 5 Topic Materials Vocabulary REVIEW/TEST Unit 1 Learning Targets: Expressions and Solving Equations Key Idea Equation and Inequality Vocabulary Solving Equations Standard Targets: I can… A.SSE.1a ● A.SSE.1b ● I can identify the parts of an algebraic expression, including terms, variables, coefficients, and factors. I can interpret expressions in the context of a problem. A.SSE.2 ● ● ● I can combine like terms. I can apply the distributive property. I can factor out a monomial. A.REI.1 ● A.REI.3 ● ● ● I can apply order of operations and inverse operations to solve equation. I can solve a linear equation in one variable. I can construct an argument to justify my solution process when solving equations. I can solve a linear inequality in one variable. ● I can solve literal equations for a given variable. A.CED.4 NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 2: Linear Basics Day Standard Topic Materials Vocabulary 1 A.REI.10 ● ● Slope-Intercept Form Verify a point is a solution to an equation y=mx+b Slope-Intercept Form Slope Y-intercept 2 F.IF.6 ● Calculating Slope (Table, Graph, 2-points) Applications of slope Rate Average Rate of Change Slope Formula ● 3 F.IF.7 A.CED.4 ● ● Graphing a linear equation Changing equations from standard to slope-intercept form Standard Form 4 A.CED.2 F.LE.5 ● Writing an equation in slope-intercept form from a graph or slope and a point Include writing equations for verbal models Starting Value Rate ● 5 6 A.CED.2 F.LE.5 A.REI.12 F.LE.5 ● ● Writing an equation in slope-intercept form from two points or a table Include writing equations for verbal models ● ● ● Graphing a two-variable inequalities Writing a two-variable inequality Include writing inequalities for verbal models 7 REVIEW 8 TEST Unit 2 Learning Targets: Linear Basics Key Idea Standard Pre-Req ● I can graph a linear function. F.IF.6 ● I can calculate and interpret the average rate of change (slope) of a linear function given a graph or a table. F.IF.7 ● I can graph linear functions and identify intercepts. A.REI.10 ● ● I can explain that every point (x, y) on the graph represents values that make the equation true. I can verify that a point on a graph is a solution to an equation through substitution. A.REI.12 ● I can graph a linear inequality in two variables A.CED.2 ● I can write a linear function given a written situation, equation, table or graph. F.LE.5 ● I can interpret the parameters (slope, y-intercept, etc.) given a linear function in context. A.CED.4 ● I can convert from standard to slope-intercept form. Graphing Writing Linear Equations Targets. I can… NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 3: Linear Functions Day Standard Topic Materials Vocabulary 1 F.IF.1 ● ● 2 F.IF.1 ● ● 3 F.IF.1 4 F.IF.2 ● Linear Sequences Common Difference Arithmetic Sequence Explicit Formula 5 F.IF.3 ● Recursive Sequences (like the Fibonacci sequence) Recursive Formula 6 F.IF.2 N.Q.2 N.Q.3 ● ● Independent vs. Dependent Variables Writing Linear Functions that model written scenarios Independent Dependent 7 N.Q.1 ● Graphing Linear Functions from a function or table 8 F.BF.4 ● Creating the Graph of the Inverse of a Linear Function Inverse 9 F.BF.4 ● Writing the Inverse of Linear Function Inverse 10 ● ? 11 ● ? 12 REVIEW 13 TEST Function Notation Evaluating Functions for inputs in from the domain Domain and Range Determine the domain and range from the following...written scenario, set of ordered pairs, mapping or graph Note: Include non-linear examples Function Domain Domain Range Function Table ● ● Vertical Line Test Determine if the following is a function...written scenario, set of ordered pairs, mapping graph Note: Include non-linear examples NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 3 Learning Targets: Linear Functions Key Idea Standard Targets. I can… Pre-Req. ● ● I can evaluate variable expressions for given numerical values I can identify independent and dependent variables. F.IF.1 ● ● I can identify f(x) as ‘y’, the dependent variable. I can determine domain and range from written scenarios, ordered pairs, maps or plots. I can determine if a written scenario, set of ordered pairs, mapping, or graph is a function. ● Functions F.IF.2 ● ● Linear Patterns Graphing Linear Functions I can use function notation to evaluate functions for inputs in a domain. I can connect variables in a function within a context. Example: h(t) would connect height to time. F.IF.3 ● I can recognize that some sequences are functions, which are sometimes defined recursively. N.Q.2 ● I can choose appropriate units for given problems. N.Q.3 ● I can decide whether a problem calls for a rough estimate, approximation or an exact answer. N.Q.1 ● I can choose and interpret the scale and the origin in graphs and data displays. I can use units as a way to understand problems and guide solutions. ● F.BF.1 ● I can write a linear function that describes a relationship between two quantities. F.BF.4 ● I can determine inverses of linear functions. Inverses of Linear Functions NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 4: Solving Systems of Equations Day Standard Topic Materials 1 A.REI.6 A.REI.11 ● ● ● Introduction to Systems No Solution and Infinite Solutions on a Graph Solve a System by Graphing systems of equations solution ordered pair no solution infinite solution parallel lines 2 A.REI.6 A.REI.5 ● Solve a System by Substitution substitution 3 A.REI.6 A.REI.5 ● ● Solve a System by Substitution No Solution and Infinite Solutions Algebraically no solution infinite solution 4 A.REI.6 A.REI.5 ● Solve a System by Elimination elimination 5 A.REI.6 A.REI.5 ● ● Solve a System by Elimination No Solution and Infinite Solutions Algebraically no solution infinite solution 6 A.REI.6 A.REI.5 ● ● Which one is the best method? Solving Systems--Written Scenarios 7 A.REI.12 ● ● Solving Systems of Inequalities Verify solutions with a test point 8 Review 9 Test NCSD Algebra Scope and Sequence Working Document Vocabulary systems of inequalities 6/20/2012 Unit 4 Learning Targets: Solving Systems of Equations Key Idea Standard A.REI.5 A.REI.6 Solving Systems A.REI.11 Targets. I can… ● ● ● ● ● I can solve a system of equations in two variables graphically. I can solve a system of equations in two variables using substitution. I can solve a system of equations in two variables by elimination. I can determine if a system of equations in two variables has no solutions, one solution, or infinitely many solutions. I can use a graphing calculator to approximate the solution to a system of equations in two variables. A.REI.12 ● I can solve linear system of inequalities graphically. A.CED.1 ● A.CED.3 ● I can write and solve the equation or inequality that best models a realworld problem. I can write and solve a system of equations or inequalities that best models a real-world problem END SEMESTER 1: 1 or 2 days - Review for Final, Finals Week NCSD Algebra Scope and Sequence Working Document 6/20/2012 BEGIN SEMESTER 2 Unit 5: Properties of Exponents Day Standard Topic Materials Vocabulary 1 Pre-Req. ● ● Product Property Power Property exponent (exponential form) constant 2 Pre-Req. ● ● Quotient Property Quotient Power Property quotient canceling/cancellation Pre-Req. ● ● Zero Property Negative Exponent Property zero exponent negative exponent 4 Pre-Req. ● ● Scientific Notation Multiplying and Dividing number in Scientific Notation scientific notation 5 N.RN.2 ● Rewrite between radical form and rational exponents radical radical sign rational exponents 3 Example: 6 REVIEW 7 TEST Note: 2012-13 it may not be possible to teach applying the exponent properties to rational exponents, but the expectation for the next year (2013-14) is to do so (N.RN.1). Unit 5 Learning Targets: Properties of Exponents Key Idea Standard Targets Pre-Req. ● ● ● ● ● ● ● Apply the Product Rule. Apply the Quotient Rule. Apply the Power Rule. Apply the Power of a Product Rule. Apply the Power of a Quotient Rule. Use negative exponents. Apply the zero property. N.RN.1 ● Apply rules to rational exponents. N.RN.2 ● ● Rewrite between radical and rational exponents. Evaluate radical and rational expressions with and without a calculator. Rules of Exponents with Integers Extend Rules to Rational Exponents Convert between radical and rational exponents NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 6: Exponential Functions Day Standard Topic Materials Vocabulary 1 F.IF.4 ● Graphing Exponential Functions with a Table ○ Increasing/Decreasing Graphs Function Table 2 F.IF.4 F.BF.3 ● Intercepts Asymptote Domain Translate ● Identifying Key Features of the graph for an Exponential Functions ○ Intercepts ○ Increasing/Decreasing ○ Asymptotes (restrictions on the domain) ○ Domain Translate Exponential Graphs, vertically only Initial Value Growth Rate/ Constant Multiplier Time Exponential Growth Exponential Decay 3 F.IF.8 ● ● Form of an Exponential Function f(x) = Exponential Patterns 4 F.IF.8 F.LE.5 ● Exponential Growth/Decay 5 F.LE.5 ● Identify the parts of a Growth/Decay function ○ Percent Growth/Decay ○ Initial Value 6 F.BF.1 F.LE.2 ● Write an exponential function from a table or graph 7 F.LE.1 ● Which is a better fit? Linear vs. Exponential Functions (looking at written scenarios) 8 F.LE.1 ● Comparing the graphs and tables of Linear and Exponential Functions 9 REVIEW 10 TEST Percent Change Linear Note: For the 2013-14 school year, students will need to write arithmetic and geometric sequences, and use them to build models. (F.BF.2) NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 6 Learning Targets: Exponential Functions Key Idea Standard Targets Pre-Req. ● Graph a function using a t-table. F.IF.4 ● ● Graph an exponential function with a table. Interpret key features of graphs and tables, and sketch graphs using key features. ◦ Intercepts ◦ Increasing/decreasing ◦ Asymptotes (restrictions on domain) F.IF.5 ● Relate the domain of a function to its graph. F.BF.3 ● Vertically translate exponential functions. F.IF.8 ● ● ● Write functions in equivalent forms to reveal/explain properties. Use properties of exponents to identify exponential growth/decay. Use properties of exponents to identify percent increase/decrease. F.BF.1 F.LE.2 F.LE.5 ● I can construct an exponential function from a graph or table, or description of a relationship (situation). I can interpret the parameters (initial value, growth rate/constant multiplier, etc.) given an exponential function in context. F.LE.1 ● Distinguish between situations modeled by linear and exponential functions. F.BF.2 ● Write arithmetic and geometric sequences, and use them to build models. Graphing Exponential Functions Writing Exponential Functions Distinguish Between Linear and Exponential Functions Sequences ● NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 7: Quadratic Functions Day Standard Topic 1 A.APR.1 ● ● Classifying Polynomial/Descending Order Adding/Subtracting Polynomials monomial binomial trinomial polynomial 2 A.APR.1 A.REI.4 ● ● Multiplying Monomials Factoring the GCF GCF 3 A.APR.1 A.REI.4 ● Multiplying Binomials and Special Cases (FOIL) FOIL 4 A.REI.4 ● Factoring (coefficient is 1) factoring 5 A.REI.4 ● Factoring (coefficient is greater than 1) 6 F.IF.4 ● Properties of a Quadratic Graph ○ Min/Max ○ Axis of Symmetry ○ Intercepts/Roots Graphing a Quadratic Function with a table ● Materials ○ Vocabulary minimum maximum axis of symmetry intercepts/roots/zeros vertex Vertex Formula 7 A.SSE.3 ● ● Review Graphing a Quadratic Function Solving Quadratics with Square Roots Radical Radical Sign 8 A.REI.4 ● Solving Quadratics by Factoring Zero Product Property 9 A.SSE.3 ● ● Completing the Square Vertex Form and converting to/from General Form Completing the Square Vertex Form 10 A.SSE.3 ● Solving Quadratics with the Quadratic Formula Quadratic Formula ● Application of Quadratics ○ Falling Objects ○ Projectile Motion ● Inverse of Simple Quadratic Functions 11 12 F.BF.4 Inverse Example: 13 REVIEW 14 TEST NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 7 Learning Targets: Quadratic Functions Key Idea Standard Targets. I can… A.APR.1 ● ● I can add and subtract polynomials. I can multiply polynomials. Pre-req ● I can construct a graph of a quadratic function using a table. N.RN.3 ● ● I can identify a number as rational or irrational. I can show the sum of rational numbers is rational, and product of a nonzero rational and an irrational is irrational. A.SSE.3 ● ● ● ● I can take square roots of a quadratic. ( ) I can identify the roots of a quadratic given a graph. I can use the quadratic formula to reveal the zeros. I can complete the square in a quadratic expression to reveal the vertex. I can factor a quadratic expression to reveal the zeros. I can graph a linear, exponential, and quadratic function using technology. I can find the roots of a quadratic using technology. Operations on Polynomials Solving Quadratic Equations A.REI.4 F.IF.8 ● ● ● F.IF.4 ● ● Graph a quadratic function with a table. Interpret key features of graphs and tables, and sketch graphs using key features. ◦ Intercepts ◦ Symmetry ◦ Vertex, Maximum, Minimum F.IF.5 ● Relate the domain of a function to its graph. F.IF.6 ● Calculate and interpret average rate of change. F.BF.3 ● Vertically and horizontally translate quadratic functions. F.IF.8 ● Write functions in equivalent forms to reveal/explain properties (convert between general and vertex form). F.BF.1 ● ● Write a function that describes a relationship between two quantities. I can interpret the parameters (Vertex, Maximum, Minimum) of a quadratic function in context. ● I can determine the inverse of a simple quadratic function. Graphing Quadratic Functions Writing Quadratic Functions F.LE.5 Inverses of Functions F.BF.4 NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 8: Statistics Day Standard Topic 1 ● Review Data Displays: Dot Plots, Histograms, Box Plots, Stem and Leaf Dot Plot Histogram Bin Width Box Plot First/Third Quartile range Stem and Leaf Plot S.ID.1 S.ID.2 ● ● ● Collecting and Organizing Data Review Calculating Measures of Central Tendency Compare measures of central tendency and interquartile range between two or more plots Mean Median Mode Outlier Interquartile Range S.ID.2 ● Compare the standard deviation between two or more plots Describe the shape and distribution of the data Standard Deviation Line of Best Fit Correlations Pre-Req. S.ID.1 2 Materials Vocabulary 3 ● 4 S.ID.6 S.ID.7 ● ● Fitting a linear function to a scatter plot. Interpret the slope and intercept of a linear model in context 5 S.ID.6 ● Fitting functions to non-linear data using technology. 6 REVIEW 7 TEST Note: 2013-14 technology needs to be used to introduce fitting data to linear, exponential, and quadratic models. NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 8 Learning Targets: Statistics Key Idea Standard Targets Pre-Req. ● ● ● ● Display data as dot plots, histograms, and box plots Determine mean, median and interquartile range. Use data from a random sample to draw inferences about a population and inferences about two populations compared. Construct and interpret plots for bivariate measurement data, describe patterns such as clustering, outliers, linear/non-linear and positive/negative correlation. Recognize linear trends in data, putting slope and intercept in context. S.ID.1 ● ● ● Represent data with plots on the real number line. Dot Plots, histograms, box plots Stem and Leaf, Box and Whisker plots S.ID.2 ● Use statistics appropriate to the shape of the data distribution to compare center and spread. Calculate and compare mean and median. Calculate and compare interquartile range, and standard deviation. ● Represent and interpret data using a single variable. Represent and interpret using two quantitative variables. ● ● S.ID.3 ● Interpret differences in shape, center, and spread in the context of the data sets, accounting for outliers. S.ID.5 ● ● ● Summarize data for two categories in two-way frequency tables. Include joint, marginal, and conditional relative frequencies. Recognize possible associations and trends in the data. S.ID.6 ● Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to data quadratic, linear and exponential models. Informally assess the fit of the function by plotting and analyzing residuals. Fit a linear function to a scatter plot that suggests a linear association. ● ● ● Analyzing Linear Data Fitting S.ID.7 ● Interpret the slope and intercept of a linear model in context. S.ID.8 ● Compute (using technology) and interpret the correlation coefficient of a linear fit. S.ID.9 ● Distinguish between correlation and causation. NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 9: Comparing Functions Day Standard Topic Materials Vocabulary 1 F.LE.1 F.LE.3 ● Compare key characteristics of linear, exponential, and quadratic functions ○ Functions ○ Graphs 2 F.LE.1 F.LE.3 ● Compare key characteristics of linear, exponential, and quadratic functions ○ Tables 3 F.LE.1 ● Translating the Graphs of linear, exponential and quadratic functions 4 A.REI.7 F.LE.3 ● Solve systems of linear, quadratic, and exponential equations graphically NCSD Algebra Scope and Sequence Working Document 6/20/2012 Unit 9 Learning Targets: Comparing Functions Key Idea Standard Targets. I can… ● F.LE.1 Comparing Linear, Exponential, and Quadratic Functions ● ● ● ● ● F.LE.3 ● ● ● A.REI.7 Analyzing Graphs Graphing Key Features of Functions Writing Functions I can define a linear function as y = mx + b, an exponential function as y = abx, and a quadratic function as y = ax2+bx+c. I can identify a graph as being linear, exponential, or quadratic. I can define a linear function as having a constant rate of change. I can define an exponential function as having a common ratio over equal intervals. I can use graphs or tables to compare the rates of changes of linear, quadratic, and exponential functions. I can use graphs or tables to compare the output values of linear, exponential, or quadratic functions. I can use technology to find the point at which the graphs of two functions intersect. I can solve a system algebraically and graphically consisting of a linear and quadratic equation. I can explain why exponential functions eventually have greater output values than linear or quadratic functions. F.IF.4 ● ● I can identify maxima/minima in quadratic and absolute value functions. I can identify the intercepts of linear, exponential, quadratic and absolute value. F.IF.5 ● F.IF.9 ● I can identify the domain for linear, exponential, quadratic, absolute value, step and piecewise functions from a graph. I can compare properties of functions represented in different ways (one as a graph, the other as a table or description). F.IF.6 ● I can calculate the average rate of change over a specified interval.* F.BF.3 ● I can explain why f(x) + k translates the original graph of f(x) up k units and why f(x) – k translates the original graph of f(x) down k units. I can explain why f(x+k) translates the original graph of f(x) left k units and why f(x-k) translates the original graph of f(x) right k units. ● F.IF.7 F.BF.1 ● I can graph linear, exponential, quadratic, absolute value, step and piecewise functions and show their intercepts, maxima/minima, “holes”, and other key features. ● I can write a linear, exponential, quadratic, absolute value, step and piecewise function from a table, or a graph. I can write a linear, exponential, quadratic, absolute value, step and piecewise function for a written scenario. ● NCSD Algebra Scope and Sequence Working Document 6/20/2012