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Enriched Algebra A September - Linear Models October - Linear Graphing November - Linear Inequalities Essential Questions How do you use scatter plots to find How do we create graphs given the equation of a line? What is the difference between equations and correlations between variables? How do How can we find the linear equation for a specific inequalities? How can real-life situations be you write the equation of a line? How do graph? How can we use graphs to model real world modeled through the use of inequalities? How you use an equation to make predictions scenarios? What is a function, and how can it be does absolute value relate to linear equations? about data? evaluated? How do you make and use a stem & leaf plot and a box & whisker plot to order data and find measures of central tendency? Content 1) Scatter Plots showing: 1) Graph an equation with one & two variables (slope – 1) Solving & graphing simple and compound no correlation intercept graphs) inequalities in one variable positive correlation 2) Write the equation of the line for a given graph 2) Problem solving using inequalities and negative correlation 3) Determine the intercepts for an equation compound inequalities 2) Data Collection 4) Sketch graphs using intercepts 3) Graphing linear inequalities in two variables 3) Use scatter plots to make predictions 5) Determine possible solutions for an equation 4) Solving absolute value equations and 4) Draw the line of best fit 6) Parallel & Perpendicular Lines inequalities 5) Calculate the slope of a line from a table, from 7) Functions & Relations 5) Number line graphs for absolute value a graph and from the formula 8) Evaluating functions inequalities 6) Write the equation of a line: 9) Identify the Domain & Range of a function 6) Graphs of absolute value equations given point & slope 10) TI – 84 Usage 7) Stem & Leaf Plots given 2 points 8) Box & Whisker Plots 7) Interpolation & Extrapolation within data 9) Measures of Central Tendency 8) TI – 84 Training/Navigator Training Skills 1) Create graphs of scatter plots (by hand at first, 1) Graph equations in one variable 1) Solve and graph inequalities in one variable then mainly on the TI-84) & make general 2) Write the equation for the vertical or horizontal graph 2) Solve and graph compound inequalities predictions about trends 3) Sketch a 2 variable equation using slope-intercept form 3) Use and write inequalities to model real life 2) Determine the correlation between the (check graphs using the TI-84) situations variables 4) Write the equation of the line given the graph 4) Create graphs for 2 variable inequalities 3) Draw the line of best fit 5) Find the intercepts of an equation 5) Solve & graph absolute value equations 4) Find the slope of the best fitting line, using 2 6) Create a graph using only the intercepts 6) Solve & graph absolute value inequalities data points 7) Determine possible solutions for an equation or modeled 7) Organize data using a stem & leaf plot 5) Write the equation of the best fitting line (by situation 8) Determine the mean, median & mode of a set of hand & using calculator) 8) Use intercepts, and intercept graphs, to model real world numbers 6) Make predictions using interpolation & scenarios 9) Arrange data using a box & whisker plot extrapolation with the equation 9) Explore relationships between parallel & perpendicular 7) Collect data, create graphic models of data, lines using graphic & algebraic means compute & graph trend line, use line to make 10) Identify relations that are functions, graphically and predictions for data using a set of ordered pairs (vertical line test) 11) Evaluate functions for a given variable 12) Identify the restrictions of a function or relation (domain & range) 13) Apply domain & range concepts to determining the appropriate window for equations & data CH 3.11 (3,4,6,7); 3.14 (5,6,10); 3.17 ( 2-5); 3.15 3.11 (3,5); 3.14 (1,2); 3.15 (4); 3.17 (2,3); 3.18 (1,2,4,7); 3.14 (8,9); 3.11 (3,5); 3.17 (1,2,3); 3.18 (1,2,4,6,7); Standards/Benchmarks (1,6); 3.12 (7,13,15); 3.13 (13-20) 3.19 (1,2) 3.19;(1,2,3) Assessments 1) Chapter Test & Quizzes 1) Chapter Test & Quizzes 1) Chapter test & Quizzes 2) TI-84/Navigator Activities 2) TI-84/Navigator Activities 2) TI-84/Navigator Activities 3) Homework & Practice Worksheets 3) Barbie Bungee Lab 3) Homework & Practice Worksheets 4) Homework & Practice Worksheets Enriched Algebra A December - Linear Systems January - Exponential Functions February / March - Polynomials Essential Questions How do you solve a system of linear How do you use the properties of exponents in How do you recognize and apply the sum, systems by: graphing, substitution, & linear algebra? How do you use exponential growth and difference, and product of polynomials in combination? How do you use linear decay to model real-life situations? What is the real-life situations? How do you break a systems to model and compare real life difference between a linear and exponential model? polynomial into factors? How do you use problems? How do you write the equation for an exponential factoring to solve a quadratic function? trend? Content 1) Solving a system by graphing. 1) Multiplication properties of exponents. 1) Adding, subtracting, & multiplying polynomials 2) Solving a system by substitution. 2) Negative and Zero exponents 2) Multiplying polynomials, including special cases 3) Solving by linear combination. 3) Division properties of exponents 3) Perimeter & Area of geometric figures with 4) Problem solving using systems. 4) Growth and Decay Graphs unknown sides 5) Solving Special Types of systems. 5) Problem solving 4) Factoring using GCF 6) Solving systems of linear inequalities. 5) Factoring special products and quadratic trinomials (a = 1 & a ≠ 1) 6) Factoring by grouping Skills 1) Solving systems by graphing (by hand and 1) Evaluate powers 1) Classify polynomials by degree & number of using a TI-84 – intersection function) 2) Simplify algebraic expressions using properties of terms 2) Solving systems by substitution (check exponents 2) Add & Subtract Polynomials solution graphically on TI-84) Product of powers 3) Multiply Polynomials by 3 methods: 3) Solving systems by linear combination (check Power of a power distribution, sum & difference, & square of a solution graphically on TI-84) Power of a product binomial 4) Special Systems – graphic representations Negative exponents Distribution 1 solution (2 intersecting lines) Zero as an exponent Sum & Difference no solution (2 parallel lines) Quotient of powers Binomials Squared infinitely many solutions (2 coinciding Power of a quotient 4) Factoring special products and quadratic lines) 3) Exponential Growth & Decay Models trinomials 5) Special Systems – algebraic representation Real life applications (i.e. dosage of medication in GCF 1 solution (a specific point of intersection) bloodstream, savings account, population growth, Difference of 2 squares no solution (false statement) depreciation of value, increase & decrease in company Perfect square trinomials infinitely many solutions (true statement) sales, etc.) Quadratic trinomials (a = 1 & a ≠ 1) 6) Identifying the number of solutions of a linear 4) Graphing exponential functions 5) Factoring by grouping system T chart (x values of -2, -1, 0, 1, 2) 7) Solving a system of linear inequalities TI – 84 (graphically by hand & on TI-84) Identifying if functions model growth or decay 8) Analyze, write and solve systems of equations Trend of y values, as x increases & as x decreases, for and inequalities the graphs Using slope intercept form Using standard form 5) Given a graph, write the exponential model ( y a bx ) CH 3.11 (3,5,7); 3.14 (3,8,9); 3.17 (2,3,4,5); 3.11 (3,5);3.12 (3); 3.17 (1,2,3); 3.18 (1,2,4,6,7); 3.11 (2,3);3.14 (11,12); 3.17 (2,3); 3.18 Standards/Benchmarks 3.18 (1,2,3,4,7); 3.19 (1,2,3,4) 3.19 (1,2); 3.20 (1,2) (1,2,4,7); 3.19 (1,2,3) Assessments 1) Chapter test & Quizzes 1) Chapter test & Quizzes 1) Chapter test & Quizzes 2) TI-84/Navigator Activities 2) TI-84/Navigator Activities 2) TI-84/Navigator Activities 3) CBL Lab- Meet You at the Intersection 3) Homework & Practice Worksheets 3) Homework & Practice Worksheets 4) Homework & Practice Worksheets Enriched Algebra A March / April - Quadratic Functions April / May - Rational Expressions June - Radicals & Geometric Ideas Essential Questions How can real-life situations be modeled How do you simplify, multiply/divide, add/subtract, How do you find the distance between two with quadratic equations? How do you and solve rational expressions? points? How do you find the mid-point of a create graphic models of quadratics? How segment? How do you find the length of a do you solve & graph quadratic equations side using a right triangle? without factoring? How you do you algebraic perform operations using radicals? Content 1) Operations with Radicals 1) Solving proportions (that create both linear & quadratic 1) Pythagorean Theorem 2) Square roots, square root method for solving equations) 2) Distance Formula quadratics 2) Simplifying rational expressions 3) Mid-Point Formula 3) Graphs of quadratic equations, by finding 3) State domains for original & simplified expressions specific characteristics 4) Geometric Probability 4) Quadratic formula 5) Multiplying & Dividing Rational Expressions 5) Vertical Motion Models 6) Writing & using rational models with multiplication & 6) Using the discriminate division 7) Graphing quadratic inequalities 7) Adding & Subtracting rational expressions 8) Writing & using rational models with addition & subtraction 9) Dividing polynomials 10) Solving rational equations Skills 1) Operations with Radicals 1) Solving proportions (that create both linear & quadratic 1) Pythagorean Theorem Addition & Subtraction, Multiplication, equations) 2) Real Life application for Pythagorean Theorem Division, Rationalizing denominators (with 2) Simplifying rational expressions – using GCF, special 3) Distance Formula and without conjugate) cases, & trinomial factoring 4) Real Life application for Distance Formula 2) Evaluating square roots in two ways: exact & 3) State domains for original & simplified expressions in set 5) Mid-Point Formula calculator notation 6) Real Life application for Mid-Point Formula 3) Solving quadratic equations by square roots 4) Geometric Probability (using rectangles, circles & (i.e. 3(2 x 4) 6 21 ) triangles) 2 5) Real world application for geometric probability 4) Solving using the quadratic formula 6) Multiplying & Dividing Rational Expressions (include 5) Standard & Vertex forms of quadratic functions 3 x x2 9 difficult simplification i.e. ) 6) Graphs of quadratic equations, by finding 4x2 2 Vertex 7) Writing & using rational models with multiplication & Concavity & Max/Min identification division (i.e. rational models for averages, total sales, X-intercepts (by factoring, square root number of units, etc.) method, & quadratic formula) 8) Adding & Subtracting rational expressions (finding LCD) Y-intercept 9) Writing & using rational models with addition & Axis of symmetry subtraction (perimeter, total distance traveled, total time Point symmetrical to y-intercept traveled, etc.) Domain & Range 10) Dividing polynomials (monomial & long division) 7) Vertical Motion models 11) Solving rational equations (finding LCD) 8) Using the discriminate, determine the possibilities of solutions for a quadratic 9) Use real life applications to model and solve quadratics (graphically & algebraically) 10) Sketching the graph of quadratic inequalities CH 3.11 (2,3,5); 3.14 (10,20); 3.17 (1,2,3); 3.18 3.11(2,3); 3.12 (1,2,3); 3.15 (1,4); 3.17 (1,2); 3.18 3.11 (2,3); 3.12 (8,9,10); 3.14 (4,5); 3.16 (1); Standards/Benchmarks (1,2,4,7); 3.19 (1,2); 3.20 (1,2) (1,2,4,7); 3.19 (1,2) 3.17 (1,2); 3.18 (1,2,4); 3.19 (1) Assessments 1) Chapter test & Quizzes 1) Chapter test & Quizzes 1) Chapter test & Quizzes 2) TI-84/Navigator Activities 2) TI-84/Navigator Activities 2) TI-84/Navigator Activities 3) Homework 3) Homework/Worksheets 3) Homework