Module 1: Equations and Inequalities (30 days) Word Problems Literal Equations (Scientific Applications) Justifying solutions Algebraic Proofs Represent constraints by equations and inequalities Graphing equations on a coordinate axis with two variables and interpret solutions Solving Equations: Use decimals and integers Properties: Sections 1-1 to 1-6 as well as whole numbers. o Addition 1-2 o Subtraction 1-2 o Multiplication 1-3 o Division 1-3 o Commutative 1-4 o Associative of Addition 1-2 o Associative of Multiplication 1-3 o Multiplicative Identity and Inverse 1-3 o Multiplicative Property of Zero o Additive Identity and Inverse 1-2 o Distributive 1-4 o Identity and contradiction solutions (identity or no solutions ex. 5 = 5 or 6 = 5) o Properties of Inequality by positive and negative numbers o Symmetric o Reflexive o Transitive o Substitution Solve different types of equations and inequalities with justification (Algebraic Proof) o One-Step 1-2, 1-3 2-2, 2-3 o Two-Step 1-4, 2-4 o Variables on both sides 1-5, 2-5 o Distributive (keep, change, change) 1-4, 1-5, 2-5 o Combining like terms o Literal Equations 1-6 o Solving Compound Inequalities 2-6 Word Problems with Equations and Inequalities Sections 1-1 to 1-6 and 2-1 to 2-6 o Diagrams How to read it Extracting important information Mapping out procedure (no math focus on reading) o Show how to solve a word problem and use the procedure (using traditional problems money, age, consecutive, number, area/perimeter, etc.) Let statement Equation and Inequalities Solve Check and make sure it s appropriate (constraints) Reading and interpreting a graph 3-1
Real-Life Word Problems Sections 1-8 to 1-10 o Units 1-8, 1-9, 1-10 o Solve and check (constraints) 1-8 to 1-10 o Create a word problem that correlates to a given equation 1-8, 1-9 Module 2: Statistics (20 days) Represent and interpret data (dot plots, histograms and box plots) Represent two quantitative variables and describe how they are related Regression techniques fitting a proper model Measures of central tendency (mean, median, mode) and spread (interquartile range, standard deviation) Effects of outliers Relative frequency (joint, marginal and conditional relative frequencies) Scatterplots and assessing the fit of a function by analyzing residuals Interpret the slope (rate of change) and interpret (constant term) of a linear model in the context of the data Distinguishing between correlation and causation Interpreting correlation coefficient Measures of Central Tendency and measures of spread o Mean, Median and Mode 10-3 o On graphing calculator Graphical representation o Two-Way Frequency Tables 10-1 o Histograms 10-2 o Box and Whisker Plot 10-3 o Scatter Plots 3-5 o Correlation coefficient 3-5 Data analysis o Effects of outliers 10-4 o Relative frequency (cumulative frequency data) 10-2 (10 days) Bivariate Data o Scatterplots 3-5 o Linear Regression 3-5, 4-8 o Interpreting slope and y-intercept 3-5 o Correlation Coefficient 3-5,9-4 o Residuals (what is left over) 4-8, 9-4 o Distinguishing between correlation and causation 3-5 (10 days)
Module 3: Linear and Exponential Relationships (40 days) Systems of Equations and Inequalities Functions Graphically Domain and range Concepts of a Function and Function Notation Exploring functions including sequences and defining them recursively Linear, quadratic, exponential, square root, cube root, piecewise, step functions and absolute value functions Interpreting them graphically, numerically, symbolically and verbally, translate between representations Build a function that models a relationship between two quantities Translations of Functions (linear and quadratic) Key Features (intercepts, even/odd, maximums/minimums, increasing/decreasing, end behavior, and continuity) Exponential Functions - Growth and Decay Linear Functions o Identifying Linear Functions 4-1 o Using Intercepts 4-2 o Rate of Change and Slope 4-3 o The Slope Formula 4-4 o Transformations of Functions 4-5 o Graphing and Writing Linear Functions 4-6 o Point Slope Form 4-7 o Residuals and Linear Regression 4-8 o Slopes of Parallel and Perpendicular Lines 4-9 o Transforming Linear Functions 4-10 Systems of Equations and Inequalities o Graphing 5-1 o Substitution with proof 5-2 o Elimination with proof 5-3 o Solving Special Systems 5-4 o Linear Inequalities 5-5 o Systems of Linear Inequalities 5-6 o Word problems involving systems (including constraints) 5-1 to 5-6 (15-20 days) Functions o Function Notation 3-2 o Domain and range 3-2 o Functions Operations and Inverses 3-3 o Families of Functions (linear, quadratic, exponential, square root, cube root, piecewise, step functions and absolute value functions) 9-5 o Piece Functions 3-4 o Key Features (intercepts, even/odd, maximums/minimums, increasing/decreasing, end behavior, and continuity) o Translations linear and quadratic 4-10, 8-4
(20 days) o Writing a function rule 3-3 o Average rate of change (non-linear) o Exploring functions with sequences (common difference (Arithmetic) or common ratio (Geometric)) 3-6, 9-1 o Growth and Decay 9-2, 9-3 Module 4: Polynomials - (30 Days) Arithmetic operations on Polynomials Factoring Completing the Square Identify the zeroes and sketching the function recognize no real roots Interpreting expressions that represent a quantity ( ex. P(1 + r) n ) Quadratic Formula (derive from (x p) 2 = q) Closure Literal equations for quadratics Operations with Polynomials o Closure 6-2 o Laws of Exponents (integer exponents only) 6-1 o Polynomials 6-3 o Adding and Subtracting Polynomials 6-4 o Multiplying Polynomials 6-5, 6-6 Solving Quadratics o Factoring all types of factoring and solving by factoring 7-1, 7-2, 7-3, 7-4, 7-5 o Completing the square 8-8 o Quadratic formula 8-9 o Nature of the roots (identifying as rational, irrational, or non-real) o Literal equations (from scientific formulas) o Solving factored polynomial equations 8-5,8-6 (20 Days)
Module 5: Graphing Quadratics (30 days) Key features of the graphs Restrictions on domain and range Estimate the average rate of change of a function Symmetry of a graph Key Features (even/odd, maximums/minimums, increasing/decreasing, end behavior, and continuity) Linear and quadratic systems Translations Modeling for Quadratics o Graphing parabolas by hand 8-2, 8-4 o Symmetry 8-1, 8-2 o Max/Min 8-1,8-2 o Translations 8-4 o Real life applications (15 Days) Linear and Quadratic Systems o Graphically and Algebraically 8-10 o Real life applications 8-1 to 8-10 (15 Days)