Number Theory and Basic Algebra. (10 days)

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1 LEARNING GUIDE: Algebra 2 Main Resources: Algebra 2 Glencoe/McGraw Hill Copyright: 2010 Standards: MA 12.1: Number Sense: Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. MA 12.2: Geometric/Measurement: Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. MA 12.3: Algebraic: Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. MA 12.4: Data Analysis/Probability: Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines Unit: (days) Number Theory and Basic Algebra. (10 days) Sub-Standards: Indicators: Learning Objectives: Vocabulary: Resources: MA Students will represent and show relationships among complex numbers. MA Students will demonstrate the meaning and effects of arithmetic operations with real numbers. MA Students will compute fluently and accurately using appropriate strategies and tools. MA a Demonstrate multiple equivalent forms of irrational numbers. MA b Compare, contrast and apply the properties of numbers and the real number system, including the rational, irrational, imaginary, and complex numbers. MA a Use drawings, words, and symbols to explain the effects of such operations as multiplication and division, and computing positive powers and roots on the magnitude of quantities. MA a Compute accurately with real numbers. MA d Select, apply, and explain the method of computation when problem solving using real numbers. MA a Model contextualized problems using various representations. MA b Represent a variety of quantitative relationships using linear equations and one variable inequalities. MA a Explain/apply the reflexive, symmetric, and transitive properties of equality. MA g Solve linear equations and inequalities including absolute value. MA h Identify and explain the properties used in solving MA o Solve an equation involving several variables for one variable in terms of the others. 1. Review order of operations. 2. Use order of operations to solve problems with formulas. 3. Identify and apply properties of equality. 4. Simplify expressions using properties of equality. 5. Identify the subsets of the real number system that a number belongs to and compare numbers. 6. Solve linear algebra 7. Solve absolute value 8. Solve linear and absolute value inequalities. 1.Additive/multiplicative inverse. 2. Algebraic expression. 3. Coefficient. 4. Exponent. 5. Integers. 6. Irrational. 7. Like terms. 8. Natural. 9. Rational. 10. Real Number. 11. Variable Addition property of equality. 12. Subtraction property of equality. 13. Multiplication property of equality. 14. Division property of equality. 15. Inequality. 16. Absolute value equation. 17. Absolute value inequality. Chapter 1 Resource s for each objective. Assessments: Formative, Summative, Rubric

2 Functions (20 Days) MA Students will generalize, represent, and analyze relationships using algebraic symbols. MA Students will develop and evaluate inferences to make predictions. MA a Represent, interpret, and analyze functions with graphs, tables, and algebraic notation and convert among these representations (e.g., linear, non-linear) MA b Identify domain and range of functions represented in either symbolic or graphical form (e.g., linear, non-linear) MA c Identify the slope and intercepts of a linear relationship from an equation or graph MA d Identify characteristics of linear and nonlinear MA e Graph linear and non-linear functions MA f Compare and analyze the rate of change by using ordered pairs, tables, graphs, and equations MA g Graph and interpret linear inequalities 1. Identify and analyze relations and 2. Identify, analyze, graph and write linear 3. Find slope and rate of change. 4. Analyze scatter plots. 5. Write equations using linear regression. 6. Analyze and graph absolute value, piece-wise and greatest integer 7. Apply transforms to a parent function to create a family of 8. Graph transformations of a know parent 9. Find the domain and range of a function/relation in any form. 10. Find the inverse of a 11. Graph linear and absolute value 1.Relation. 2.Function 3.Domain. 4.Range. 5.Inverse. 6.Linear 7.Absolute value 8.Quadratic 9.Piece-Wise Function. 10.Greatest integer 11.Parent 12.Transform. 13.Translation. 14.Dilation. 15.Reflection. 16. Scatter plot. 17.Regression line. 18.Prediction/Regression equation. Chapter 2 Resource s for each objective. Group work with TI-84 calculators. Lab Questions/Packet. MA h Represent, interpret, and analyze functions and their inverses MA i Determine if a relation is a MA a MA b MA c Analyze situations to determine the type of algebraic relationship (e.g., linear, nonlinear) MA c Develop linear equations for linear models to predict unobserved outcomes using regression line and correlation coefficient

3 Systems. (15 Days.) MA a MA p Analyze and solve systems of two linear equations in two variables algebraically and graphically 1. Solve linear systems by graphing. 2. Solve linear systems by substitution. 3. Solve linear systems by elimination. 4. Use systems to represent and solve application based problems. 5. Solve systems of inequalities by graphing. 6. Use linear programming to find the min and max of a (Application based) 7. Solve systems of equations in 3 variables. 1. System. 2. Consistent. 3. Inconsistent. 4. Dependent. 5. Independent. 6. Substitution method. 7. Elimination method. 8. System of inequalities. 9. Linear Programming. 10. Constraints variable system. Chapter 3 Resource Matrices (20 Days.) N.A. (Lessons are material that is in addition to the standards.) 1. Indentify the dimensions of a matrix. 2. Identify specific elements of a matrix. 3. Perform addition/subtraction with matrices. 4. Perform scalar multiplication with matrices. 5. Multiply matrices. 6. Perform transforms on the coordinate plane with matrices. 7. Find the determinant of a square matrix. 8. Apply the determinant of a matrix using Cramer s rule. 9. Use a determinant to find the area of a triangle on the coordinate plane. 10. Find the inverse of a matrix. 11. Use an inverse matrix to solve systems. 1. Matrix. 2. Row. 3. Column. 4. Element. 5. Square Matrix 6. Determinant. 7. Cramer s rule. 8. Inverse Matrix. Chapter 4 Resource TI-84 group work. Lab Packet

4 Quadratics. (20 Days.) Polynomial Expressions. (30 Days.) MA e Factor polynomials MA i Solve quadratic equations (e.g., factoring, graphing, quadratic formula) MA c MA b Simplify algebraic expressions involving exponents (e.g., (3x 4 ) 2 ) MA c Add and subtract polynomials MA d Multiply and divide polynomials (e.g., divide x 3 8 by x 2, divide x 4 5x 3 2x by x 2 ) MA e MA j Add, subtract, and simplify rational expressions MA k Multiply, divide, and simplify rational expressions 1. Graph Quadratics and analyze them. 2. Solve quadratics by graphing. 3. Solve quadratics by completing the square. 4. Solve quadratics using the quadratics formula. 5. Simplify roots. 6. Simplify expressions containing complex numbers. 8. Graph quadratic inequalities. 1. Utilize rules for powers to multiply monomials and numbers in scientific notation. 2. Utilize rules for powers to divide monomials and numbers in scientific notation. 3. Identify the type and degree of a polynomial as well as write equivalent forms in different orders. 4. Add and Subtract Polynomials. 5. Multiply Polynomials. 6. Divide polynomials. 7. Add, subtract, multiply and divide rational expressions. 8. Graph and analyze polynomial 9. Solve polynomial equations using a variety of theorems. 1. Quadratic equation. 2.Standard form of a quadratic. 3. Vertex. 4. Zero of the 5. Minimum. 6. Maximum. 7. Parabola. 8. Quadratic formula. 9. Completing the square. 10. Complex number. 1. Exponent. 2. Monomial. 3. Scientific Notation. 4. Polynomial. 5. Degree. 6. Ascending order. 7. Descending order. 8. Like terms. 9. FOIL. 10. Synthetic division. 11. Rational expression. 12. Zero of a 13. Remainder and Factor Theorems. 14. Descartes rule of signs. 15. Rational root theorem. Chapter 5 Resource Chapter 6 Resource Group work with TI-84 Calculator.

5 Probability and Statistics (20 Days.) MA Students will formulate a question and design a survey or an experiment in which data is collected and displayed in a variety of formats, then select and use appropriate statistical methods to analyze the data. MA Students will apply and analyze concepts of probability. MA a Interpret data represented by the normal distribution and formulate conclusions MA b Compute, identify, and interpret measures of central tendency (mean, median, mode) when provided a graph or data set MA d Describe the shape and determine spread (variance, standard deviation) and outliers of a data set MA e Explain how statistics are used or misused in the world MA g Explain the impact of sampling methods, bias, and the phrasing of questions asked during data collection and the conclusions that can rightfully be made MA h Explain the differences between randomized experiment and observational studies MA a Construct a sample space and a probability distribution 1. Find the number of outcomes using the counting principle. 3. Find the number of outcomes using permutations. 4. Find the number of outcomes using combinations. 5. Find basic probability. 6. Find compound probability. 7. Identify sampling techniques that are random or contain bias. 8. Find measures of central tendency, sample error, and standard deviation. 9. Find conditional probability. 10. Read and create probability distributions. 11. Analyze situations that are normally distributed. 12. Find probabilities that are binomial distributions. 1. Counting priniciple 2. permutation. 3.combination. 4.probability. 5.central tendancy. 6.random sample. 7. biased. 8. normal distribution. 9. binomial distribution. Chapter 12 Resource MA b Identify dependent and independent events and calculate their probabilities MA c Use the appropriate counting techniques to determine the probability of an event (e.g.,combinations, permutations) MA d Analyze events to determine if they are mutually exclusive MA e Determine the relative frequency of a specified outcome of an event to estimate the probability of the outcome

6 Compositionof Functions/Radical Expressions. (10 Days.) MA Students will represent and show relationships among complex numbers. MA a MA d MA n Combine functions by composition, as well as by addition, subtraction, multiplication, and division 1. Simplify square roots. 2. Simplify expressions containing square roots. 3. Perform operations with expressions containing square roots. 4. Solve equations containing square roots. 5. Combine functions by performing operations and function composition. 6. Find the inverse of a 1. Square root. 2. Radical expression. 3. Square factors. 4. Rationalizing a denominator. 5. Radical 6. Radical equation. 7. Composition of 8. Inverse Chapter 7 Resource Exponentials and Logarithms. (10 days.) MA d 1. Graph exponential 2. Solve exponential 3. Simplify logarithmic expressions. 4. Solve logarithmic 5. Simplify expressions/solve equations using properties of logarithms. 6. Simplify expressions containing common logarithms and natural logarithms. 7.Solve equations using common and natural logs. 8. Solve application based problems using common and natural logs involving exponential growth and decay. 1. Exponential 2.Logarithm. 3.Common Logarithm. 4.Natural Logarithm. 5.Exponential growth and decay. Chapter 8 Resource TI-84 group work.

Sub-Standards: Indicators: Learning Objectives: Vocabulary: Resources:

Sub-Standards: Indicators: Learning Objectives: Vocabulary: Resources: LEARNING GUIDE: Algebra 1 Main Resources: Algebra 1 Glencoe/McGraw Hill Copyright: 2008 Stards: MA 12.1: Number Sense: Students will communicate number sense concepts using multiple representations to