ALGEBRA II Aerospace/Engineering

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1 ALGEBRA II Program Goal 5: The student recognizes the importance of mathematics. Number Systems & Their Properties Demonstrate an understanding of the real # system; recognize, apply, & explain its properties; and extend these properties to algebraic expressions. Name, use, & explain number properties. Addition & multiplication properties of equations & inequalities Commutative, associative, distributive, & substitution properties Identity & inverse properties of addition & multiplication Zero product property Transitive, reflexive, & symmetric properties Solve real-world problems using very large and very small numbers. Use applications from business, economics, chemistry, and physics. Scientific formulas Teacher assessment embedded within every unit of the curriculum. Recognize the need for numbers beyond the real. imaginary numbers imaginary plane conjugate imaginary roots ALGEBRA II

2 Number Sense Demonstrate number sense for real numbers and algebraic expressions in a variety of situations. Compare and order real numbers or algebraic expressions & explain the relative magnitude among them. Know and use equivalent representations of the same real # and/or algebraic expressions. integers, scientific notation, algebraic expressions, irrationals order of operations (PEMDAS) integers, decimals, fractions, percents, ratios, scientific notation, absolute value, numbers with integer exponents very large and very small numbers (i.e. one trillion and one-millionth) Solve real-world problems using very large and very small numbers. Use a variety of computational methods including mental mathematics, paper and pencil, manipulatives, and calculators. Use applications from business, economics, chemistry, and physics. Number tiles Scientific formulas Students must use equivalent expressions for the same real # and/or algebraic expression including integers, decimals, fractions, percents, ratios, scientific notation, & numbers with integer exponents. Students will use and understand real numbers that are very large & small (i.e. one trillion and one-millionth). Determine the reasonableness of solutions. problems involving real numbers & algebraic expressions

3 ALGEBRA II Computation The student explains & performs computation with real numbers and algebraic expressions in a variety of situations. Explain & perform computational procedures emphasizing the order of operations. (No calculators) Simplify radical expressions. Simplify and/or evaluate expressions with exponents. Simplify the products and quotients of real number and algebraic monomial expressions Find prime factors, GCF, multiples & LCM PEMDAS real number and algebraic expressions square roots of perfect square monomials cube roots of perfect cubic monomials Real # and algebraic expressions raised to a power Algebraic binomial expressions raised to powers of 0, 1, 2, & 3. Properties of exponents algebraic expressions real numbers Solve real-world problems using very large and very small numbers. Use a variety of computational methods including mental mathematics, paper and pencil, manipulatives, and graphing calculators. Use applications from business, economics, chemistry, and physics. Number tiles Scientific formulas Factor cards Students will explain and perform computational procedures emphasizing the order of operations. (No calculator) Students will be expected to perform the following computations or manipulations of variable quantities fluidly & accurately: simplification of radical expressions including square roots of perfect square monomials, & cube roots of perfect cubic monomials simplify or evaluate real numbers and algebraic monomial expressions raised to a power and algebraic binomial expressions raised to a power of no more than three finding prime factors, GCF, multiples, and LCM of algebraic expressions and real numbers determine the percent of increase and decrease find what percent one number is of another number find a number when a percent of the number is given

4 ALGEBRA II Computation Compute with matrices Understand and compute with imaginary numbers. Addition, subtraction, multiplication, and scalar multiplication Imaginary plane Conjugate imaginary roots Add, subtract, and multiply

5 ALGEBRA II Program Goal 2: The student utilizes reasoning and analysis. expressions, and/or technology. Estimation Use numerical estimation with real numbers in a variety of situations. Use a variety of computational methods to estimate real number quantities involving rational numbers and pi. Perform estimation, explain the method they chose, and use the estimated result to check the reasonableness of results and to make predictions. Mental math Paper/pencil Concrete materials Technology (calculators and computers) Techniques: rounding special numbers clustering truncation compatible numbers simulations Quantities including real numbers and/or algebraic exponents Solve real-world problems using very large and very small numbers. Use applications from business, economics, chemistry, and physics. Number tiles Scientific formulas Student uses estimation to check the reasonableness of results and makes predictions in situations involving real numbers and algebraic expressions. The student should be able to use estimation methods such as rounding, special numbers, clustering, truncation, compatible numbers, and simulations.

6 ALGEBRA II Program Goal 2: The student utilizes reasoning and analysis. expressions, and/or technology. Patterns Recognize, describe, extend, develop, analyze, and give the general rule of patterns from a variety of situations. Recognize the generalization of a pattern using symbolic notation to represent the nth term. Recognize the same general pattern presented in different representations. Identify & continue patterns presented in a variety of formats. Explicit and recursive form Algebraic patterns including consecutive number patterns or equations of functions such as n, n+1, n+2, or f(x) = 2x-1 Geometric patterns Arithmetic & geometric sequences: classification finding particular terms (not necessarily by formula) Algebraic patterns Geometric patterns Arithmetic and geometric sequences Numeric Algebraic Visual Oral Written Kinesthetic Pictorial Tabular Graphical Listing Solve real world problems that suggest patterns. Find examples of real world data collection in newspapers or magazines. Use a variety of techniques to organize pattern information (See Key Content for Objective #3) Probability experiments (i.e. handshake problem) Graphing Calculator The student recognizes the generalization of a pattern using symbolic notation to represent the nth term in an explicit form. The student should be able to work with the following types of patterns: Algebraic patterns including consecutive number patterns or equations of functions such as n, n+1, n+2, or f(x) = 2x-1 Geometric patterns Arithmetic or geometric sequences, as well as, classifying sequences as arithmetic or geometric and finding particular terms of arithmetic or geometric sequences (not necessarily by formula). ALGEBRA II

7 Program Goal 2: The student utilizes reasoning and analysis. expressions, and/or technology. Patterns Create a pattern and generalize it using a written and/or algebraic description. Algebraic pattern (n, n+1, n+2, or f(x) = 2x-1) Geometric pattern Arithmetic and geometric sequences Exponential patterns (growth and decay) Conceptual foundation of limits (i.e. ½, 1/3, ¼, approaches 0) Cyclical patterns (Ferris wheel, and pendulum) Combinatorics patterns (Pascal s triangle and Fibinacci s sequence) Use M & M lab activities ALGEBRA II

8 Program Goal 5: The student recognizes the importance of mathematics. Variables, Equations, & Inequalities Use variables, symbols, real numbers, and algebraic expressions to solve equations and inequalities in a variety of situations. Set up & solve equations and inequalities. Linear equations & inequalities analytically & graphically no calculator standard, slope-intercept, and point-slope form slope as rate of change Quadratic equations with rational and real solutions factoring zero-product property completing the square graphing discriminant quadratic formula Systems of linear equations & inequalities with 2 unknowns graphing substitution linear combination matrices Radical equations with no more than one inverse operation around the radical expression extraneous roots Graphing calculator Linear programming Number tiles Algeblocks Factor cards Real-world applications from business, economics, chemistry, and physics. Set up and solve the following equations and inequalities without the use of a calculator: Linear equations and inequalities both analytically and graphically Quadratic equations with rational solutions (factorable quadratic equations) Systems of linear equations with 2 unknowns Radical equations involving no more than one inverse operation around the radical expression. Rational equations such as: 3 = 5 (x+2) (x-3) Exponential equations containing the same base Equations & inequalities involving absolute value quantities containing one variable (could be solved using the number line) % problems which include finding a number when a % of the number is given, finding what % one # is of another #, and finding % increase and decrease. ALGEBRA II

9 Program Goal 5: The student recognizes the importance of mathematics. Variables, Equations, & Inequalities Use a variety of ways to represent problem situations which involve variable quantities. Rational equations involving algebraic binomials asymptotes ratios and proportions Exponential equations containing the same base (no calculator) Equations & inequalities involving absolute value quantities containing one variable % problems including % of increase and decrease Symbols Variables Expressions Inequalities Equations Simple systems of linear equations Formulates and solves problems involving symbols, percents, variables, expressions, inequalities, equations, and simple systems. Linear equations and inequalities both analytically and graphically Quadratic equations with rational solutions (factorable) systems of linear equations with 2 unknowns Radical equations involving no more than one inverse operation around the radical expression. Rational equations such as: 3 = 5 (x+2) (x-3) Equations & Inequalities involving absolute value quantities containing one variable (could be solved using the number line) % problems which include finding a number when a % of the number is given, finding what % one # is of another #, and finding % increase and decrease. ALGEBRA II

10 Program Goal 5: The student recognizes the importance of mathematics. Variables, Equations, & Inequalities Formulate & solve problems involving symbols, percents, variables, expressions, inequalities, equations, & simple systems. Linear equations & inequalities both analytically & graphically Quadratic equations with rational solutions Systems of linear equations with 2 unknowns Radical equations involving no more than one inverse operation around the radical expression Rational equations involving algebraic binomials Equations & inequalities involving absolute value quantities containing 1 variable % problems involving % of increase and decrease Use symbols, variables, expressions, inequalities, equations, and simple systems of linear equations to represent problem situations that involve variable quantities. ALGEBRA II

11 Functions The student analyzes functions in a variety of situations. Interpret & describe functions. Evaluate & graph functions and compositions of functions. Function notation Domain & range (values approaching infinity) Independent & dependent variables Vertical line test Linear equations constant step greatest integer piecewise direct & inverse variations Absolute values Quadratic equations Exponential functions (growth & decay) Radical Polynomials possible rational roots synthetic division Logarithmic Functions with transformations Use paper and pencil and graphing calculators to evaluate and analyze functions real world applications (No calculator) Recognizes how changes in constants and/or slope within a linear function changes the appearance of a graph Interprets the meaning of points on a graph in the context of a real world situation. Students should be able to make contextual interpretations involving the x and y intercepts, the slope, points on and off the line, and a line of best fit. Recognize how variations in constants and/or slope changes the appearance of a graph. Interpret the meaning of points on a graph in the context of a real world situation. linear equations x and y intercepts slope points on and off the line line of best fit

12 ALGEBRA II Modeling Develop and use models to represent and justify mathematical relationships found in a variety of situations involving algebraic knowledge and skills. Use the mathematical modeling process to represent & explain mathematical concepts & procedures and to show the relationship between 2 or more things. # line to model the relationship between real numbers & operations on real numbers Coordinate plane to model ordered pairs, linear and quadratic functions, and graphs of rectangles, triangles, and circles. Equations & inequalities to model numerical and geometric relationships Diagrams or pictures to represent problem situations 2-D or 3-D models to model surface area & volume Use a variety of models in contextual situations involving real life applications. 2-D and 3-D geometric models Graphing Calculators Use the mathematical modeling process to make inferences about real world situations. Students should be able to work with the following types of models. # line to model the relationship between real numbers & operations on real numbers Coordinate plane to model ordered pairs, linear and quadratic functions, and graphs of rectangles, triangles, and circles. Equations & inequalities to model numerical and geometric relationships Diagrams or pictures to represent problem situations 2-D or 3-D models to model surface area & volume

13 ALGEBRA II Geometry Use an algebraic perspective to analyze the geometry of 2 dimensions in a variety of situations. Recognize, classify, & discuss properties of conic sections Calculate the slope of a line from a list of ordered pairs & explain how the graph of the line is related to its slope. (No calculator) Find & explain the relationships between slopes of different lines. Determine if a triangle is a right triangle & find the side lengths when the triangle is presented on the coordinate plane. Parabola, circle, ellipse, & hyperbola Lines of symmetry, foci, axis (major & minor), asymptotes line of best fit If Ax + By = C, then m = -a/b parallel and perpendicular lines distance formula slope Graphing calculators Real world applications Use maps Calculate the slope of a line from a list of ordered pairs on the line and explain how the graph of the line is related to its slope. Find or explain the relationship between the slopes of perpendicular and parallel lines. (No calculator) Recognize an equation of a line in any form, transform the equation into slope-intercept form in order to identify characteristics such as slope and the y-intercept and use this form to graph the line. Recognize & describe single & multiple transformations on eq s. graphically & algebraically conics & absolute values eq s Explain how variations in constants, exponents, and/or coefficients within the equation change the appearance of the graph of the equation. line, absolute value eq s, polynomial eq s, & conics

14 ALGEBRA II Program Goal 2: The student utilizes reasoning and analysis. Program Goal 5: The student recognizes the importance of mathematics. Problem Solving Apply algebraic content/objectives to solving problems in a variety of contexts. Use appropriate representations of real numbers and algebraic expressions to formulate and solve real-world problems. Use properties of the real # system to formulate & solve real- world problems. equivalent representations for the same real number and/or algebraic expression integers, decimals, fractions, percents, ratios, scientific notation, & numbers with integer exponents very large and very small numbers (i.e. 1 trillion and 1- millionth Identity: Additive & Mult. Inverse: Add. & Mult. Commutative Associative Distributive Zero Product Substitution Reflexive, Symmetric, & Transitive Problem solving strategy (PPPR) Plan Prepare Perform Reflect Graphing Calculator Ten problem solving strategies act it out or use objects make a picture or diagram use or make a table make an organized list guess and check use or look for a pattern work backwards use logical reasoning look at a simpler problem brainstorm All objectives/indicators and key content items in the problem solving section are tested on the state assessment.

15 ALGEBRA II Program Goal 2: The student utilizes reasoning and analysis. Program Goal 5: The student recognizes the importance of mathematics. Problem Solving Use arithmetic operations and inverse relationships to formulate and solve real-world problems involving real numbers and algebraic expressions with special emphasis on topics such as: finding the volume & surface area when formulas are given applications from business, economics, chemistry, & physics (avoiding logs.) probabilities and exponential growth & decay. Use a variety of ways to represent problem situations which involve variable quantities. Simplify radical expressions (square roots of perfect square monomials and cube roots of perfect cubic monomials). Simplify and evaluate real # and algebraic monomial expressions raised to a power and algebraic binomial expressions raised to a power of no more than 3. Simplify products and quotients of real # and algebraic monomial expressions using the properties of exponents. Prime factors, GCF, multiples, & LCM of algebraic expressions and real numbers Percents Symbols Variables Expressions Inequalities Equations Simple systems of linear equations

16 ALGEBRA II Program Goal 2: The student utilizes reasoning and analysis. Program Goal 5: The student recognizes the importance of mathematics. Problem Solving Formulate & solve problems involving symbols, percents, variables, expressions, inequalities, equations, & simple systems. Interpret the meaning of points on a graph in the context of a real world situation. Linear equations & inequalities both analytically & graphically Quadratic equations with rational solutions Systems of linear equations with 2 unknowns Radical equations involving no more than one inverse operation around the radical expression Rational equations involving algebraic binomials Equations & inequalities involving absolute value quantities containing 1 variable % problems involving % of increase and decrease x and y intercepts slope points on and off the line line of best fit ALGEBRA II

17 Program Goal 2: The student utilizes reasoning and analysis. Program Goal 5: The student recognizes the importance of mathematics. Problem Solving Use the mathematical modeling process to make inferences about real world situations. Use theoretical or experimental probability to make predictions about realworld events such as work in economics, quality control, genetics, meterorology, & other areas of science, games, and situations involving geometric probability. # line to model the relationship between real numbers & operations on real numbers Coordinate plane to model ordered pairs, linear and quadratic functions, and graphs of rectangles, triangles, and circles. Equations & inequalities to model numerical and geometric relationships Diagrams or pictures to represent problem situations 2-D or 3-D models to model surface area & volume geometric probability percentages derived from actual or simulated events probability of a simple event probability of a compound event composed of 2 or more simple, independent events. ALGEBRA II

18 Program Goal 2: The student utilizes reasoning and analysis. Program Goal 5: The student recognizes the importance of mathematics. Data Analysis Apply probability theory to analyze the validity of arguments, draw conclusions, and make decisions in a variety of situations. Explain the relationship between probability and odds and compute one given the other. Use theoretical or experimental probability to make predictions about realworld events such as work in economics, quality control, genetics, meteorology, and other areas of science, games, and situations involving geometric probability. For example a 3 out of 4 probability is equivalent to 3 to 1 odds. Real life applications Geometric probability Percentages derived from actual or simulated events Determine the probability of a simple event or a compound event composed of 2 or more simple, independent events. Combinations and permutations Conduct experiments Compare results to what is expected. Explain the relationship between probability and odds and compute one given the other. Use theoretical of experimental probability to make predictions about realworld events such as work in economics, quality control, genetics, meteorology, and other areas of science, games, and situations involving geometric probability. ALGEBRA II Program Goal 2: The student utilizes reasoning and analysis.

19 Program Goal 5: The student recognizes the importance of mathematics. Data Analysis Generate, organize, and interpret real number and other data in a variety of situations. Use data analysis to make accurate inferences, decisions, & predictions, & to develop convincing arguments from data displayed in a variety of formats. Data displays: frequency distributions box and whisker plots stem & leaf plots histograms scatter plots/discrete graphs bar, line, & circle graphs Venn diagrams/pictorial displays charts and tables Statistical measures: measure of central tendency (mean, median, mode) range quartiles interquartile range linear, quadratic, and exponential regression correlation coefficient Effects of outliers on the mean, median, & range of a real # set Line of best fit given a scatter plot Predictions using the equation of a line of best fit or the best fit model Graphing calculators Read, Create & compare/contrast various data displays. (Use test score data or postage stamp data) Real life applications Create graphs from data Use M and M lab activities Use penny lab activities Use data analysis to make accurate inferences, decisions, & predictions & to develop convincing arguments from data displayed in a variety of formats. Recognize or explain the affects of scale and/or interval changes on graphs of data sets. ALGEBRA II Program Goal 2: The student utilizes reasoning and analysis.

20 Program Goal 5: The student recognizes the importance of mathematics. Data Analysis Recognize or explain the affects of scale &/or interval changes on graphs of data sets. Data displays: frequency distribution box & whisker plots stem & leaf plots histograms scatter plots/discrete graphs bar, line, circle graphs Venn diagrams (pictorial displays) charts & tables

MATH Spring 2010 Topics per Section

MATH Spring 2010 Topics per Section MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line