Integrated Algebra Curriculum

Transcription

1 Integrated Algebra Curriculum Course Description: Course Essential Questions: Integrated Algebra Regents Exam Information: Approximate Percentage of Questions Assessing Each Strand Strand: Percent: Time allotted: Focus Unit(s): Number Sense and Operations: 6-10% (? weeks) 1, 11, 14 Algebra: 50-55% (? weeks) 2 9, 12 Geometry: 14-19% (? weeks) 10 Measurement: 3-8% (? weeks) Probability and Statistics: 14-19% (? weeks) 13, 14 Format: Question Type: Number of Questions: Multiple-choice 30 2-credit open ended 3 3-credit open ended 3 4-credit open ended 3 Integrated Algebra Curric.doc 1

2 Reference Sheet: The Regents Examination in Integrated Algebra will include a reference sheet containing the formulas specified below. Integrated Algebra Curric.doc 2

3 Integrated Algebra Mathematical Language The language below is language that all students should be familiar with and should be used throughout instruction. Definitions for most words and expressions can be found in the HS Glossary. Problem Solving algebraically concept conjecture constraint equivalent Reasoning and Proof appropriate approximation argument claim conclusion conjecture Communication accuracy analyze argument coherent communicate comprehension conclusion conjecture decoding Connections coherent whole concept connection Representation angle of elevation array chart compare diagram equation function formulate generalization graphically multiple representations numerically counterexample explain inductive reasoning logical argument mathematical conjecture proof elicit equation evaluate extend formula function graph interpretation mathematical visual formulate physical model procedure graph interpret mathematical phenomena organize physical phenomena profit record parameter pattern relative efficiency strategy verbally refute systematic approach validity Venn diagram verify rationale standard (mathematical) notation strategy table technical writing terminology valid quantitative model representation social phenomena symbol table technology translate Integrated Algebra Curric.doc 3

4 Number Sense and Operations absolute value algebraic problem arithmetic operation arrangements (permutations) associative property closure property commutative property counting techniques decimal denominator discount distributive property exponential expression Algebra acute angle adjacent side/angle algebraic equation algebraic expression algebraic fraction analyze axis of symmetry binomial coefficient common base complement of a subset coordinates cosine dependent difference of two perfect squares element equation exponent exponential growth and decay expression factoring fractional expression greatest common factor (GCF) hypotenuse independent variable inequality integer expression factorial field fraction Fundamental Principle of Counting group identity property inverse property like/unlike radical terms number theory numerator percent of increase/ decrease integral coefficient integral exponent integral root(s) intersection of sets interval notation lead coefficient legs of a right triangle line parallel to the xor y- axis linear equation in one variable linear inequality in one variable literal equation lowest terms fraction monomial multiplication property of zero opposite side/angle parabola parallel polynomial product properties of exponents proportion Pythagorean Theorem quadratic equation quantitative quotient ratio product properties of the Real numbers proportionality/direct variation quotient radical radicand real numbers scientific notation simplest form variable relation right angle right triangle root(s) of an equation roster form set set-builder notation sine slope solution set subset sum system of linear inequalities systems of linear equations tangent translate (from verbal to symbolic) trigonometry trinomial undefined union of sets universal set variable verbal expression verbal sentence vertex x-axis y-axis Integrated Algebra Curric.doc 4

5 Geometry absolute value function angle area axis of symmetry of a parabola circle coefficient cylinder decagon exponential function function generalize geometric shape graph of a relation hexagon Measurement appropriate unit conversion cubic unit error Statistics and Probability appropriateness biased bivariate box-and-whisker plot calculated probability categorize causation central tendency complement conditional probability correlation cumulative frequency distribution table cumulative frequency histogram data dependent events dependent variable element investigate nonagon octagon ordered pair parabolic function parallelogram pentagon perimeter polygon quadrilateral quarter-circle rational coefficient rectangle rectangular solid regular polygon linear measure linear unit magnitude measurement system empirical probability experimental design extrapolation favorable event finite sample space five statistical summary frequency distribution table histogram independent events independent variable interpolation line of best fit linear transformation maximum mean measure of central tendency median relation rhombus roots of a parabolic function sector of a circle semi-circle spatial reasoning square surface area trapezoid triangle vertex visualization volume rate relative error square unit unit minimum mode mutually exclusive events not mutually exclusive events percentile rank probability qualitative quantitative quartiles (specifically: first, second, third or lower, middle, upper) range sample space scatter plot series univariate Integrated Algebra Curric.doc 5

6 Integrated Algebra Unit Sequence and Timeline: (Note: Due to the need to include an additional unit in January for 8 th grade students, the timeframes given are not valid for 8 th grade classes. Please modify the calendar as needed.) Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit A Unit 6 Unit 7 Unit 8 Unit 9 Number and Operations ~ 3 weeks Early September to late September Variables and Expressions ~ 1.5 weeks Late September Solving Linear Equations and Inqualities ~ 5 weeks Early October to early November Multiplying and Dividing Polynomials ~ 1.5 weeks Mid-November Factoring and Solving Quadratics ~ 3 weeks Early December to late December 8 th Grade Geometry Unit ~ 5 weeks Early January Algebraic Fractions ~ 2 weeks Early January to mid-january Functions and Relations ~ 1 week Mid-January to late January Coordinate Geometry ~ 3.5 weeks Late January to mid-february Systems of Equations ~ 2.5 weeks Late February to early March Integrated Algebra Curric.doc 6

7 Unit 10 Unit 11 Unit 12 Unit 13 Unit 14 Unit 15 Working with Shapes ~ 1.5 weeks Mid-March to late March Radicals ~ 1.5 weeks Late March to early April Trigonometry ~ 2 weeks Mid-April to late April Statistics ~ 3 weeks Early May to late May Probability ~ 2 weeks Late May to early June Review for Regents Exam ~? weeks Mid-June Integrated Algebra Curric.doc 7

8 Unit 1 Numbers and Operations ~ 3 weeks Early September to late September A.N.1 Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) Note: Students do not need to identify groups and fields, but students should be engaged in the ideas. A.M.2 Solve problems involving conversions within measurement systems, given the relationship between the units All mathematics is governed by specific rules (properties). to identify by example commutative prop of addition and multiplication, associative property of addition and multiplication, distributive property to identity properties of addition and multiplication, inverse properties of addition and multiplication, multiplicative property of zero. to identify and give examples of rational and irrational numbers to apply operations to signed numbers to apply the rules of order of operations to define absolute value and evaluate absolute value expressions to evaluate exponential expressions to convert between fractions, decimals and percents to convert within a measurement system and solve problems using conversions Amsco: Ch. 1, 2, and 5 Unified: Ch1, 7 Integrated Algebra Curric.doc 8

9 Unit 2 Variables and Expressions ~ 1.5 weeks Late September A.N.6 Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s) A.A.1 Translate a quantitative verbal phrase into an algebraic expression A.A.2 Write a verbal expression that matches a given mathematical expression A.A.13 Add, subtract, and multiply monomials and polynomials Mathematics can be used to model real situations. to recognize and utilize algebraic terminology to add and subtract polynomials to translate verbal phrases into algebraic expressions to translate algebraic expressions in verbal phrases Amsco: Ch. 4 Unified: 7-3; Ch. 3 Integrated Algebra Curric.doc 9

10 Unit 3 Solving Linear Equations and Inequalities ~ 5 weeks Early October to early November A.N.1 Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) Note: Students do not need to identify groups and fields, but students should be engaged in the ideas. A.N.5 Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation A.A.3 Distinguish the difference between an algebraic expression and an algebraic equation A.A.4 Translate verbal sentences into mathematical equations or inequalities A.A.5 Write algebraic equations or inequalities that represent a situation A.A.6 Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable A.A.21 Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable A.A.22 Solve all types of linear equations in one variable A.A.23 Solve literal equations for a given variable A.A.24 Solve linear inequalities in one variable A.A.25 Solve equations involving fractional expressions Note: Expressions which result in linear equations in one variable. A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equations A.M.1 Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail) Many real life situations can be modeled and analyzed using linear equations. to identify the difference between an expression and an equation to simplify and solve linear equations (including all multi-step ) to describe the steps of solving equations through use of properties to clear fractions in a linear equation before solving to solve literal equations to solve and check linear inequalities to graph linear inequalities using a number line to translate verbal sentences into equations and inequalities to write algebraic equations/inequalities that represent a situation to analyze and solve problems with linear equations/inequalities to form and solve proportions Integrated Algebra Curric.doc 10

11 to solve verbal problems including fractions, percents (increase/decrease ) ratio, and proportions to compare rates Split Unit: one test for solving equations and inequalities one test for applications Amsco: Ch 6; Ch 9; Ch 12; Ch Unified: Ch3; Ch4; Integrated Algebra Curric.doc 11

12 Unit 4 Multiplying and Dividing Polynomials ~ 1.5 weeks Mid-November A.N.4 Understand and use scientific notation to compute products and quotients of numbers A.A.12 Multiply and divide monomial expressions with a common base, using the properties of exponents Note: Use integral exponents only. A.A.13 Add, subtract, and multiply monomials and polynomials A.A.14 Divide a polynomial by a monomial or binomial, where the quotient has no remainder All of the rules that apply to numbers also apply to variables. Scientific notation makes it easier to work with very large and very small numbers (really). to multiply monomials by monomials to multiply monomials by polynomials to multiply binomials by binomials to divide monomials by monomials to divide polynomials by monomials to convert between numbers in scientific notation to multiply numbers expressed in scientific notation to divide numbers expressed in scientific notation Amsco: Ch. 8 Unified: Ch. 7 Integrated Algebra Curric.doc 12

13 Unit 5 Factoring and Solving Quadratics ~ 3 weeks Early December to late December A.A.8 Analyze and solve verbal problems that involve quadratic equations A.A.19 Identify and factor the difference of two perfect squares A.A.20 Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF) A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equations A.A.27 Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots A.A.28 Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression Many real life situations can be modeled and analyzed using quadratic equations. to factor out the greatest common factor to factor trinomials with coefficient a = 1 to factor a difference of 2 perfect squares to factor completely; GCF first, then as 2 binomials ( a =1 ) to compare linear and quadratic equations to solve quadratic equations using multiplication property of zero to recognize the relationship between roots and factors of quadratic equations to analyze and solve verbal problems including proportions that result in quadratics Split unit assessment: one test on factoring one test on solving quadratics Amsco: Ch 18; ; 21-6 Unified: Ch 7 Integrated Algebra Curric.doc 13

14 Unit A 8 th Grade Geometry Unit ~ 5 weeks Early January 8.A.12 Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines 8.G.1 Identify pairs of vertical angles as congruent 8.G.2 Identify pairs of supplementary and complementary angles 8.G.3 Calculate the missing angle in a supplementary or complementary pair 8.G.4 Determine angle pair relationship when given two parallel lines cut by a transversal 8.G.5 Calculate the missing angle measurements when given two parallel lines cut by a transversal 8.G.6 Calculate the missing angle measurements when given two intersecting lines and an angle 8.G.7 Describe and identify transformations in the plane using proper function notation (rotations, reflections, translations, dilations) 8.G.8 Draw the image of a figure under rotations of 90 and 180 degrees 8.G.9 Draw the image of a figure under a reflection over a given line 8.G.10 Draw the image of a figure under a translation 8.G.11 Draw the image of a figure under a dilation 8.G.12 Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation to apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines to identify pairs of vertical angles as congruent to identify pairs of supplementary and complementary angles to calculate the missing angle in a supplementary or complementary pair to determine angle pair relationship when given two parallel lines cut by a transversal to calculate the missing angle measurements when given two parallel lines cut by a transversal to calculate the missing angle measurements when given two intersecting lines and an angle to describe and identify transformations in the plane using proper function notation ( rotations, reflections, translations, dilations. ) to draw the image of a figure under rotations of 90 and 180 degrees Integrated Algebra Curric.doc 14

15 to draw the image of a figure under a reflection over a given line to draw the image of a figure under a translation to draw the image of a figure under a dilation to identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation Utilize the 8th grade curriculum. This chapter must be completed after Unit 5 to ensure that it is done before the assessment. Integrated Algebra Curric.doc 15

16 Unit 6 Algebraic Fractions ~ 2 weeks Early January to mid-january A.A.15 Find values of a variable for which an algebraic fraction is undefined A.A.16 Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms A.A.17 Add or subtract fractional expressions with monomial or like binomial denominators A.A.18 Multiply and divide algebraic fractions and express the product or quotient in simplest form Properties of fractions apply to algebraic fractions the same way they apply to fractions. All the rules that apply to numeric fractions also apply to algebraic fractions. to identify for what values an algebraic fraction is undefined to simplify algebraic fractions by factoring: GCF and binomial factors to multiply algebraic fractions (and simplify) to divide algebraic fractions (and simplify) to add and subtract algebraic fractions with like and unlike monomial denominators (and simplify) to add and subtract algebraic fractions with like binomial denominators (and simplify) Amsco: Ch. 19 Unified: supplement Integrated Algebra Curric.doc 16

17 Unit 7 Functions and Relations ~ 1 week Mid-January to late January A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form A.A.30 Find the complement of a subset of a given set, within a given universe A.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets) A.G.3 Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations A function denotes a special relationship between independent and dependent variables. to define and identify the difference between relations and functions to identify when a relation is a function to read and use set builder notation to read and use interval notation to identify the intersection of 2 or more sets to identify the complement of a set Amsco: supplement Unified: supplement Integrated Algebra Curric.doc 17

18 Unit 8 Coordinate Geometry ~ 3.5 weeks Late January to mid-february A.A.9 Analyze and solve verbal problems that involve exponential growth and decay A.A.32 Explain slope as a rate of change between dependent and independent variables A.A.33 Determine the slope of a line, given the coordinates of two points on the line A.A.34 Write the equation of a line, given its slope and the coordinates of a point on the line A.A.35 Write the equation of a line, given the coordinates of two points on the line A.A.36 Write the equation of a line parallel to the xor y-axis A.A.37 Determine the slope of a line, given its equation in any form A.A.38 Determine if two lines are parallel, given their equations in any form A.A.39 Determine whether a given point is on a line, given the equation of the line A.A.41 Determine the vertex and axis of symmetry of a parabola, given its equation (See A.G.10) A.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions A.G.5 Investigate and generalize how changing the coefficients of a function affects its graph A.G.6 Graph linear inequalities A.G.8 Find the roots of a parabolic function graphically Note: Only quadratic equations with integral solutions. Graphs can help you analyze the relationship between two variables. to identify the difference between a relation and a function graphically. to recognize the solution set of a linear equation of two variables is represented by a line to determine if a given point is a solution ( on the line ) given the equation to find slope given two points on a line to identify the slope and y intercept given an equation in any form to graph linear equations using slope/intercept method to compare graphs of functions and their coefficients to identify if two lines are parallel given their equations to identify and graph linear equations parallel to the x and y axes to write the equations of lines parallel to x and y axes to write the equation of a line given its slope and one point to write the equation of a line given 2 points to graph linear inequalities to define vertex and axis of symmetry Integrated Algebra Curric.doc 18

19 to find vertex and axis of symmetry given the equation of a quadratic to graph parabolas to identify the roots, vertex and axis of symmetry given a parabola to compare parabolic graphs and coefficients to graph absolute value functions to graph exponential functions to apply graphs of linear, quadratic, exponential growth and decay to real world applications i.e. interpret slope as a rate of change Split Unit: one test on graphing linear equations one on graphing quadratic equations Amsco: ; 16-13; 21-8; supplement exponential graphs Unified: Ch 13; supplement parabolas, absolute value, exponential graphs Websites: Here is a great resource for Exponential Growth and decay: Integrated Algebra Curric.doc 19

20 Unit 9 Systems of Equations ~ 2.5 weeks Late February to early March A.A.7 Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables A.A.10 Solve systems of two linear equations in two variables algebraically (See A.G.7) A.A.11 Solve a system of one linear and one quadratic equation in two variables, where only factoring is required Note: The quadratic equation should represent a parabola and the solution(s) should be integers A.A.40 Determine whether a given point is in the solution set of a system of linear inequalities A.G.7 Graph and solve systems of linear equations and inequalities with rational coefficients in two variables (See A.A.10) A.G.9 Solve systems of linear and quadratic equations graphically Note: Only use systems of linear and quadratic equations that lead to solutions whose coordinates are integers. Systems allow analysis of more complicated situations. to solve linear systems graphically to solve linear systems algebraically by substitution method to solve linear systems algebraically by addition (elimination) method (include least common multiple) to analyze and solve verbal problems as systems of equations to solve linear/quadratic systems by graphing to solve linear/quadratic systems algebraically ( only factoring required, quadratic is a parabola, solutions are integers ) to determine the solution set of system of inequalities by graphing to determine if a point is in the solution set of a system of inequalities Amsco: Ch 17; 21-10; Unified: Ch 14 Integrated Algebra Curric.doc 20

21 Unit 10 Working with Shapes ~ 1.5 weeks Mid-March to late March A.G.1 Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle Note: Figures may include triangles, rectangles, squares, parallelograms, rhombuses, trapezoids, circles, semi-circles, quarter-circles, and regular polygons (perimeter only). A.G.2 Use formulas to calculate volume and surface area of rectangular solids and cylinders A.M.3 Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure Perimeter/circumference is one dimensional; area is two dimensional; volume is three dimensional. to identify when to use perimeter, area, and volume to find perimeter/circumference of polygons, circles, and circle sectors to find area of polygons, circles and circle sectors to find surface area of rectangular solids and cylinders to find the volume of rectangular solids and cylinders to apply appropriate formula given a real life situation to calculate and analyze relative error in measuring square and cubic units when error occurs in linear measure Amsco: Unified: Ch 10; Ch 6 Integrated Algebra Curric.doc 21

22 Unit 11 Radicals ~ 1.5 weeks Late March to early April A.N.2 Simplify radical terms (no variable in the radicand) A.N.3 Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form Radicals are exponents. Therefore, all the rules for exponents apply to radicals. to simplify radicals (no variable in the radicand) to multiply and divide radicals ( like and unlike radicals ) to add and subtract radicals ( like and unlike radicals ) Amsco: Ch 20 Unified: Ch 8 Integrated Algebra Curric.doc 22

23 Unit 12 Trigonometry ~ 2 weeks Mid-April to late April A.A.42 Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides A.A.43 Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle A.A.44 Find the measure of a side of a right triangle, given an acute angle and the length of another side A.A.45 Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sides Given certain information about a right triangle, you can find the measures of sides and angles. to apply the Pythagorean Theorem to real world applications to identify and form trigonometric ratios ( sine, cosine, tangent) to find an acute angle given lengths of sides to find length of a side given an acute angle and one side to trigonometric ratios to real world problems i.e. angle of depression and angle of elevation to determine when to use the Pythagorean theorem versus trigonometry Amsco: 21-5; 21-5; Ch 22 Unified: Supplement Integrated Algebra Curric.doc 23

24 Unit 13 Statistics ~ 3 weeks Early May to late May A.S.1 Categorize data as qualitative or quantitative A.S.2 Determine whether the data to be analyzed is univariate or bivariate A.S.3 Determine when collected data or display of data may be biased A.S.4 Compare and contrast the appropriateness of different measures of central tendency for a given data set A.S.5 Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set of data A.S.6 Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a box-and-whisker plot A.S.7 Create a scatter plot of bivariate data A.S.8 Construct manually a reasonable line of best fit for a scatter plot and determine the equation of that line A.S.9 Analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-and-whisker plot A.S.10 Evaluate published reports and graphs that are based on data by considering: experimental design, appropriateness of the data analysis, and the soundness of the conclusions A.S.11 Find the percentile rank of an item in a data set and identify the point values for first, second, and third quartiles A.S.12 Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none) A.S.13 Understand the difference between correlation and causation A.S.14 Identify variables that might have a correlation but not a causal relationship A.S.15 Identify and describe sources of bias and its effect, drawing conclusions from data A.S.16 Recognize how linear transformations of one-variable data affect the data s mean, median, mode, and range A.S.17 Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation Statistics can be used to analyze data to help you make decisions. Statistics can be used to mislead people (including you). to categorize data as qualitative or quantitative Integrated Algebra Curric.doc 24

25 to determine univariate or bivariate to determine if collected or displayed data is bias to identify source of bias and effect ( using data ) to determine measures of central tendency and when each is most appropriate for a given set of data to recognize how linear transformations of 1 variable data affect the data s mean, median, mode and range to construct frequency and cumulative frequency histograms to find percentile rank and find points values for quartiles to find minimum, maximum and quartiles of a set of data to construct a box and whisker plot to analyze and interpret histograms and box and whisker plots to create bivariate scatter plot to determine line of best fit and its equation to utilize line of best fit to make predictions (involving interpolation or extrapolation) to identify relationship of independent and dependent variables from scatter plot (pos, neg, none) to identify the difference between correlation and causation to identify variables that might have correlation without causal to evaluate published reports and graphs based on data: experimental design, appropriateness of data analysis, soundness of conclusions Amsco: > 15-6; 16-9 Unified: Ch 12; supplement most Integrated Algebra Curric.doc 25

26 Unit 14 Probability ~ 2 weeks Late May to early June A.N.6 Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s) A.N.7 Determine the number of possible events, using counting techniques or the Fundamental Principle of Counting A.N.8 Determine the number of possible arrangements (permutations) of a list of items A.S.18 Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces A.S.19 Determine the number of elements in a sample space and the number of favorable events A.S.20 Calculate the probability of an event and its complement A.S.21 Determine empirical probabilities based on specific sample data A.S.22 Determine, based on calculated probability of a set of events, if: some or all are equally likely to occur one is more likely to occur than another whether or not an event is certain to happen or not to happen A.S.23 Calculate the probability of: a series of independent events a series of dependent events two mutually exclusive events two events that are not mutually exclusive Any event in life has a probability associated with it that ranges from certain to impossible. to recognize the difference between theoretical vs. empirical to determine empirical probabilities based on data to analyze the sample space of an experiment to determine the likelihood a given event will occur (include complement) to know the definition of conditional probability to utilize conditional probability to solve for probabilities in finite sample spaces to know the difference between and find the probability of single and compound events to calculate the probability of a series of independent events to calculate the probability of a series of dependent events to calculate the probability of two mutually exclusive events Integrated Algebra Curric.doc 26

27 to calculate the probability two events that are not mutually exclusive to use the counting principle to determine the number of possible outcomes to evaluate factorials to determine the number of possible arrangements (permutations) of a list of items Amsco: Ch 13; > 14-5 Unified: Ch 11 Integrated Algebra Curric.doc 27

28 Unit 15 Review for Regents Exam ~? weeks Mid-June All Passing the Integrated Algebra Regents Exam is a graduation requirement. to ace the Integrated Algebra Regents exam Integrated Algebra Curric.doc 28