Ref: GIS Math G 8 A, B, E, F

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1 Ref: GIS Math G 8 A, B, E, F SUBJECT : Math TITLE OF COURSE : Algebra 1, Geometry GRADE LEVEL : 8 DURATION : ONE YEAR NUMBER OF CREDITS : 1.25 Goals: The Number System 8.NS Know that there are numbers that are not rational, and approximate them by rational numbers. 1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of 2, show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Expressions and Equations 8.EE Work with radicals and integer exponents. 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, = 3 3 = 1/33 = 1/ Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. 3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as and the population of the world as 7 109, and determine that the world population is more than 20 times larger. 4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of

2 appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Understand the connections between proportional relationships, lines, and linear equations. 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. 6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Analyze and solve linear equations and pairs of simultaneous linear equations. 7. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8. Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Functions 8.F Define, evaluate, and compare functions. 1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1 2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1),(2, 4) and (3, 9), which are not on a straight line. Use functions to model relationships between quantities. 4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and

3 initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Geometry 8.G Understand congruence and similarity using physical models, transparencies, or geometry software. 1. Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. 2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. 5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Understand and apply the Pythagorean Theorem. 6. Explain a proof of the Pythagorean Theorem and its converse. 7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. 8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Resources: 1- HMH Algebra 1, Geometry text book. 2- Online resources 3- HMH attached resources CD S (lesson tutorial videos, power point presentations, one stop planer,..) 4- Internet. 5- E-games and links 6- Teacher s Handouts

4 Course Content and Objectives: Algebra 1 Unit 1: Quantities and Modeling Module 2: Algebraic Models 2.2: Creating and solving equations Creating Equations from Verbal Descriptions Creating and Solving Equations Involving the Distributive Property Creating and Solving Equations with Variables on Both Sides Constructing Equations from an Organized Table 2.3: Solving for a variable Rearranging Mathematical Formulas Rearranging Scientific Formulas Rearranging Literal Equations 2.4: Creating and solving inequalities Creating Inequalities from Verbal Descriptions Creating and Solving Inequalities Involving the Distributive Property Creating and Solving Inequalities with Variables on Both Sides 2.5: Creating and solving compound inequalities Solving Compound Inequalities Involving AND Solving Compound Inequalities Involving OR Creating Compound Inequalities From Graphs Expressing Acceptable Levels with Compound Inequalities Unit 2: Understanding functions Module 3: Functions and models 3.1: Graphing relationships Interpreting Graphs Relating Graphs to Situations Sketching Graphs for Situations 3.2: Understanding relations and functions Understanding Relations Recognizing Functions Understanding the Vertical Line Test 3.3: Modeling with functions Identifying Independent and Dependent Variables Applying Function Notation Modeling Using Function Notation Choosing a Reasonable Domain and Range 3.4: Graphing functions Graphing Functions Using a Given Domain Graphing Functions Using a Domain of All Real Numbers Using a Graph to Find Values Modeling Using a Function Graph

5 Unit 3: Linear functions, equations, and inequalities Module 5: Linear functions 5.1: Understanding linear functions Recognizing Linear Functions Proving Linear Functions Grow by Equal Differences Over Equal Intervals Graphing Linear Functions Given in Standard Form Modeling with Linear Functions 5.2: Using intercepts Identifying Intercepts Determining Intercepts of Linear Equations Interpreting Intercepts of Linear Equations Graphing Linear Equations Using Intercepts 5.3: Interpreting rate of change and slope Determining Rates of Change Determining the Slope of a Line Determining Slope Using the Slope Formula Interpreting Slope Module 6: Forms of linear equations 6.1: Slope- intercepts form Graphing Lines Given Slope and y-intercept Creating Linear Equations in Slope-Intercept Form Graphing from Slope-Intercept Form Determining Solutions of Equations in Two Variables 6.2: Point-slope form Deriving Point-Slope Form Creating Linear Equations Given Slope and a Point Creating Linear Models Given Slope and a Point Creating Linear Equations Given Two Points Creating A Linear Model Given Two Points 6.3: Standard form Comparing Forms of Linear Equations Creating Linear Equations in Standard Form Given Slope and a Point Creating Linear Equations in Standard Form Given Two Points Creating Linear Models in Standard Form 6.4: Transforming Linear Functions Building New Linear Functions by Translating Building New Linear Functions by Stretching, Shrinking, or Reflecting E Understanding Function Families Interpreting Parameter Changes in Linear Models 6.5: Comparing properties of linear functions Comparing Properties of Linear Functions Given Algebra and a Description Comparing Properties of Linear Functions Given Algebra and a Table Comparing Properties of Linear Functions Given a Graph and a Description

6 Unit 5: Linear systems and piecewise-defined functions Module 11: Solving systems of linear equations 11.1: Solving linear systems by graphing Solving Consistent, Independent Linear Systems by Graphing Solving Special Linear Systems by Graphing Estimating Solutions of Linear Systems by Graphing Interpreting Graphs of Linear Systems to Solve Problems 11.2: Solving linear systems by substitution Exploring the Substitution Method of Solving Linear Systems Solving Consistent, Independent Linear Systems by Substitution Solving Special Linear Systems by Substitution Solving Linear System Models by Substitution 11.3: Solving linear systems by adding or subtracting Exploring the Effects of Adding Equations Solving Linear Systems by Adding or Subtracting Solving Special Linear Systems by Adding or Subtracting Solving Linear System Models by Adding or Subtracting 11.4: Solving linear systems by multiplying first Understanding Linear Systems and Multiplication Proving the Elimination Method with Multiplication Solving Linear Systems by Multiplying First Solving Linear System Models by Multiplying First Module 12: Modeling with linear systems 12.1: Creating systems of linear equations Creating Linear System Models by Changing Parameters Creating Linear System Models from Verbal Descriptions Creating Linear System Models from Tables Creating Linear System Models from Graphs 12.2: Graphing systems of linear inequalities Determining Solutions of Systems of Linear Inequalities Solving Systems of Linear Inequalities by Graphing Graphing Systems of Inequalities with Parallel Boundary Lines 12.3: Modeling with linear systems Modeling Real-World Constraints with Systems Modeling Real-World Constraints with Systems of Linear Equations Modeling Real-World Constraints with Systems of Linear Inequalities Unit 7: Polynomial Operations Module 17: Adding and subtracting polynomials 17.1: Understanding polynomial expressions Identifying Monomials Classifying Polynomials Writing Polynomials in Standard Form Simplifying Polynomials Evaluating Polynomials 17.2: Adding polynomials expressions Adding Polynomials Using a Vertical Format

7 Adding Polynomials Using a Vertical Format Adding Polynomials Using a Horizontal Format Modeling with Polynomials 17.3 Subtracting polynomial expressions Subtracting Polynomials Using a Vertical Format Subtracting Polynomials Using a Horizontal Format Modeling with Polynomials 18.1 Multiplying Polynomial Expressions by Monomials Multiplying Monomials Multiplying a Polynomial by a Monomial Multiplying a Polynomial by a Monomial to Solve a Real-World Problem 18.2 Multiplying polynomial expressions Modeling Binomial Multiplication Multiplying Binomials Using the Distributive Property Multiplying Binomials Using FOIL Multiplying Polynomials Modeling with Polynomial Multiplication 18.3 Special Products of Binomials Multiplying (a + b) 2 Multiplying (a - b) 2 Multiplying (a + b)(a b) Modeling with special products Geometry Unit 1: Transformations and congruence Module 1 Tools of Geometry 1.1: Segment length and midpoints. Exploring Basic Geometric Terms Constructing a Copy of a Line Segment Using the Distance Formula Finding a Midpoint Finding Midpoints on the Coordinate Plane 1.2 Angle Measures and Angle Bisectors. Constructing a Copy of an Angle Naming Angles and Parts of an Angle Measuring Angles Constructing an Angle Bisector 1.3 Representing and Describing Transformations Performing Transformations Using Coordinate Notation Describing Rigid Motions Using Coordinate Notation Describing Non rigid Motions Using Coordinate Notation 1.4 Reasoning and Proof.

8 Exploring Inductive and Deductive Reasoning Introducing Proofs Using Postulates about Segments and Angles Using Postulates about Lines and Planes Module 2 Transformations and symmetry 2.1 Exploring translations Translating Figures using vectors Drawing translations on a coordinate plane Specifying Translation vectors 2.2Reflections Exploring reflections Reflection figures using graph paper Drawing reflections on a coordinate plane Specifying Lines of reflection Applying reflections 2.3 Rotations Exploring Rotations Rotating figures using a ruler and protractor Drawing rotations on a coordinate plane Simplifying rotation Angles 2.4 Investigating Symmetry Identifying Line symmetry Identifying rotational symmetry Describing Symmetries Module 3 Congruent Figures 3.1Sequences of transformations Combining rotations or reflections Combining rigid transformations Combining non rigid transformations Predicting the effect of transformations 3.2 Proving figures are congruent using rigid motions Confirming congruence Determining if figures are congruent Finding a sequence of rigid motions Investigating Congruent segments and angles 3.3 Corresponding Parts of Congruent Figures are Congruent Exploring Congruence of Parts of Transformed Figures Exploring Congruence of Parts of Transformed Figures. Corresponding Parts of Congruent Figures Are Congruent Applying the Properties of Congruence. Using Congruent Corresponding Parts in a Proof. Unit 2: Lines angles and triangles Module 4 Lines and Angles

9 4.1 Angles Formed by Intersecting Lines. Exploring Angle Pairs Formed by Intersecting Lines Exploring Angle Pairs Formed by Intersecting Lines Proving the Vertical Angles Theorem Using Vertical Angles Using Supplementary and Complementary Angles. 4.2 Transversals and Parallel Lines. Exploring Parallel Lines and Transversals Proving that Alternate Interior Angles are Congruent. Proving that Corresponding Angles are Congruent. Using Parallel Lines to Find Angle Pair Relationships. 4.3 Proving Lines are Parallel. Writing Converses of Parallel Line Theorems Proving that Two Lines are Parallel Constructing Parallel Lines Using Angle Pair Relationships to Verify Lines are Parallel 4.4 Perpendicular Lines Constructing Perpendicular Bisectors and Perpendicular Lines. Proving the Perpendicular Bisector Theorem Using Reflections Proving the Converse of the Perpendicular Bisector Theorem Proving Theorems about Right Angles 4.5 Equations of Parallel and Perpendicular Lines Exploring Slopes of Lines Writing Equations of Parallel Lines Writing Equations of Perpendicular Lines Module 5 Triangle Congruence Criteria 5.1 Exploring What Makes Triangles Congruent Transforming Triangles with Congruent Corresponding Parts Deciding If Triangles are Congruent by Comparing Corresponding Parts Applying Properties of Congruent Triangles 5.2 ASA Triangle Congruence Drawing Triangles Given Two Angles and a Side Justifying ASA Triangle Congruence Deciding Whether Triangles Are Congruent Using ASA Triangle Congruence Proving Triangles Are Congruent Using ASA Triangle Congruence 5.3 SAS Triangle Congruence Drawing Triangles Given Two Sides and an Angle Justifying SAS Triangle Congruence Deciding Whether Triangles are Congruent Using SAS Triangle Congruence Proving Triangles Are Congruent Using SAS Triangle Congruence 5.4 SSS Triangle Congruence Constructing Triangles Given Three Side Lengths Justifying SSS Triangle Congruence Proving Triangles Are Congruent Using SSS Triangle Congruence Applying Triangle Congruence

10 Module 6 Applications of Triangle Congruence 6.1 Justifying Constructions Using a Reflective Device to Construct a Perpendicular Line Justifying the Copy of an Angle Construction Proving the Angle Bisector and Perpendicular Bisector Constructions 6.2 AAS Triangle Congruence Exploring Angle-Angle-Side Congruence Justifying Angle-Angle-Side Congruence Using Angle-Angle-Side Congruence. Applying Angle-Angle-Side Congruence 6.3 HL Triangle Congruence Is There a Side-Side-Angle Congruence Theorem? Justifying the Hypotenuse-Leg Congruence Theorem Applying the HL Triangle Congruence Theorem Course Sequence. Algebra 1 Term 1 Module 2: Algebraic Models 2.2: Creating and solving equations 2.3: Solving for a variable 2.4: Creating and solving inequalities 2.5: Creating and solving compound inequalities Module 3: Functions and models 3.1: Graphing relationships 3.2: Understanding relations and functions 3.3: Modeling with functions 3.4: Graphing functions Module 5: Linear functions 5.1: Understanding linear functions 5.2: Using intercepts Term 2 Module 5: Linear functions 5.3: Interpreting rate of change and slope Module 6: Forms of linear equations 6.1: Slope intercept form 6.2: Point-slope form 6.3: Standard form Module 11: Solving systems of linear equations 11.1: Solving linear systems by graphing

11 11.2: Solving linear systems by substitution 11.3: Solving linear systems by adding or subtracting 11.4: Solving linear systems by multiplying first Term 3 Module 12: Modeling with Linear Systems 12.1 : Creating Systems of Linear Equations 12.2 : Graphing Systems of Linear Inequalities 12.3 : Modeling with Linear Systems Module 17: Adding and subtracting polynomials 17.1: Understanding polynomial expressions 17.2: Adding polynomials expressions 17.3: Subtracting polynomial expressions Module 18: Multiplying polynomials 18.1: Multiplying polynomial expressions 18.2: Multiplying polynomial expressions 18.3: Special products of binomials Geometry Term 1 Module 1 Tools of Geometry 1.1: Segment length and midpoints. 1.2 Angle Measures and Angle Bisectors. 1.3 Representing and Describing Transformations 1.4 Reasoning and Proof. Module 2: Transformations and symmetry 2.1: Translations 2.2: Reflections 2.3: Rotations 2.4: Investigating Symmetry Module 3: Congruent figures 3.1: Sequences of transformations 3.2: Proving figures are congruent using rigid motions Term 2 Module 3: Congruent figures 3.3: Corresponding parts of congruent figures are congruent. Module 4 Lines and Angles 4.1 Angles Formed by Intersecting Lines. 4.2 Transversals and Parallel Lines. 4.3 Proving Lines are Parallel 4.4 Perpendicular Lines 4.5 Equations of Parallel and Perpendicular Lines

12 Module 5 Triangle Congruence Criteria 5.1 Exploring What Makes Triangles Congruent 5.2 ASA Triangle Congruence 5.3 SAS Triangle Congruence 5.4 SSS Triangle Congruence Term 3 Module 6 Applications of Triangle Congruence 6.1 Justifying Constructions 6.2 AAS Triangle Congruence 6.3 HL Triangle Congruence Assessment Tools and Strategies: Strategies o 1 st The students will be provided with study guides or mock tests on the school website in the students portal, based on our curriculum manual, bench marks and objectives before every quiz, test, or exam. o 2 nd The students will be tested based on what they have practiced at home from the study guides or mock tests mentioned before. o 3 rd The evaluation will be based on what objectives did the students achieve, and in what objectives do they need help, through the detailed report that will be sent to the parents once during the semester and once again with the report card. Tests and quizzes will comprise the majority of the student s grade. There will be one major test given at the end of each chapter. Warm-up problems for review, textbook assignments, worksheets, etc. will comprise the majority of the daily work. Home Works and Assignments will provide students the opportunity to practice the concepts explained in class and in the text. Students will keep a math notebook. In this notebook students will record responses to daily warmup problems, lesson activities, post-lesson wrap-ups, review work, and daily textbook assignments. Class work is evaluated through participation, worksheets, class activities and group work done in the class. Passing mark 60 % Grading Policy: Term 1 Terms 2 and 3 Weigh t Frequency Weight Frequency Class Work (Should include MAP to Khan and Beyond the 20% Formative (For every New lesson) and Class Work (Should include MAP to Khan and Beyond the 25% Formative (For every New

13 standard Questions). Summative (once a term) standard Questions). lesson) and Summative (once a term) Homework 5% At least 4 times Homework 5% At least 4 times Quizzes (Should include MAP to Khan and Beyond the standard Questions). Project Based Learning 30% 2 / term Quizzes (Should include MAP to Khan and Beyond the standard Questions). 10% Once in a term. Project Based Learning 40% 2/term 15% Once in a term. POP Quizzes 10% At least 5 times per term. POP Quizzes 10% At least 5 times per term. MAP (Based on students results) 5% Once per term. MAP (Based on students results) 5% Once per term Student s/gr oup work. Bonus (3 %) Student s/gro up work. Bonus (3 %) Mid-Year Exam 20% Total 100 Total 100 Performance Areas (skills). Evaluation, graphing, Application, and Analysis of the Mathematical concepts and relating them to daily life, through solving exercises, word problems and applications... Communication and social skills: through group work, or presentation of their own work. Technology skills: using digital resources and graphic calculators or computers to solve problems or present their work. Note: The following student materials are required for this class:

14 Graph paper. Scientific Calculator (Casio fx-991 ES Plus) Done by Femi Antony Math teacher

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