act/sat math preparation - findlay city · pdf fileact/sat math preparation (course #049)...

ACT/SAT Math Preparation (Course #049)

Course of Study

Findlay City Schools 2008

ACT/SAT Math Preparation

Table of Contents

1. Findlay City Schools Mission Statement and Beliefs 2. ACT/SAT Math Preparation Curriculum Map

3. ACT/SAT Math Preparation Indicators and Course of

Study

ACT/SAT Math Preparation Course of Study Writing Team

Ellen Laube

Karen Ouwenga

ACT/SAT Math Preparation CURRICULUM MAP

WEEK CHAPTER TOPIC INDICATORS 1 Pre Test Diagnostic Test,

Scoring and Analysis All

2 6 Pre Algebra I (8N1) (8N2) (8N3) (8N4) (8N7) (8N8) (9N1) (9N2) (9N3) (9N4) (9N5)

3 6 Pre Algebra I (8N1) (8N2) (8N3)

(8N4) (8N7) (8N8) (9N1) (9N2) (9N3) (9N4) (9N5)

4 7 Pre Algebra II (8N6) (8P7) (8P8)

(8P9) (8D4) (8D11) (9D7) (9D8) (9D9) (9D10) (10D1) (10D2)

5 7 Pre Algebra II (8N6) (8P7) (8P8)

(8P9) (8D4) (8D11) (9D7) (9D8) (9D9) (9D10) (10D1) (10D2)

6 8 Elementary Algebra (8P3) (8P7) (8P8)

(8P12) (9P11) (9P10)

7 8 Elementary Algebra (8P3) (8P7) (8P8) (8P12) (9P11) (9P10)

8 9 Intermediate Algebra (8P8) (8P9) (8P10)

(8P11) (8P12) (9P4) (9P5) (9P6) (9P9) (9P10) (10P6) (10P7) (11N1) (11N3) (11N4) (11N7) (12N1)

9 9 Intermediate Algebra (8P8) (8P9) (8P10) (8P11) (8P12) (9P4) (9P5) (9P6) (9P9) (9P10) (10P6) (10P7) (11N1) (11N3) (11N4) (11N7) (12N1)

10 10 Coordinate Geometry (8P1) (8P3) (8P7) (8P9)

(8P10) (8P11) (8P12) (8P13) (8P15) (9P6) (9P8) (9P9) (9P15) (10P8) (10P9) (10P10) (11P3) (11P10)

11 10 Coordinate Geometry (8P1) (8P3) (8P7) (8P9) (8P10) (8P11) (8P12) (8P13) (8P15) (9P6) (9P8) (9P9) (9P15) (10P8) (10P9) (10P10) (11P3) (11P10)

12 10 Coordinate Geometry (8P1) (8P3) (8P7) (8P9)

(8P10) (8P11) (8P12) (8P13) (8P15) (9P6) (9P8) (9P9) (9P15) (10P8) (10P9) (10P10) (11P3) (11P10)

13 11 Plane Geometry (8M4) (8M5) (8M10)

(9M3) (9M4) (8G1) (8G2) (8G3) (8G4) (8G5) (10G1) (10G2) (10G3) (10G4) (10G5)(10G6) (10G10)

14 11 Plane Geometry (8M4) (8M5) (8M10)

(9M3) (9M4) (8G1) (8G2) (8G3) (8G4) (8G5) (10G1) (10G2) (10G3) (10G4) (10G5)(10G6) (10G10)

15 12 Trigonometry (9G1) (9G2) (11G4)

(12G2)

16 12 Trigonometry (9G1) (9G2) (11G4)

(12G2)

17 Exam Review EXAM REVIEW All

18 EXAMS – 1st

SEMESTER Textbook Name: Preparing for the ACT Mathematics and Science Reasoning (Semester 1) Publisher: Amsco Authors: Robert D. Postman ISBN # 1-56765-511-4 Indicator Key: Grade Strand Indicator# Example: 11G2: 11th grade, Geometry strand, Indicator #2

N = Number, Number Sense M = Measurement G = Geometry P = Patterns, Functions and Algebra D = Data Analysis and Probability

STANDARD: Number Sense BENCHMARKS: (A) Use scientific notation to express large numbers and numbers less than one. (B) Identify subsets of the real number system. (C) Apply properties of operations and the real number system, and justify when they hold for a set of numbers, (E): Compare order and determine equivalent forms of real numbers. (F) Explain the effects of operations on the magnitude of quantities. (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (H) Find the square root of perfect squares, and approximate the square root of non-perfect squares (I) Estimate, compute, and solve problems involving scientific notation, square roots, and numbers with integer exponents. (8N1) Use scientific notations to express large numbers and small numbers (8N2) Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system. (8N3) Apply order of operations to simplify expressions and perform computations involving integer’s exponents and radicals, (8N4) Explain and use the inverse and identify properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations, (8N7) Find the square root of perfect square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., Square root of 130 is between 11 and 12, Formulas) to generalize situations and solve problems (8N8) Add, subtract, multiply, divide and compare numbers written in scientific notation. (9N1) Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication, (9N2) Compare order and determine equivalent forms for rational and irrational numbers. (9N3) Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities. (9N4) Demonstrate fluency in computations using real numbers. (9N5) Estimate the solutions for problem situations involving square and cube roots.

TOPIC/UNIT: Chapter 6 Pre Algebra I Time Line: 10 days KNOW

• Whole numbers • Whole number computations • Decimals • Decimal Computation • Factors, Divisibility, and

Primes • Square Roots, Exponents, and

Scientific Notation • Fractions • Addition and Subtraction of

Fractions and Mixed Numbers • Multiplication and Division of

Fractions and Mixed Numbers • Positive and Negative

Numbers • Order of Operations

DO • Compute problems involving

whole numbers, decimals, fractions, positive and negative numbers and scientific notation

• Identify factors and prime numbers

• Interoperate numbers raised to a power

• Use order of operations in computations

PRE-ASSESSMENT: • Informal questioning • Teacher observation • Model Math ACT I pgs. 463-

470 student text

ASSESSMENT: • Teacher generated

GRAPHIC ORGANIZER & OR TECHNOLOGY: Calculator Tips pgs. 44, 45, 48, 50, 55, 61, 62, 65, 66, 68, 77, 81.

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Model Act Problem pgs. 46, 50, 53, 57, 60, 63, 70, 74, 76, 80, 82. Cumulative ACT Practice pgs. 84-85

BEST PRACTICES: • Cooperative Learning • Group work • Guided Practice

RESOURCES: • Student Manual

TESTING VOCABULARY: • Whole numbers pg. 44 • Whole number computations

pg. 48 • Decimals pg. 52 • Decimal Computation pg. 55 • Factors, Divisibility, and

Primes pg. 58 • Square Roots, Exponents, and

Scientific Notation pg. 61 • Fractions pg. 64 • Addition and Subtraction of

Fractions and Mixed Numbers pg. 68

• Multiplication and Division of Fractions and Mixed Numbers pg. 72

• Positive and Negative Numbers pg. 75

• Order of Operations pg. 81

HISTORICAL/MODERN LINK:

• Pay Checks pg. 51 • Averages pg. 58 • Packaging pg. 71

STANDARD: Number, Number Sense and Operation BENCHMARKS: (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (8N6) Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. STANDARD: Patterns, Functions and Algebra BENCHMARK: (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (F) Solve and graph linear equations and inequalities. (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (8P8) Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. (8P9) Solve linear equations and inequalities graphically, symbolically and using technology. STANDARD: Data Analysis and Probability BENCHMARK: (A) Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatter plots, measures of center and variability. (C) Compare the characteristics of the mean, median, and mode for a given set of data, and explain which measure of center best represents the data (D) Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data. (H) Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes. (I) Model and solve problems situations involving direct and inverse variation. (J) Compute probabilities of compound events, independent events, and simple dependent events. (K) Make predictions based on theoretical probabilities and experimental results. (8D4) Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range,

percentiles). (8D11) Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities. (9D7) Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations. (9D8) Describe, create and analyze a sample space and use it to calculate probability. (9D9) Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about, probabilities associated with those events. (9D10) Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events. (10D1) Describe measures of center and the range verbally, graphically and algebraically. (10D2) Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology. (10D4) Identify outliers on a data display; e.g., use interquartile range to identify outliers on a box-and-whisker plot. TOPIC/UNIT: Chapter 7 Time Line: 10 Days

KNOW • Percent • Percent Problems • Ratio and Proportion • Statistics-Mean, Median,

Mode • Data Collections,

Representation, and Interpretation

• Probability • Elementary Counting

Techniques • Writing Linear Expressions

and Equations • Solving Linear Equations • Cumulative ACT Practice-Pre-

Algebra

DO • Solve problems involving

percent, ratio, proportion, mean, median, mode and probability

• Collect, interpret and display data.

• Write linear expressions and equations

• Solve linear equations

PRE-ASSESSMENT: Informal questioning Teacher observation Model Math ACT I pgs. 87, 92, 96, 99, 103, 108, 113, 115, 120 student text

ASSESSMENT: Teacher generated Subtest pg. 123

GRAPHIC ORGANIZER & OR TECHNOLOGY: Calculator Tips pgs. 87, 91, 95, 98, 110, 117

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Model Act Problem Cumulative ACT Practice pgs. 122-123

BEST PRACTICES: Cooperative Learning Group work Guided Practice

RESOURCES: Student Manual

TESTING VOCABULARY: Topic Review

• Percent pg.86 • Percent Problems pg. 89 • Ratio and Proportion pg. 94 • Statistics-Mean, Median,

Mode pg. 98 • Data Collections,

Representation, and Interpretation pg. 101

• Probability pg. 107 • Elementary Counting

Techniques pg. 110 • Writing Linear Expressions

and Equations pg. 114 • Solving Linear Equations • Cumulative ACT Practice-Pre-

Algebra pg. 117


• Free Throws pg. 87 • Sales Tax pg. 94 • Gas Prices pg. 97 • Monthly Budget pg 102

STANDARD: Patterns, Functions and Algebra BENCHMARKS: (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs, or equations. (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (G) Solve quadratic equations with real roots by graphing, formula and factoring (8P3) Identify functions as linear or nonlinear based on information given in a table, graph or equation. (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (8P8) Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. (8P12) Solve simple quadratic equations graphically. (9P11) Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only). (9P10) Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology. TOPIC/UNIT: Chapter 8 Time Line: 10 Days

KNOW • Evaluating Formulas and

Expressions • Exponents and Radicals • Operations with Radicals • Polynomials • Operations on Polynomials • Factoring Polynomials • Quadratic Equations

DO • Manipulate polynomials • Solve problems involving

radicals and exponents • Solve quadratic equations

PRE-ASSESSMENT: Informal questioning Teacher observation Model Math ACT I pgs. 127, 130, 133, 139, 143, 147 student text


GRAPHIC ORGANIZER & OR TECHNOLOGY: Calculator Tips pgs. 125, 130, 132, 136, 141, 146.

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Model Act Problem Cumulative ACT Practice pg. 149 pgs. 151-153.




• Evaluating Formulas and Expressions

• Exponents and Radicals • Operations with Radicals • Polynomials • Operations on Polynomials • Factoring Polynomials • Quadratic Equations


• Distance pg. 150 • Voltage pg. 149

STANDARD: Patterns, Functions and Algebra 8-10 BENCHMARKS: (D): Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers. (E): Compare, order and determine equivalent forms of real numbers. (F) Explain the effects of operations on the magnitude of quantities. (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (H) Find the square root of perfect squares, and approximate the square root of non-perfect squares (8P8) Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. (8P9) Solve linear equations and inequalities graphically, symbolically and using technology. (8P10) Solve 2 by 2 systems of linear equations graphically and by simple substitution. (8P11) Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution. (8P12) Solve simple quadratic equations graphically. (9P4) Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words. (9P5) Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. (9P9) Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology. (9P10) Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology. (10P6) Solve equations and inequalities having rational expressions as coefficients and solutions. (10P7) Solve systems of linear inequalities. STANDARD: Number, Number Sense and Operations Standard 11-12 BENCHMARK: A. Demonstrate that vectors and matrices are systems having some of the same properties of the real number system. C. Apply factorials and exponents, including fractional exponents, to solve

practical problems. D. Demonstrate fluency in operations with real numbers, vectors and matrices, using mental computation or paper and pencil calculations for simple cases and technology for more complicated cases. E. Represent and compute with complex numbers. (11N1) Determine what properties hold for matrix addition and matrix multiplication; e.g., use examples to show addition is commutative and when multiplication is not commutative. (11N3) Represent complex numbers on the complex plane. (11N4) Use matrices to represent given information in a problem situation. (11N7) Compute sums, differences, products and quotients of complex numbers. (12N1) Determine what properties (closure, identity, inverse, commutative and associative) hold for operations with complex numbers. STANDARD: Patterns, Functions and Algebra 11-12 BENCHMARKS: A. Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior. (11P7) Model and solve problems with matrices and vectors. TOPIC/UNIT: Chapter 9 Time Line: 10 Days

KNOW • Intermediate Algebra • Solving Inequalities • Absolute Value Equations and

Inequalities • Solving Systems of Linear

Equations • Rational and Radical

Expressions • Solving Quadratic Equations • Solving Quadratic Inequalities • Complex Numbers • Patterns, Sequences, and

Modeling • Matrices

DO • Solve problems involving

inequalities, absolute values, systems of equations, quadratic equations and inequalities, complex numbers and matrices.

• Evaluate rational and radical expressions.

PRE-ASSESSMENT: Informal questioning Teacher observation Model Math ACT I pgs. 463-470 student text


GRAPHIC ORGANIZER & OR TECHNOLOGY: Calculator Tips pgs. 163, 171

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Model Act Problems pgs. 160, 162, 165, 169, 171, 174, 176, 179, 181. Cumulative ACT Practice pg. 184




• Intermediate Algebra pg. 157 • Solving Inequalities pg. 161 • Absolute Value Equations and

Inequalities pg. 163

HISTORICAL/MODERN LINK: • Swimming pools pg. 172 • Picture frames pg. 172

• Solving Systems of Linear Equations pg. 167

• Rational and Radical Expressions pg. 170

• Solving Quadratic Equations pg. 173

• Solving Quadratic pg 175 Inequalities pg 177 • Complex Numbers pg. 177 • Patterns, Sequences, and

Modeling pg. 180

STANDARD: Patterns, Functions and Algebra 8-10 BENCHMARKS: (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs, or equations. (C) Translate information from one representation (words, table, graph, or equation) to another representation of a relation or function. (D) Use algebraic representations, such as tables, graphs, expressions, functions, and inequalities, to model and solve problem situations. (F) Solve and graph linear equations and inequalities., (G) Solve quadratic equations with real roots by graphing, formula and factoring (H) Solve systems of linear equations involving two variables graphically and symbolically., (J) Describe and interpret rates of change from graphical and numerical data. (8P1) Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. (8P3) Identify functions as linear or nonlinear based on information given in a table, graph or equation. (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (8P9) Solve linear equations and inequalities graphically, symbolically and using technology. (8P10) Solve 2 by 2 systems of linear equations graphically and by simple substitution. (8P11) Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution. (8P12) Solve simple quadratic equations graphically. (8P13) Compute and interpret slope, midpoint and distance given a set of ordered pairs. (8P15) Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. (9P8) Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point.

(9P9) Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology. 9P15) Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs. (10P8) Graph the quadratic relationship that defines circles. (10P9) Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals. (10P10) Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions. STANDARD: Patterns, Functions and Algebra 11-12 BENCHMARK: A. Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior. (11P3) Describe and compare the characteristics of the following families of functions: quadratics with complex roots, polynomials of any degree, logarithms, and rational functions; e.g., general shape, number of roots, domain and range, asymptotic behavior. (11P10) Describe the characteristics of the graphs of conic sections. TOPIC/UNIT: Chapter 10 Time Line: 15 Days

KNOW • Graphing Inequalities on a

Number Line • Graphing Equations on the

Coordinate Plane • Distance and Midpoint

Formulas • Graphing Systems of

Inequalities on the Coordinate Plane

• Graphing Conic Sections

DO • Graph inequalities, equations,

systems of equations, systems of inequalities and conic sections.

PRE-ASSESSMENT: Informal questioning Teacher observation Model Math ACT I pgs. 463-470 student text

ASSESSMENT: Teacher generated Subtest pgs. 215-216

GRAPHIC ORGANIZER & OR TECHNOLOGY: Calculator Tips pgs. 187, 189, 192, 199, 204, 207

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Model Act Problems pgs. 187, 194, 198, 203, 211 Cumulative ACT Practice pgs. 214-215 and 217-218.




• Graphing Inequalities on a Number Line pg. 186

• Graphing Equations on the Coordinate Plane pg. 189

• Distance and Midpoint Formulas pg. 197

• Graphing Systems of Inequalities on the

HISTORICAL/MODERN LINK: NA

Coordinate Plane pg. 200 • Graphing Conic Sections pg.

206

STANDARD: Measurement BENCHMARKS: (A) Solve increasingly complex non-routine measurement problems and check for reasonableness of results, (B) Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision (C) Apply indirect measurement techniques, tools and formulas, as appropriate to find perimeter, circumference and area of circles, triangles, quadrilaterals and composite shapes, and to find volume of prisms, cylinders, and pyramids, (D) Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates. (E) Estimate and compute various attributes, including length, angle measure, area surface area and volume, to a specified level of precision (8M4) Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find: a. the surface area of a cylinder as a function of its height and radius; b. that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height. (8M5) Determine surface area for pyramids by analyzing their parts. (8M10) Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision. (9M3) Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively. (9M4) Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures. STANDARD: Geometry and Spatial Sense BENCHMARK: (A) Formally define geometric figures, (B) Describe and apply the properties of similar and congruent figures: and justify conjectures involving similarity and congruence, (C) Recognize and apply angle relationships in situations involving intersection lines, perpendicular lines and parallel lines, (D) Use coordinate geometry to represent and examine the properties of geometric figures.

(E) Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology (F) Represent and model transformations in a coordinate plane and describe the results, (G) Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system. (H) Establish the validity of conjectures about geometric objects, their properties and relationships by counterexample, inductive and deductive reasoning, and critiquing arguments made by others (8G1) Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three- dimensional objects., (8G2) Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal. (8G3) Use proportions in several forms to solve problems involving similar figures (part-between figures)., (8G4) Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex., (8G5) Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translation (10G1)Formally define and explain key aspects of geometric figures, including: a. interior and exterior angles of polygons; b. segments related to triangles (median, altitude, midsegment); c. points of concurrency related to triangles (centroid, incenter, orthocenter, circumcenter); d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle). (10G2) Recognize and explain the necessity for certain terms to remain undefined, such as point, line and plane. (10G3) Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including: a. prove the Pythagorean Theorem; b. prove theorems involving triangle similarity and congruence; c. prove theorems involving properties of lines, angles, triangles and quadrilaterals; d. test a conjecture using basic constructions made with a compass and straightedge or technology.

(10G4) Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software. (10G5) Construct congruent figures and similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software. (10G6) Identify the reflection and rotation symmetries of two- and three- dimensional figures. (10G7) Perform reflections and rotations using compass and straightedge constructions and dynamic geometry software. (10G8) Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane. (10G9) Show and describe the results of combinations of translations, reflections and rotations (compositions); e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable (10G10) Solve problems involving chords, radii and arcs within the same circle. TOPIC/UNIT: Chapter 11 Time Line: 10 Days

KNOW • Basic Elements of Plane

Geometry • Angles • Quadrilaterals • General Properties of Triangles • Right Triangles • Similar Triangles • Concept of Proof and Proof

Techniques • Circles • Transformations in the Plane • Geometric Formulas • Geometry in Three Dimensions

DO • Define, know and use all

properties of plane geometry • Complete transformations • Use geometric formulas

PRE-ASSESSMENT: Informal questioning Teacher observation Model Math ACT I pgs. 223, 227, 234, 239, 243, 249, 254, 260, 266, 273 student text


GRAPHIC ORGANIZER & OR TECHNOLOGY: Calculator Tips pgs. 238, 242, 266

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Model Act Problem Cumulative ACT Practice pgs. 276-278




• Basic Elements of Plane Geometry pg. 22

• Angles pg. 225

HISTORICAL/MODERN LINK: NA

• Quadrilaterals pg. 230 • General Properties of Triangles

pg. 233 • Right Triangles pg. 236 • Similar Triangles pg. 242 • Concept of Proof and Proof

Techniques pg. 247 • Circles pg. 253 • Transformations in the Plane

pg. 258 • Geometric Formulas pg. 265 • Geometry in Three Dimensions

pg. 269

STANDARD: Geometry and Spatial Sense 8-10 BENCHMARKS: (I) Use right triangles trigonometric relationships to determine lengths and angle measures (9G1) Define the basic trigonometric ratios in right triangles: sine, cosine and tangent. (9G2) Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures. STANDARD: Geometry and Spatial Sense 11-12 BENCHMARK: A. Use trigonometric relationships to verify and determine solutions in problem situations. (11G4) Use trigonometric relationships to determine lengths and angle measures; i.e., Law of Sines and Law of Cosines. (12G2) Derive and apply the basic trigonometric identities; i.e., angle addition, angle subtraction and double angle. TOPIC/UNIT: Chapter 12 Time Line: 10 Days KNOW

• Right Triangle Trigonometry • Trigonometry Identities • Unit Circle Trigonometry • Graphs of Trigonometric

Functions

DO • Solve problems using trig

ratios • Use trig identities • Use the unit circle to solve for

trig ratios for any given angle • Graph trig functions

PRE-ASSESSMENT: Informal questioning Teacher observation Model Math ACT I pgs. 293, 297student text


GRAPHIC ORGANIZER & OR TECHNOLOGY: Calculator Tips pg. 282

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Model Act Problem Cumulative ACT Practice pg. 301




• Right Triangle Trigonometry pg. 281

• Trigonometry Identities pg. 286

• Unit Circle Trigonometry pg. 290

• Graphs of Trigonometric Functions pg. 295


• Leaning ladder pg. 284 • Flying pg. 285 • Heights pg. 301

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