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Page 1 Preparation for the AGS Geometry (Distance Delivery Course) Course Syllabus and Correlation to Alaska Performance Standards Course Title Grade Levels Offered Credit Awarded Content Area of Study Prerequisites Geometry 9-12 1 Credit/SY Mathematics Pre-Algebra (required) Algebra 1 (suggested) Required or Elective Elective Course Description This course is the study of lines, angles, and basic shapes and figures in one, two, and three dimensions. Topics covered include the properties of geometric shapes; symmetry; calculations and measurements of angles, lengths, areas, and volumes; geometric postulates and theorems; linear and quadratic equations, and the use of algebra to solve geometric problems. Skills covered include the transformations of figures, graphing on a coordinate plane, geometric proofs and constructions, creating and solving algebraic equations, and deductive and inductive reasoning; AGS Geometry will be used as the text. This course is designed to meet the Yukon-Koyukuk School District Curriculum, State of Alaska Performance Standards, and National Council of Teachers of Mathematics Standards. Alaska Performance Standards Note: Performance standards this course primarily supports include Geometry, Functions and Relationships, and Numeration. Process Skills (including Problem Solving, Communication, Reasoning, and Connections) and Measurements are covered adequately as these topics relate to Geometry. Estimation and Computation, and Statistics and Probability are nominally covered in this course, but not emphasized. Textbook(s) and/or Materials Geometry 2005 AGS Publishing ISBN 0-7854-3830-0 Student Progress Evaluations Students will complete 104 lessons and 11 chapter tests. Quarter Progress Evaluations First Quarter 25 lesson quizzes 3 chapter tests Joe Marley, Geoff Johnson Second Quarter 30 lesson quizzes 3 chapter tests AGS Geometry Third Quarter 25 lesson quizzes 3 chapter tests Fourth Quarter 24 lesson quizzes 2 chapter tests Page 2 COURSE OUTLINE Semester One Quarter One: Performance Standards Focus: Chapter 1 “Exploring Geometry: Points, Lines and Angles in the Plane” Performance Standards Focus: Quarter Two: Chapter 4 “Using Algebra: Lines in the Coordinate Plane” 1-1 Points and Lines in the Plane M5.2.7 4-1 Naming Points 1-2 Ruler Postulates M1.4.1 4-2 Horizontal Lines 1-3 Copying and Bisecting Angles M5.3.7 M2.3.3 4-3 Vertical Lines 1-4 Angle Measurement M5.3.7 M2.3.1 M2.3.3 4-4 Slope of a Line 1-5 Complementary and Supplementary Angles 4-4 Calculator Practice 1-5 Calculator Practice M5.4.6 M4.3.5 M4.4.3 1-6 Algebra and Angles M4.3.5 4-6 Writing the Equation of a Line 1-7 Algebra Connection: Positive Exponents M1.4.4 M1.4.5 4-6 Calculator Practice M4.4.1 M4.4.3 Application: Drawing Networks M5.4.6 M7.4.1 M10.3.2 M10.4.2 4-7 Finding the Midpoint of a Segment M4.4.5 M5.3.7 4-8 Algebra Connection: Rate and Mixture Problems M2.4.3 M8.3.1 M8.3.2 M6.4.1 M9.3.1 M10.3.2 4-5 Using Algebra: y = mx M1.4.1 M4.3.4 M5.4.5 M4.4.1 M4.3.4 M5.4.5 M10.3.2 M4.4.1 M4.3.4 M5.4.5 M4.4.1 M4.3.4 M5.4.5 M10.4.2 M4.4.1 +b Application: Screaming Slopes Chapter 2 “Thinking Geometrically: Using Proofs” 2-1 If … Then Statements 2-2 Euclid’s Five Postulates 2-3 Using Euclid’s Postulates 2-4 Axioms and Common Notions Joe Marley, Geoff Johnson AGS Geometry M4.3.4 M5.4.5 M8.3.1 M4.4.2 M5.4.5 Chapter 5 “Triangles and Quadrilaterals” M9.3.1 M9.3.2 M9.3.2 M9.4.1 M10.3.1 M5.3.1 M5.4.1 M4.4.5 M8.3.3 M8.4.2 5-1 Naming Triangles Using Their Sides 5-2 Naming Triangles Using Their Angles 5-3 Special Quadrilaterals 5-4 Quadrilaterals and Their Diagonals M5.3.1 M5.3.7 M5.3.1 M5.3.7 M5.4.1 M9.3.2 M5.4.1 M9.4.3 Page 3 2-4 Calculator Practice M1.3.3 M3.4.4 M4.4.3 M8.4.2 M9.4.3 5-5 Angle Sum of Any Triangle M5.4.1 M9.4.1 5-6 Concave and Convex Polygons 2-6 Algebra Connection: The Distributive Property M1.3.6 M4.4.5 5-7 Constructing Perpendiculars M4.3.1 M5.3.1 M10.3.1 M5.3.7 Application: Logical Deductions M9.3.1 M10.4.2 5-8 Altitudes, Angle Bisectors, and Medians 2-5 A Simple Proof 5-9 Proof of the Angle Sum Theorem 5-10 Algebra Connection: Special Polynomial Products Application: Tangram Pictures Chapter 3 “Parallel Lines and Transversals” M5.3.7 M5.4.6 M7.3.2 M4.4.3 M5.4.6 M9.4.3 M1.3.1 M4.4.5 M5.4.4 M5.3.5 M9.3.1 M10.3.1 Chapter 6 “Congruent Triangles and Transformations” 3-1 Parallel Lines M5.3.7 6-1 Corresponding Parts: SAS Postulate 3-2 Transversals M5.3.3 6-2 SSS Construction and Triangle Inequality 3-3 Theorems About Parallel Lines M7.4.1 M9.4.3 6-3 SSS and ASA Congruencies 3-4 Constructions and Problem Solving M5.3.7 M8.3.2 6-4 Special Congruencies: Right Triangles 3-5 Quadrilaterals and Parallels M5.3.7 M5.4.6 6-4 Calculator Practice 3-6 Trapezoids M5.3.1 6-5 Reflections in the Coordinate Plane 3-7 Proving Lines Parallel M5.3.7 M7.3.2 6-6 Special Reflections: Symmetries 3-8 Parallel Lines: More Theorems and Converses M9.3.2 6-7 Slides and Translations 3-9 Algebra Connection: Solving Linear Equations M4.4.2 M4.4.5 6-8 Rotations Application: Geometric Quilt Shapes M5.4.1 M10.3.1 6-9 Algebra Connection: Quadratic Equations M1.3.6 M4.4.3 Application: Tessellations M5.3.5 M5.4.4 M10.3.2 Joe Marley, Geoff Johnson AGS Geometry M5.3.3 M5.4.3 M10.3.2 M2.3.4 M5.3.3 M5.3.7 M5.3.3 M5.4.3 M10.4.2 M1.3.6 M5.3.3 M5.4.3 M4.4.3 M2.3.3 M5.3.5 M5.4.4 M5.3.5 M5.4.4 M5.3.5 M5.4.4 M8.3.2 M5.3.5 M5.4.4 Page 4 Quarter Three: Performance Standards Focus: Chapter 7 “Proportion and Similarity” 7-1 Similar Figures and Proportions 7-1 Calculator Practice 7-2 Similar Triangles 7-3 Angle Measure in Regular Polygons Calculator Practice 7-4 Enlarging Geometric Figures 7-5 Shrinking Geometric Figures 7-6 Algebra Connection: The Counting Principal Application: Gearing Up Quarter Four: Chapter 10 “Circles and Spheres” M1.3.4 M4.3.2 M4.4.5 M5.3.3 M4.3.5 M4.4.3 10-1 Definition of a Circle M4.4.3 M5.4.1 10-2 The Ratio π M2.3.4 M3.3.4 M4.4.5 M5.3.3 M10.4.2 M3.3.4 M4.3.1 M5.3.1 M5.4.1 M4.3.3 10-3 Approximating the Area of a Circle M4.3.5 M5.3.3 M10.3.2 M3.4.1 M5.4.1 M5.4.4 M5.3.5 M5.4.6 M7.4.3 M2.3.2 M5.3.3 M5.3.5 M5.4.6 M7.3.1 M4.4.4 M7.4.1 M1.3.4 M7.4.1 M10.3.2 Calculator Practice 10-4 Area and Probability M6.3.5 10-5 Formula for the Area of a Circle M4.4.2 M5.2.4 M4.4.3 10-6 Circles and Their Angles and Sectors M2.4.3 M5.4.1 10-7 Tangents, Circumcircles, and Incircles M5.4.1 M5.3.7 M5.4.1 10-8 Sine, Cosine, and Tangent 10-9 Solving Triangles Using Trigonometry 10-10 Spheres 10-11 Algebra Connection: Systems of Linear Equations Application: Statistics Chapter 8 “The Pythagorean Theorem” 8-1 Pythagorean Triples 8-2 Pythagorean Triples and a Proof Joe Marley, Geoff Johnson AGS Geometry Performance Standards Focus: M2.4.4 M4.3.5 M4.3.2 M5.3.4 M4.4.2 M4.4.3 M6.4.1 M9.3.1 M10.3.1 Chapter 11 “Solid Geometric Figures and Their Measures” M1.4.5 M2.4.4 M4.4.3 M2.4.4 M4.4.5 11-1 Basic Volume Formulas M4.4.5 M5.3.4 11-2 Volumes of Pyramids and Cones M4.4.5 M5.3.4 Page 5 8-3 Pythagorean Demonstration 8-4 Pythagorean Theorem and Similar Triangles 8-5 Special Triangles 8-6 Pythagorean Proof and Trapezoids 8-7 Distance Formula: Pythagorean Theorem 8-7 Calculator Practice 8-8 Converse of the Pythagorean Theorem 8-9 Algebra Connection: Denominators and Zero Application: Architecture and Geometric Shapes M2.4.4 M5.4.1 M2.4.4 M7.4.2 M8.4.2 M10.3.2 M10.4.2 M2.4.4 M4.4.3 M4.4.5 M5.4.1 M5.2.4 M2.4.4 M5.4.5 M5.3.6 M4.4.3 9-2 Perimeter Formulas 9-3 Perimeters and Diagonals 9-4 Area: Squares, Rectangles, and Parallelograms 9-5 Areas of Trapezoids 9-6 Areas of Triangles 9-6 Calculator Practice 9-7 Algebra Connection: Graphing Inequalities Application: Fractals Joe Marley, Geoff Johnson AGS Geometry 11-4 Surface Areas of Pyramids and Cones M5.3.4 M10.3.2 M5.3.4 M10.3.1 11-5 Measurements M2.3.2 11-6 Algebra Connection: Radicals in Equations Application: Origami M3.4.3 M4.3.5 M5.4.6 M10.3.1 M2.4.4 M5.4.5 M1.4.1 M1.4.5 M9.3.1 M10.4.2 Chapter 9 “Perimeter and Area” 9-1 Perimeters of Polygons 11-3 Surface Areas of Prisms and Cylinders Chapter 12 “Geometry and Imagination” M4.3.5 M5.2.4 M4.3.4 M5.2.2 M2.4.4 M5.4.5 M5.2.6 M2.3.2 M4.3.5 M5.2.4 M5.4.4 M10.3.2 M5.2.4 M5.4.1 M4.4.5 M5.2.4 M5.4.1 M4.4.3 M4.4.1 M5.4.5 M4.4.4 M10.3.1 12-1 Lines and Planes in Space M5.3.2 12-2 Loci in the Coordinate Plane M5.4.5 12-3 Compound Loci M9.3.1 12-4 Algebra Connection: The Quadratic Formula M4.4.1 M4.4.2 Application: Conic Sections M7.4.1 M9.3.1 Page 6 Location of performance standards covered within this course. Performance Standard Lesson, Tasks & Tools used to meet standard Numeration M1.3.1 Read, write, model, and order real numbers, explaining scientific notation (read only), exponents (square and cube only) and percents. 5-10 Algebra Connection: Special Polynomial Products M1.4.1 Read, write, model, order, and define real numbers and subsets. 1-2 Ruler Postulates 4-1 Naming Points 8-9 Algebra Connection: Denominators and Zero M1.3.3 Translate between equivalent representations of the same number. Select a representation that is appropriate for the situation. 2-4 Axioms and Common Notions (CP) M1.4.3 Compare and contrast the relationship between various applications of the same operation. none M1.3.4 Describe and model the relationship of fractions to decimals, percents, ratios and proportions. 7-1 Similar Figures and Proportions Ch. 7 Application: Gearing Up M1.4.4 Translate between equivalent representations of the same exponential expression. 1-7 Algebra Connection: Positive Exponents M1.3.5 Use, explain, and define the rules of divisibility, prime and composite numbers, multiples, and order of operations. none M1.4.5 Recognize, describe, and use properties of the real number system. 1-7 Algebra Connection: Positive Exponents 8-1 Pythagorean Triples 8-9 Algebra Connection: Denominators and Zero M1.3.6 Use commutative, identity, associative, and distributive properties with variable. 2-6 Algebra Connection: The Distributive Property 6-4 Special Congruencies: Right Triangles 6-9 Algebra Connection: Quadratic Equations Joe Marley, Geoff Johnson AGS Geometry Page 7 Measurement M2.3.1 Estimate and measure various dimensions to a specified degree of accuracy. 1-4 Angle Measurement M2.4.1 Evaluate measurements for accuracy, precision, and error with respect to the measuring tools, methods, and the computational process none M2.3.2 Estimate and convert measurements within the same system. 7-5 Shrinking Geometric Figures 9-4 Area: Squares, Rectangles, and Parallelograms 11-5 Measurements M2.4.2 Estimate and convert measurements between different systems. none M2.3.3 Use a variety of methods and tools to construct and compare plane figures 1-4 Angle Measurement 6-5 Reflections in the Coordinate Plane M2.4.3 Apply various measurement systems to describe situations and solve problems. 4-8 Algebra Connection: Rate and Mixture Problems 10-6 Circles and Their Angles and Sectors M2.3.4 Describe and apply the relationships between dimensions of geometric figures to solve problems using indirect measurement; describe and apply the concepts of rate and scale. M2.4.4 Use indirect methods, including the Pythagorean Theorem and right triangle trigonometry, to find missing dimensions. 6-2 SSS Construction and Triangle Inequality 7-2 Similar Triangles Joe Marley, Geoff Johnson AGS Geometry 8-1 Pythagorean Triples 8-2 Pythagorean Triples and a Proof 8-3 Pythagorean Demonstration 8-4 Pythagorean Theorem and Similar Triangles 8-5 Special Triangles 8-7 Distance Formula: Pythagorean Theorem 8-8 Converse of the Pythagorean Theorem 9-3 Perimeters and Diagonals 10-9 Solving Triangles Using Trigonometry Page 8 M2.3.5 Apply information about time zones and elapsed time to solve problems. none Estimation and Computation M3.4.1 Use estimation to solve problems and to check the accuracy of solutions; state whether the estimation is greater or less than the exact answer. 10-3 Approximating the Area of a Circle M3.3.2 Apply basic operations efficiently and accurately, using estimation to check the reasonableness of results. M3.4.2 Add and subtract real numbers using powers. none M3.4.3 Multiply and divide real numbers in various forms including powers. 11-6 Algebra Connection: Radicals in Equations M3.3.4 Multiply and divide rational number in various forms including fractions, decimals, and percents. 7-2 Similar Triangles 7-3 Angle Measure in Regular Polygons M3.4.4 Select, convert, and apply an equivalent representation of a number for a specified situation. 2-4 Axioms and Common Notions (CP) M3.3.5 Convert between equivalent fractions, decimals, percents, and proportions. Convert from exact to decimal representations of irrational numbers. M3.4.5 Use ratios and proportions to model and solve fraction and percent problems with variables. none none none Joe Marley, Geoff Johnson AGS Geometry Page 9 Functions and Relationships M4.3.1 Identify numeric and geometric patterns to find the next term and predict the nth term. 5-6 Concave and Convex Polygons 7-3 Angle Measure in Regular Polygons M4.4.1 Identify, graph, and describe the graphs of basic families of functions including linear, absolute value, quadratic, and exponential using a graphing calculator 4-2 Horizontal Lines 4-3 Vertical Lines 4-4 Slope of a Line 4-4 Slope of a Line (CP) 4-6 Writing the Equation of a Line (CP) 9-7 Algebra Connection: Graphing Inequalities 12-4 Algebra Connection: The Quadratic Formula 7-1 Similar Figures and Proportions 10-10 Spheres 3-9 Algebra Connection: Solving Linear Equations 4-6 Writing the Equation of a Line 10-5 Formula for the Area of a Circle 10-11 Algebra Connection: Systems of Linear Equations 12-4 Algebra Connection: The Quadratic Formula 7-3 Angle Measure in Regular Polygons (CP) 1-5 Complementary and Supplementary Angles (CP) 4-6 Writing the Equation of a Line (CP) 5-9 Proof of the Angle Sum Theorem 6-4 Special Congruencies: Right Triangles (CP) 6-9 Algebra Connection: Quadratic Equations 7-1 Similar Figures and Proportions (CP) 8-1 Pythagorean Triples 8-5 Special Triangles 8-7 Distance Formula: Pythagorean Theorem (CP) 9-6 Areas of Triangles (CP) 10-1 Definition of a Circle 10-5 Formula for the Area of a Circle (CP) 10-11 Algebra Connection: Systems of Linear Equations 4-1 Naming Points 4-2 Horizontal Lines 4-3 Vertical Lines 4-4 Slope of a Line 4-5 Using Algebra: y = mx + b 9-2 Perimeter Formulas 7-6 Algebra Connection: The Counting Principal Ch. 9 Application: Fractals 1-5 Complementary and Supplementary Angles 1-6 Algebra and Angles 7-1 Similar Figures and Proportions (CP) 9-1 Perimeters of Polygons M4.3.2 Identify and describe how a change in one variable in a function affects the remaining variables. M4.4.2 Create and solve linear equations and inequalities. M4.3.3 Use a calculator to find a missing item in arithmetic and a geometric sequence; predict the graph of each function. M4.4.3 Create and solve simple systems of equations, algebraically and graphically, using a graphing calculator M4.3.4 Translate among and use tables of ordered pairs, graphs on coordinate planes, and linear equations as tools to represent and analyze patterns. M4.4.4 Use discrete structures, such as networks, matrices, sequences, and iterations, as tools to analyze patterns, expressions, and equations. M4.3.5 Find the value of a variable by evaluating formulas and algebraic expressions for given values. Joe Marley, Geoff Johnson AGS Geometry Page 10 9-4 Area: Squares, Rectangles, and Parallelograms M4.4.5 Add, subtract, multiply, divide, and simplify rational expressions; add, subtract, and multiply polynomials. 10-2 The Ratio π 10-9 Solving Triangles Using Trigonometry 11-6 Algebra Connection: Radicals in Equations 2-6 Algebra Connection: The Distributive Property 3-9 Algebra Connection: Solving Linear Equations 4-7 Finding the Midpoint of a Segment 5-10 Algebra Connection: Special Polynomial Products 7-1 Similar Figures and Proportions 7-2 Similar Triangles 8-2 Pythagorean Triples and a Proof 8-5 Special Triangles 9-6 Areas of Triangles 11-1 Basic Volume Formulas 11-2 Volumes of Pyramids and Cones 2-3 Using Euclid’s Postulates 5-1 Naming Triangles Using Their Sides 5-2 Naming Triangles Using Their Angles 5-6 Concave and Convex Polygons 7-3 Angle Measure in Regular Polygons 2-3 Using Euclid’s Postulates Ch. 3 Application: Geometric Quilt Shapes 5-3 Special Quadrilaterals 5-4 Quadrilaterals and Their Diagonals 5-5 Angle Sum of Any Triangle 7-3 Angle Measure in Regular Polygons 8-3 Pythagorean Demonstration 8-6 Pythagorean Proof and Trapezoids 9-5 Areas of Trapezoids 9-6 Areas of Triangles 10-1 Definition of a Circle 10-3 Approximating the Area of a Circle 10-6 Circles and Their Angles and Sectors 10-7 Tangents, Circumcircles, and Incircles 10-8 Sine, Cosine, and Tangent 9-2 Perimeter Formulas 3-2 Transversals 6-1 Corresponding Parts: SAS Postulate 6-2 SSS Construction and Triangle Inequality 6-3 SSS and ASA Congruencies 6-4 Special Congruencies: Right Triangles 7-1 Similar Figures and Proportions 7-2 Similar Triangles 7-5 Shrinking Geometric Figures Geometry M5.3.1 Identify, classify, compare, and sketch regular and irregular polygons. M5.4.1 Identify and use the properties of polygons, including interior and exterior angles, and circles (including angles, arcs, chord, secants, and tangents) to solve problems. M5.2.2 Compare and contrast plane and solid figures (e.g., circle/sphere, square/cube, triangle/pyramid) using relevant attributes, including the number of vertices, edges, and the number and shape of faces. M5.3.3 Apply the properties of equality and proportionality to solve problems involving congruent or similar shapes. 10-2 The Ratio π Joe Marley, Geoff Johnson AGS Geometry Page 11 M5.4.3 Identify congruent and similar figures using Euclidean and coordinate geometries; apply this information to solve problems. 6-1 Corresponding Parts: SAS Postulate 6-3 SSS and ASA Congruencies 6-4 Special Congruencies: Right Triangles M5.2.4 Distinguish between area and perimeter; find both using a variety of methods including rulers, grid paper, and tiles. 9-1 Perimeters of Polygons 8-6 Pythagorean Proof and Trapezoids 9-4 Area: Squares, Rectangles, and Parallelograms 9-5 Areas of Trapezoids 9-6 Areas of Triangles 10-5 Formula for the Area of a Circle 10-10 Spheres 11-1 Basic Volume Formulas 11-2 Volumes of Pyramids and Cones 11-3 Surface Areas of Prisms and Cylinders 11-4 Surface Areas of Pyramids and Cones Ch. 5 Application: Tangram Pictures 6-5 Reflections in the Coordinate Plane 6-6 Special Reflections: Symmetries 6-7 Slides and Translations 6-8 Rotations Ch. 6 Application: Tessellations 9-4 Area: Squares, Rectangles, and Parallelograms 10-3 Approximating the Area of a Circle Ch. 5 Application: Tangram Pictures 6-5 Reflections in the Coordinate Plane 6-6 Special Reflections: Symmetries 6-7 Slides and Translations 6-8 Rotations Ch. 6 Application: Tessellations 7-4 Enlarging Geometric Figures 7-5 Shrinking Geometric Figures 4-1 Naming Points 4-2 Horizontal Lines 4-3 Vertical Lines 4-4 Slope of a Line 4-5 Using Algebra: y = mx + b 4-6 Writing the Equation of a Line 8-7 Distance Formula: Pythagorean Theorem 8-8 Converse of the Pythagorean Theorem 9-3 Perimeters and Diagonals 9-7 Algebra Connection: Graphing Inequalities 9-3 Perimeters and Diagonals M5.3.4 Estimate and determine volume and surface areas of solid figures using manipulatives and formulas; estimate and find circumferences and areas of circles. M5.4.4 Use transformations to demonstrate geometric properties. M5.3.5 Draw and describe the results of transformations including translations(slides), rotations(turns), reflections(flips), and dilations(shrinking or enlarging). M5.4.5 Use coordinate geometry to graph linear equations, determine slopes of lines, identify parallel and perpendicular lines, and to find possible solutions to sets of equations. M5.2.6 Locate and describe objects in terms of their position with and without compass directions; identify coordinates for a given point or locate points of given coordinates on a grid. M5.3.6 Use coordinate geometry to represent and interpret relationships defined by equations and formulas Joe Marley, Geoff Johnson AGS Geometry 8-7 Distance Formula: Pythagorean Theorem Page 12 including distance and midpoint. M5.4.6 Construct geometric models, transformations, and scale drawings using a variety of methods including paper folding, compass, straight edge, protractor, and technology. M5.2.7 Sketch and identify line segments, midpoints, intersections, parallel, and perpendicular lines. 1-1 Points and Lines in a Plane M5.3.7 Draw, measure, and construct geometric figures including perpendicular bisectors, polygons with given dimensions and angles, circles with given dimensions, perpendicular and parallel lines. 1-5 Complementary and Supplementary Angles Ch. 1 Application: Drawing Networks 5-8 Altitudes, Angle Bisectors, and Medians 7-4 Enlarging Geometric Figures 7-5 Shrinking Geometric Figures Ch. 12 Application: Origami 1-3 Copying and Bisecting Angles 1-4 Angle Measurement 3-1 Parallel Lines 3-4 Constructions and Problem Solving 4-7 Finding the Midpoint of a Segment 5-1 Naming Triangles Using Their Sides 5-2 Naming Triangles Using Their Angles 5-7 Constructing Perpendiculars 5-8 Altitudes, Angle Bisectors, and Medians 6-2 SSS Construction and Triangle Inequality 10-7 Tangents, Circumcircles, and Incircles Statistics/Probability M6.3.1 Collect, analyze, and display data in a variety of visual displays including frequency distributions, circle graphs, histograms, and scatter plots. M6.4.1 Analyze and draw inferences from a wide variety of data sources that summarize data; construct graphical displays with and without technology. none M6.3.2 Interpret and analyze information found in newspapers, magazines, and graphical displays. none M6.3.3 Determine and justify a choice of mean, median, or mode as the best representation of data for a practical situation. M6.3.4 Make projections based on available data and evaluate whether or not inferences can be made given the parameters of the data. none Joe Marley, Geoff Johnson AGS Geometry Ch. 4 Application: Screaming Slopes Ch. 10 Application: Statistics none Page 13 M6.3.5 Use tree diagrams and sample spaces to make predictions about independent events. 10-4 Area and Probability Process Skills (Problem Solving, Communication, Reasoning, Connections) Process Skills are assessed but not separately reported on individual student reports. M7.3.1 Analyze and summarize a problem using the relationships between the known facts and unknown information. M7.4.1 Recognize and formulate mathematical problems from within and outside the field of mathematics. 7-5 Shrinking Geometric Figures M7.3.2 Select, modify, and apply a variety of problem-solving strategies including graphing, inductive and deductive reasoning, Venn diagrams, and spreadsheets. 3-7 Proving Lines Parallel 5-8 Altitudes, Angle Bisectors, and Medians M7.4.2 Apply multi-step, integrated, mathematical problem-solving strategies, persisting until a solution is found or it is clear no solutions exist. M7.4.3 Verify the answer by using an alternative strategy. 8-4 Pythagorean Theorem and Similar Triangles Ch. 1 Application: Drawing Networks 7-6 Algebra Connection: The Counting Principal Ch. 7 Application: Gearing Up Ch. 12 Application: Conic Sections 7-4 Enlarging Geometric Figures M8.3.1 Use math vocabulary, symbols, and notation to represent information in the problem. 4-5 Using Algebra: y = mx + b 4-8 Algebra Connection: Rate and Mixture Problems M8.3.2 Represent a problem numerically, graphically, and symbolically; translate among these alternative representations. M8.4.2 Use numerical, graphic, and symbolic representations to support oral and written communication about math ideas. 3-4 Constructions and Problem Solving 4-8 Algebra Connection: Rate and Mixture Problems 6-7 Slides and Translations M8.3.3 Use appropriate vocabulary, symbols, and technology to explain, justify, and defend mathematical 2-4 Axioms and Common Notions Joe Marley, Geoff Johnson AGS Geometry 2-4 Axioms and Common Notions 2-5 A Simple Proof 8-4 Pythagorean Theorem and Similar Triangles Page 14 solutions. M9.3.1 Use informal deductive and inductive reasoning in both concrete and abstract contexts. M9.4.1 Follow and evaluate an argument, judging its validity using inductive or deductive reasoning and logic. 2-2 Euclid’s Five Postulates 5-5 Angle Sum of Any Triangle M9.3.2 State counterexamples to disprove statements. M9.4.3 Use methods of proofs including direct, indirect, and counterexamples, to validate conjectures. 3-3 Theorems About Parallel Lines 5-4 Quadrilaterals and Their Diagonals 5-9 Proof of the Angle Sum Theorem 2-1 If … Then Statements Ch. 2 Application: Logical Deductions Ch. 4 Application: Screaming Slopes Ch. 5 Application: Tangram Pictures Ch. 8 Application: Architecture and Geometric Shapes Ch. 10 Application: Statistics 12-3 Compound Loci Ch. 12 Application: Conic Sections 2-1 If … Then Statements 2-2 Euclid’s Five Postulates 3-8 Parallel Lines: More Theorems and Converses 5-3 Special Quadrilaterals M10.3.1 Apply mathematical skills and processes to science and humanities. 2-2 Euclid’s Five Postulates Ch. 3 Application: Geometric Quilt Shapes 5-6 Concave and Convex Polygons Ch. 5 Application: Tangram Pictures Ch. 9 Application: Fractals Ch. 10 Application: Statistics 11-4 Surface Areas of Pyramids and Cones Ch. 11 Application: Origami M10.3.2 Apply mathematical skills and processes to situations with peers and community Ch. 1 Application: Drawing Networks 4-2 Horizontal Lines Ch. 4 Application: Screaming Slopes 6-1 Corresponding Parts: SAS Postulate Ch. 6 Application: Tessellations Ch. 7 Application: Gearing Up 8-4 Pythagorean Theorem and Similar Triangles 9-4 Area: Squares, Rectangles, and Parallelograms 10-2 The Ratio π 11-3 Surface Areas of Prisms and Cylinders Joe Marley, Geoff Johnson AGS Geometry Page 15 M10.4.2 Describe how mathematics can be used in knowing how to prepare for careers. Joe Marley, Geoff Johnson AGS Geometry Ch. 1 Application: Drawing Networks Ch. 2 Application: Logical Deductions 4-4 Slope of a Line 6-3 SSS and ASA Congruencies 7-2 Similar Triangles 8-4 Pythagorean Theorem and Similar Triangles Ch. 8 Application: Architecture and Geometric Shapes