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Transcript
Concepts in Algebra and Geometry Introduction The following outline represents one possible way to structure Concepts in Algebra and Geometry, which we envision as a replacement for the current Geometry B course. It is based on the Glencoe texts Algebra: Concepts and Applications and Geometry: Concepts and Applications. All chapter and section headings in the outline are those used in the 2008 editions of those books. Our purpose in redesigning the Geometry B course is to strengthen the Algebra skills of the students, not only to bolster their performance in this course, but also to better prepare them for the Algebra IIB course that follows it. Many incoming SHS freshmen have achieved a modicum of success in Pre-Algebra and Algebra I, but have not attained the level of mastery needed for the demands of the high-school curriculum. We believe that by strengthening their Algebra skills early in the Geometry course, and then throughout the course as the subject linkages demand it, these students will achieve a level of success that will in turn enhance their confidence as math students. Much of the Algebra sequence that follows is already an informal part of Geometry B. But the formal and specific emphasis on these topics means that we will be unable to cover some of the current Geometry sequence. We believe that the Glencoe text mitigates this sacrifice by ensuring adequate coverage of the Massachusetts Curriculum Framework’s Grades 9–10 Learning Standards for Geometry and Measurement. In the outline, the chapter and section numbers and titles are those of the Geometry text. Sections from the Algebra text are labeled A1-2, A2-2, and so on. Sections in italics are to be considered optional because they repeat Algebra topics or because historically they have not been covered in the Geometry B course. In addition, the outline omits Chapter 14 (Circle Relationships) and Chapter 16 (More Coordinate Graphing and Transformations). Finally, it should be noted that the outline as presented has some flexibility built into it, to accommodate (as much as possible) the vagaries of the school’s overall schedule. It assumes a school calendar that permits 14 full cycles (approximately 77 hours) of instruction and assessment per semester. Concepts in Algebra and Geometry Term 1 35 Days of Instruction and Assessment; 23 Topics, 6 Assessments Unit One. The Basics Chapter 1 Reasoning in Geometry (9 days, 2 assessments) A1-2 A1-4 1-1 1-2 1-3 1-4 1-5 1-6 Order of Operations The Distributive Property Patterns and Inductive Reasoning Points, Lines, and Planes Postulates Conditional Statements and Their Converses Tools of the Trade A Plan for Problem Solving Chapter 2 A2-2 A3-4 A3-6 A4-4 A4-5 A4-6 2-1 2-2 2-3 2-4 2-5 Segment Measure and Coordinate Graphing (14 days, 2 assessments) The Coordinate Plane Equations Solving Addition and Subtraction Equations Solving Multiplication and Division Equations Solving Multi-Step Equations Variables on Both Sides Real Numbers and Number Lines Segments and Properties of Real Numbers Congruent Segments The Coordinate Plane Midpoints Unit Two. Angles Chapter 3 Angles (12 days, 2 assessments) 3-1 3-2 3-3 3-4 3-5 3-6 3-7 Angles Angle Measure The Angle Addition Postulate Adjacent Angles and Linear Pairs of Angles Complementary and Supplementary Angles Congruent Angles Perpendicular Lines Concepts in Algebra and Geometry Term 2 35 Days of Instruction and Assessment; 22 Topics, 6 Assessments Unit Two. Angles (continued) Chapter 4 Parallels (13 days, 3 assessments) A7-1 A7-2 A7-3 A7-5 A7-6 A7-7 4-1 4-2 4-3 4-4 4-5 4-6 Slope Writing Equations in Point–Slope Form Writing Equations in Slope–Intercept Form Graphing Linear Equations Families of Linear Graphs Parallel and Perpendicular Lines Parallel Lines and Planes Parallel Lines and Transversals Transversals and Corresponding Angles Proving Lines Parallel Slope Equations of Lines Unit Three. Triangles Chapter 5 5-1 5-2 5-3 10-6 5-4 5-5 5-6 A8-1 A8-2 A8-3 A8-5 A8-7 A14-1 A14-2 A14-3 Triangles and Congruence (22 days, 3 assessments) Classifying Triangles Angles of a Triangle Geometry in Motion Symmetry Congruent Triangles SSS and SAS ASA and AAS Powers and Exponents Multiplying and Dividing Powers Negative Exponents Square Roots The Pythagorean Theorem The Real Numbers The Distance Formula Simplifying Radical Expressions Concepts in Algebra and Geometry Term 3 35 Days of Instruction and Assessment; 28 Topics, 8 Assessments Unit Three. Triangles (continued) Chapter 6 6-1 6-2 6-3 6-4 6-5 6-6 6-7 Medians Altitudes and Perpendicular Bisectors Angle Bisectors of Triangles Isosceles Triangles Right Triangles The Pythagorean Theorem Distance on the Coordinate Plane Chapter 7 A12-1 A12-2 A12-3 A12-4 7-1 7-2 7-3 7-4 More About Triangles (8 days, 2 assessments) Triangle Inequalities (10 days, 2 assessments) Inequalities and Their Graphs Solving Addition and Subtraction Inequalities Solving Multiplication and Division Inequalities Solving Multi-Step Inequalities Segments, Angles, and Inequalities Exterior Angle Theorem Inequalities Within a Triangle Triangle Inequality Theorem Unit Four. Other Shapes Chapter 8 Quadrilaterals (8 days, 1 assessment) 8-1 8-2 8-3 8-4 8-5 Quadrilaterals Parallelograms Tests for Parallelograms Rectangles, Rhombi, and Squares Trapezoids Chapter 9 9-1 9-2 9-3 9-4 9-5 9-6 9-7 Proportions and Similarity (9 days, 2 assessments) Using Ratios and Proportions Similar Polygons Similar Triangles Proportional Parts and Triangles Triangles and Parallel Lines Proportional Parts and Parallel Lines Perimeters and Similarity Concepts in Algebra and Geometry Term 4 35 Days of Instruction and Assessment; 22 Topics, 8 Assessments Unit Four. Other Shapes (continued) Chapter 11 Circles (9 days, 2 assessments) 11-1 11-2 11-3 11-4 11-5 11-6 Parts of a Circle Arcs and Central Angles Arcs and Chords Inscribed Polygons Circumference of a Circle Area of a Circle Unit Five. Area and Volume Chapter 10 Polygons and Area (8 days, 2 assessments) 10-1 10-2 10-3 10-4 10-5 10-7 Naming Polygons Diagonals and Angle Measure Areas of Polygons Areas of Triangles and Trapezoids Areas of Regular Polygons Tessellations Chapter 12 Surface Area and Volume (10 days, 2 assessments) 12-1 12-2 12-3 12-4 12-5 12-6 12-7 Solid Figures Surface Areas of Prisms and Cylinders Volumes of Prisms and Cylinders Surface Areas of Pyramids and Cones Volumes of Pyramids and Cones Spheres Similarity of Solid Figures Unit Six. Special Topics Chapter 13 Right Angles and Trigonometry (3 days, 1 assessment) 13-1 13-2 13-3 13-4 13-5 Simplifying Square Roots 45°-45°-90°Triangles 30°-60°-90°Triangles The Tangent Ratio Sine and Cosine Ratios Chapter 15 Formalizing Proof (5 days, 1 assessment) 15-1 15-2 15-4 15-5 Logic and Truth Tables Deductive Reasoning Preparing for Two-Column Proofs Two-Column Proofs