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Middle School Grade 8 Geometry Curriculum Map Second Semester, 2012/2013 -Chapter Overview: In this Semester students will continue studying chapter 8 introducing ratio and proportions through similarity. In Chapter 9 Students will solve right triangles with trigonometry. In Chapter 10 the students will identify segments and lines related to circles, using properties of arcs and chords of circles, using inscribed angles and properties of inscribed polygons .Students find the lengths of the segments of chords, tangents, and secants, they find the equation of a circle and use it to graph it to graph and solve problems. The chapter ends by students drawing loci that satisfy given condition. Chapter 11 explores many topics which relate to the area of polygons and circles. It begins by finding the measures of the interior and exterior angles of polygons. Then students are introduced to the circumference of a circle and the area of a sector of a circle. The chapter ends by introducing geometric probability. IN Chapter 12 students will investigate the surface area and volume of solids. First, they will learn to distinguish polyhedral from other solids and to classify polyhedral. They will identify the Platonic solids and use Euler’s Theorem, They will use different methods to explore and identify surface areas and volumes. From algebra 1 curriculum the students will move on to solving systems of linear inequalities with quadratic equations and their graphs. The unit then ends will factor polynomial expressions and use factoring to solve quadratic equations. -Focus Standards: Geometry G.10 G.3.1 G.11 G.3.1 G.4 G.7 G.2.3 G.3.2 G8 G.3.2 G.12 G.3.1 G.14 G.3.1 G.13 G.3.1 Algebra: A.12 AI.3.2 A.12 AI.2.2 Learning Objectives, students will be able to: Geometry: Use similar polygons to solve real-life problems. be able to draw dilations A.11 AI.2.1 A.9 AI.2.1 be able to solve problems involving similar right triangle use Pythagorean Theorem Be able to use trigonometric ratios. Use arcs, angles and segments in circles to solve real-life problems. Be able to use the graph of an equation of a circle to model real-life situations. find angle measures and areas of polygons compare perimeters and areas of similar figures Find the circumference and area of a circle and find other measurements related to circles. calculate the surface area and volume of various solids use surface area and volume in real-life situations Use surface area and volume in real-life situations. Calculate the surface area and volume of various solids. Algebra: use linear combinations and substitution to solve a system of linear equations Solve a polynomial equation in factored form. Be able to factor a quadratic expression Use the distributive property to factor a polynomial. -Terminology, literary terms/vocabulary list to be studied: Geometry: Similar polygons Dilation Enlargement Pythagorean triples Special right triangles Trigonometric ratios Angle of elevation Angle of depression Magnitude of a vector Direction vector Circle Secant Tangent Point of tangency Central angle Arc Measure of an arc Inscribed angle Intercepted arc Inscribed polygon Circumscribed circle Standard equation of a circle Locus Apothem of a polygon Central angle of a regular polygon Circumference Arc length 2 Sector of a circle Probability Geometric probability Polyhedron Platonic solids Prism Cylinder Pyramid Circular cone Sphere Algebra: Factoring form Zero-product property Factor a quadratic expression Factor completely -Suggested works/ themes/selections/readers: We will study the geometry text book together with algebra 1 sheets. From the geometry textbook lessons: 8.4 Similar Triangles 8.5 Proving Triangles are Similar 8.6 Proportions and Similar Triangles 8.7 Dilations 9.1 Similar Right Triangles 9.2 The Pythagorean Theorem 9.3 The Converse of the Pythagorean Theorem 9.4 Special Right Triangles 9.5 Trigonometric Ratios 9.6 Solving Right Triangles 9.7 Vectors 10.1 Tangents to Circles 10.2 Arcs and Chords 10.3 Inscribed Angles 10.4 Other Angle Relationships in Circles 10.5 Segment Lengths in Circles 10.6 Equations of Circles 11.1 Angle Measures in Polygons 11.2 Areas of Regular Polygons 11.3 Perimeters and Areas of Similar Figures 11.4 Circumference and Arc Length 11.5 Areas of Circles and Sectors 11.6 Geometric Probability 12.1 Exploring Solids 12.2 Surface Area of Prisms and Cylinders 3 12.3 Surface Area of Pyramids and Cones 12.4 Volume of Prisms and Cylinders 12.5 Volume of Pyramids and Cones 12.6 Surface Area and Volume of Spheres 12.7 Similar Solids From Algebra 1 textbook we will cover the following lessons 7.2 Solving Linear Systems by Substitution 7.3 Solving Linear Systems by Linear Combinations 7.6 Solving Systems of Linear Inequalities 9.4 Solving Quadratic Equations by Graphing 9.5 Solving Quadratic Equations by the Quadratic Formula 9.6 Applications of the Discriminant 10.3 Special Products of Polynomials 10.4 Solving Polynomial Equations in Factored Form 10.5 Factoring x2 + bx + c 10.6 Factoring ax2 + bx + c 10.7 Factoring Special Products 10.8 Factoring Using the Distributive Property -Curriculum Activities: Activity on dividing a segment into equal parts p. 500 Activity on index cards p.527 Focus on career (architect) design of a skyscraper p.537 Activity on Inscribed Angles p.612 Activity on segment Lengths p.628 Timekeeping research p.648 Activity on the sum of polygon angle measures p.661 Activity on Surface area p.727 Activity on Volumes p.751 Focus on career (construction) Concrete Weighs p.745 -Suggested Interdisciplinary unit: Geometry on a Sphere Textbook page 714 - 718 -Assessment: Homework Assignments Class work Quizzes Project Tests Quarter Exam Uniform Punctuality Class preparation Class contribution Attendance 10% 10% 20% 10% 20% 25% 5% 4