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Geometry Pre-AP – FBISD – 3rd 9 weeks 2013 – 2014 (Subject to Change) Monday January 6 Campus Staff Dev. Student Holiday 13 5-5 Inequalities in Two Triangles (Hinge Thm.) Obj: Apply theorems about inequalities in triangles. (The sum of any two sides of a triangle is greater than the third. If two sides of a triangle are unequal, then the larger angle lies opposite the longer side. If two angles of a triangle are unequal, then the longer side lies opposite the larger angle.) Discuss Hinge Theorem in class – p. 293 #-30 p. 294 (35-37) Tuesday 7 Wednesday 8 Parts of Similar Triangles & 5-5 Inequalities in Triangles Campus Staff Dev. Student Holiday 14 8.2 Special Rt Triangles Obj: Derive and apply the patterns for special right triangles. Study guide – Case 1 & Case 2 (Begin Wednesday’s notes) Friday 10 5-5 Inequalities in Triangles Obj: Apply theorems about inequalities in triangles. (The sum of any two sides of a triangle is greater than the third. If two sides of a triangle are unequal, then the larger angle lies opposite the longer side. If two angles of a triangle are unequal, then the longer side lies opposite the larger angle.) WS – Parts of Similar Triangles #1-9 WS – Solving Compound Inequalities Inform students that they need to buy a copy of Sphereland and have it by February 9th In class page 292 (1-28, 31-32) 15 8.2 Special Rt. Triangles 16 Obj: Apply the special right triangle patterns and Pythagorean Theorem to solve problems. (Define isosceles trapezoid. Do some sample problems.) Worksheet on Right Triangles p. 428 #15-23, 25-26 WS 8.2 A WS 8.2 Special Right Triangles Thursday 9 5-5 Inequalities in Triangles WS – Inequalities in One Triangle & Finish p. 292 (1-28, 31-32) Right Triangles Obj: Solve right triangle problems. Apply the Pythagorean Theorem to the rectangular prism and to the regular square pyramid. Worksheet – Right Triangle Practice WS - Pythaorgean Theorem More or Less 17 Pyth. Thm. in 3D Obj: Apply the Pythagorean Theorem to 3D figures. Assess special right triangles and the Pythagorean Theorem. WS – Pythagorean Theorem in Three Dimensions Possible Quiz over Special Right Triangles and Pythagorean Theorem?? Quiz over Parts of Similar Triangles and 5-5 Inequalities in Triangles WS-Inequalities in 2 Triangles 20 M. L. King Day No School 21 8.3 & 8.4 Trig Ratios Obj: Define and analyze the trig ratios – tangent, sine, and cosine. Use the calculator to find segment lengths and angle measures. 22 8.5 Angles of Elevation & Depression Obj: Define and apply angles of elevation and depression to solve problems. p. 447 #1-8 & p. 442 #25, 2829 (in class) WS – Trig Ratios in Right Triangles 27 Review Obj: Compare and contrast methods for solving problems involving right triangles. 28 “SNOW” DAY 23 8.5 Angles of Elevation & Depression Obj: Apply all of the trigonometric techniques to solve problems. Assess understanding of the Pyth. Thm. in 3D and trig ratios. p. 437 (53-58) p. 447 #9-18, 23, 28, 29 p. 434 #10, 22, 23 WS – Angles of Elevation & Depression p. 441 #10, 17, 22, 24, 31, 33 Class Activity – Too Tall to Measure (daily grade) 29 Review Obj: Compare and contrast methods for solving problems involving right triangles. 30 Test over Right Triangles (chapter 8) Obj: Assess understanding of chapter 8, right triangles. Go over quiz & worksheet. WS – Ch. 8 Extra Practice (with answers) 24 “SNOW” DAY 31 6.1 Define Special Quads 6.2 Properties of Parallelograms Obj: Define special quadrilaterals. Derive and apply the properties of parallelograms. HW: p. 308 (1-12, 19-26, 45-48) WS – Parallelograms p. 316 (12-16, 31-33, 41) End of Progress 5 Quiz over Pyth. Thm. in 3D and Trig. February 3 6.3 Prove Quad. is a Parallelogram Obj: Derive and apply the ways of proving that a quad. is a parallelogram. Verify that a quad. is or is not a parallelogram by coordinate methods. Introduce verifying parallelogram from coord. of 4 points WS – 6.3 Parallelograms (front & back) Page 325 (14-19, 26) 4 6.4 Special Parallelograms Obj: Derive the properties of special parallelograms. Extend coordinate methods to the rectangle and the rhombus. Study Guide WS – Rectangles, Squares & Rhombi (6.4) (32 problems) 5 6 7 6.5 Trap. & Isos. Trap. Obj: Analyze isosceles trapezoids and apply their properties to find segment lengths and angle measures. 6.5 Kites & Coord Work 6.6 Placing Figures in the Coord. Plane Obj: Analyze the best placement of figures in the coordinate plane. Study Guide WS- Trapezoids (6.5) Quiz over 6.1-6.3 (Subject to change) Obj: Derive and apply the properties of a kite. Classify quadrilaterals by coordinate methods. Work a couple more coord. examples in class WS – Kites & Coord Work with Quadrilaterals Use Practice 6-6 as a study guide Introduce Kite Project (daily grade) Due March 7th Teach 6.7 today Pg. 344 (2-7, 9-15, 22-27) 10 11 12 13 14 6.7 Proofs using Coord Geom. Obj: Prove properties of Comparing & Contrasting Quads. Obj: Compare and contrast quadrilaterals and their properties. Midpt. Quads. Review Test on Quadrilaterals Obj: Analyze quadrilaterals formed by connecting the midpoints of consecutive sides. Obj: Review quadrilaterals, their properties, and coordinate methods for verifying each. Obj: Assess understanding of Quadrilaterals, chapter 6. 20 21 Continue 10-3 and 10-5 Obj: Review Heron’s Formula and review circumference and area of a circle. special quadrilaterals by coordinate methods. Use Ex. on page. 349 in class and problem 1 to illustrate choices of coordinates. WS – 6.7 Proofs Using Coordinate Geometry Quiz over Special Parallelograms & Trapezoids Pg. 309 (29-41, 50-53, 56-59) WS –Quadrilateral Relationships WS-Quad. from Midpoints (in class) Fill in Chart of properties of quadrilaterals WS – Connecting Midpoints WS – Chapter 6 Review (note: review sheet does not include sections 6.6 & 6.7) Page 359 (30-34) 19 10-3 Area of Regular Polygons and 10-5 Trigonometry and Area Obj: Derive the formula for finding the area of a regular polygon, including the special cases of equilateral triangle, square, and regular hexagon. Use trigonometry to find any missing parts. 17 18 10-1 Area of Parallelograms & Triangles 10-2 Area of Trapezoids, Rhombuses & Kites (include geoboard methods) Obj: Analyze and apply methods for finding the area of parallelograms and triangles, including the dissection and surround methods. Obj: Develop and apply the formulas for area of a trapezoid and for quadrilaterals with perpendicular diagonals – rhombus, kite, square, and others. HW: p. 536 (1-9; 12-14; 19-27; 32-39) Geoboard Worksheet HW: pg. 542 (4, 8-18, 22-32, 35) 24 10-6 Circles and Arc 25 10-4 Perimeters and and 10-7 Areas of Circles & Sectors Obj: Apply ratios to find arc length and area of sector. Analyze the area of a segment of a circle as a sector minus a triangle. Areas of Similar Polygons Obj: Apply ratios to find perimeters and areas of similar polygons. 26 p. 555 (2, 3, 5-10, 13-16, 19-22, 28-32, 35-37, 41-44) WS - Chapter 10 Review p. 571 (57-59) p. 578 (22, 25-28, 30, 32, 35, 40) Worksheet – Arc Length, Sector Area, Segment Area March 3 Worksheet with Heron’s Theorem and Circle Area/Perimeter pg. 561 (2, 11-17, 25) Quiz on 10-1 and 10-2 pg. 548 (1-3,10-18,24-25, 29) pg. 561 (1, 4, 7, 8) End of Progress 6 District Assessment 27 28 10-8 Geometric Probability 1-2 Drawings, Nets, and Other Models Obj: Apply concepts of probability to distance and area. HW: Worksheet – Algebra & Areas p. 13 (1-9, 18-20, 35) Worksheet Isometric dot paper & square dot paper provided for book work Review (Homework due Monday) p. 584 (1-6, 15-20, 23-26, 32-35, 47) Worksheet – Shaded Areas Quiz 10-3 & 10-5 4 Test on Ch. 10 Chapter 10 Obj: Compare and contrast methods for finding the perimeter and area of polygons, circles, sectors, segments, and composite figures. Obj: Find area of triangles by trig. Find shaded areas by applying all of the area formulas. Obj: Assess understanding of Area and Perimeter – Chapter 10. Obj: Apply algebraic skills to find area. Finish the homework on 12 from Friday 2/28 5 6 1-2 continued 11-1 Space figures and Cross Sections In groups of 2 or 3, find 8 different nets for a pyramid with a square base. Use polyhedrons (clicktogethers). Obj: Describe and analyze cross sections of solid figures. Use plastic cubes with colored water to “see” cross sections. p. 13 (11-16, 23-30, 34) “Packet” of pattern folding, etc. 7 Kite Day! In class using cubes p. 603 (46-54) HW: p. 601 (1-19, 21-29, 36) Spring Break—March 10-14 17 18 11-2 Surface Areas of Prisms and Cylinders 11-3 Surface Areas of Pyramids and Cones Obj: Derive and apply the formulas for lateral area and surface area of right prisms and cylinders. Obj: Derive and apply formulas for lateral area and surface area of regular pyramids and cones. p. 612 (5-12, 16, 19, 21, 22, 24, 27-30, 33-35) p. 253 (1-4) p. 620 (1, 2, 4, 5, 9-11, 18, 19, 21, 23, 27-30) 19 Review Obj: Solve lateral area and surface area problems, including some nonformula problems. HW: Worksheet - Fun with Lateral Area and Surface Area Worksheet - Review of 11.2 and 11.3 20 21 11-3 continued Obj: Apply formulas for lateral area and surface area of pyramids, cones, prisms, and cylinders.. p. 620 (3, 6, 8, 12, 17, 3135, 37-40, 43) 11-4 Volumes of Prisms & Cylinders Quiz 1-2, 11-1, 11-2, & Algebra and Areas Obj: Derive and apply the formulas for volumes of prisms and cylinders. Page 627 (1, 2, 4-6, 10-12, 15, 17-19, 22, 26-35, 37 (part a only), 38) End 3rd Nine Weeks (Subject to change) Geometry Pre-AP – FBISD – 4th 9 weeks 2013 – 2014 (Subject to Change) Monday 24 Extra day to review Come up with additional review sheet or activity Tuesday 25 Review for Test Obj: Solve lateral area and surface area problems, including some nonformula problems. Wednesday 26 TEST 1.2, 11.1 – 11.3 Homework: page 75 #119 (TAKS Tune-up) Thursday 28 11-5 Volumes of Pyramids & Cones 11-6 Surface Area & Volume of a Sphere Obj: Derive and apply the formulas for surface area and volume of a sphere. Describe and draw the intersection of a given plane with a sphere. Orange Activity Obj: Derive and apply the formulas for volumes of pyramids and cones from models. Page 634 (1, 2, 6, 8, 9, 11, 13-16, 18, 20-25, 27, 2931) 31 April 1 2 Composite figures STAAR English I Writing & Reading STAAR English II Writing & Reading Obj: Apply volume concepts to find the volume of composite figures, including cones made by removing a sector from a circle. Page 642 (40-43, 47) Page 644 (10) WS - More Practice Quiz over 11.4 and 11.5 7 Volume of Rotational Solids Card Deck Matching Activity – Volumes of rotation(for a daily grade) 8 9 Test Review 10-6 Circles and Arcs 12-1 Tangent Lines Obj: a. Understand and apply relationships between central angles and arcs. b. Understand and apply properties of tangent lines. Finish Card Deck if needed And review for test. Due Friday: p. 570 (15-26, 42-47, 4953, 70) p. 665 (1-4, 8-15, 20, 22, 25, 26, 28) Hw: Create a test review? Bring an orange for tomorrow 3 11.7 Areas & Volumes of Similar Solids Obj: Use ratios to solve problems involving similar figures. Page 648 (1-10, 12-15, 1718, 20, 22, 24, 29, 34, 35) 11 Test over Surface Area and Volume (11-3 – 11-7 & WS) 12-2 Chords and Arcs Obj: Develop and apply relationships between circles, chords, and arcs. p. 673 (3-8, 11-18, 26, 27, 30-32, 34) Hw: Finish the homework from Wednesday Hand out Sphereland study sheets. Read through page 26 by Friday, April 17 End of Progress 7 16 17 12-4 Angle Measures and Circles (exterior) 12-4 Segments and Circles (Interior) Obj: Apply relationships between circles, arcs, angles, and segments. p. 691 (9, 11-28, 36, 40, 41) p. 685 Checkpoint Obj: Find the surface area and volume of frustums by applying similar solids. Apply concepts of surface area and volume to solve problems. 10 15 Obj: Understand and apply relationships between segments and circles. 4 Frustums & More Practice Page 636 (32, 34) Page 649 (11, 16, 37) Worksheet - Frustums Page 652 (1-2) 12-3 Inscribed Angles Obj: Understand and apply relationships between angles with their vertex in the interior and in the exterior and their intercepted arcs. HW: Page 640 (1, 2, 5, 8, 10, 12, 13, 16-24, 29, 34, 35, 37, 38) Worksheet – Area and Volume Review 14 Obj: Understand and apply relationships between angles with their vertex on the circle and their intercepted arcs. Find the center of a circle without measurement. Friday 27 18 Good Friday No School Quiz on 12-1 through the angle part of 12-4 WS – Chapter 12 Assign Sphereland, Part I The Straight World – pages 27-82 p. 681 (5-24, 28, 42-44) p. 691 (1-8) and WS Finding Angle Measures in Circles 21 22 23 24 25 Sphereland Sphereland TEST over Circles – 10-6 and 12-1 to 12-4 Obj: Understand the social and mathematical progress through history by an analysis of dimensions in Sphereland. Obj: Understand the social and mathematical progress through history by an analysis of dimensions in Sphereland Obj: Review relationships between circles, arcs, angles, and segments. Discuss the introduction through page 26. Show Flatland video Sphereland Obj: Summarize the strands throughout Sphereland: possibility of third dimension, role of women, attitude of society, and kinds of reasoning. Discuss Sphereland through page 82 (Part I) HW: Finish Part I pages 2782 , start part II pages 83 – 119 Study for the test HW: Finish Sphereland Part I 27-82 and study guide, work on Part II pages 83 - 119 Obj: Assess understanding of relationships between circles, arcs, angles, and segments. HW: Finish Sphereland, Part II pages 83 -119, start Part III pages 120 – 170 (Subject to change) 28 Sphereland Obj: Understand the social and mathematical progress through history by an analysis of dimensions in Sphereland 29 Sphereland Obj: Understand the social and mathematical progress through history by an analysis of dimensions in Sphereland 30 May 1 Sphereland Obj: Examine the rolls of women, social structure and history by Discussing Sphereland Part IV Sphereland Discuss Part II Obj: Summarize the strands throughout Sphereland and their relevance to today. 2 Obj: Summarize the strands throughout Sphereland and their relevance to today. Review Sphereland with “I have, who has?” Card Act Show Sphereland Video Discuss Part III HW: Sphereland, Part III – pages 120 – 170 for Monday, Finish the book, pages 170-205 and do Part IV Assign Sphereland, Part IV – pages 170 – 205 5 6 7 STAAR Algebra I* STAAR Biology* STAAR U.S. History STAAR Algebra I* STAAR Biology* STAAR U.S. History STAAR Algebra I* STAAR Biology* STAAR U.S. History 8 Sphereland End of Progress 8 9 Quiz over all of Sphereland (2 daily grades) 12-5 Circles in the Coordinate Plane Obj: Derive and apply the equation of a circle in the plane. p. 697 (1, 3, 6, 8, 11, 12, 14, 17, 20, 21, 24, 27, 29, 32, 33, 35, 37, 40, 42-47, 53, 55, 57) 12 13 14 15 3D Coordinate System 3D Coordinate System More Locus work More Locus work 16 More Locus Work Obj: Understand coordinate geometry from a dimensional viewpoint. Locate points in space. Locate planes in space. Obj: Match equations, pictures, and descriptions of planes in space. Obj: Understand and describe verbally and algebraically a locus of points that satisfies given condition(s). Obj: Assess understanding of equation of circle and of 3D coordinate system. Review Locus of Points. Obj: to discuss what happens when two Loci intersect. p. 703 (9-12, 18-20, 26, 31, 32, 33-40, 44) and WS – Locus of Points and Intersection of Loci p. 703 (1-8, 14-17) and WS Examples for Locus of Points Quiz over 12-5 and 3D coordinate system 20 21 22 23 Test over 12-5, 3D coordinate system, Locus of Points, and Intersection of Loci Spherical Geometry Taxicab Geometry Networking and Graph Theory Obj: To expose student to another type of Geometry, including how the basics of Geometry change when applied to a spherical surface. Obj: To expose students to another type of Geometry, including the new rules of Taxicab Geometry and the history behind it. WS – Coordinate Geometry from a Dimensional Viewpoint; WS- Coordinates in 3D 19 Review 3D Card Matching Activity (counts as a daily grade) WS 2 - Coordinates in Space WS – Intersection of Loci WS – Locus of Points Obj: Understand the development of graph theory and networking WS – Taxicab Geometry WS – Graph Theory – Polygons as Networks 28 Review for Quiz and Exams 29 30 4 Semester Exams 5 Semester Exams 2nd Period Exam 4th Period Exam 3rd Period Exam 5th Period Exam WS – comparing Planar and Spherical Geometry 26 27 Memorial Day No School Topology Obj: Determine if two objects are topologically equivalent under homeomorphism classes and under homotopy classes. WS - Topology June 2 Semester Exams 3 Spherical, Taxi and Euclidean Geometry Review. Obj: To review the three types of Geometry and compare and contrast the different rules. Quiz over Spherical Geometry, Taxicab, Networking, and Topology (not droppable) Review for final exam 7 Semester Exams Teacher Workday 6th Period Exam (12:30 – 2:30) (Subject to change) 1st Period Exam 7th Period Exam (Subject to change)