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Transcript
1st Quarter Essential Questions Unit 1 (Weeks 1-3/4) How can we represent real figures algebraically and geometrically? Unit 2 (Weeks 4/5-7) How can we prove geometric relationships within and among figures? Major Content Basic geometric figures: points, lines, planes, angles, and polygons Logical basis and structure of formal proof. Common Focus/Skills 1. Identify points, lines, and planes by name and relationship (e.g. collinear, coplanar, intersecting, perpendicular, parallel). 1. Make conjectures and find counterexamples. 2. Use distance and midpoint formulas. 3. Measure and classify angles and their parts. 4. Identify and use special angle relationships (e.g. adjacent, vertical, linear pair, supplementary, and complementary) 2. Use logic to determine the truth of conjunctions, disjunctions, and conditional statements. 3. Use postulates and theorems to write proofs in paragraph and twocolumn form regarding segment and angle relationships. IL Standards /Performance Descriptors 9C/H3 Represent, solve, and explain numerical and algebraic relationships using geometric concepts. 9A/I8 Calculate 2. Use slope of two lines to determine parallelism or perpendicularity. 3. Write the equation of a line in slope-intercept and point-slope form. 4. Represent and find the distance between a point and a line and between two parallel lines. 5. Determine what can and cannot be assumed from a diagram. 6. Identify and name polygons and find their perimeters. 9A/H5 Solve pictorial or word problems that involve geometric relationships within a single shape or figure, including the Pythagorean Theorem. Unit 3 (Weeks 8-10) What special properties arise from the intersection or nonintersection of two lines? Parallel lines/transversals, slopes and equations of lines, distance between points, lines, and planes. 1. Identify and use properties of special angle pairs created by parallel lines and transversals (e.g. consecutive interior, alternate interior, alternate exterior, and corresponding). 9C/I3 Provide a counterexample to disprove a conjecture. 9C/J2 Extend the ideas of formal and informal proof to non-geometric situations. 9C/I2 Develop a formal proof for a given geometric situation on the plane. 9A/I2 Classify angle relationships for two or more parallel lines crossed by a transversal. 9A/I3 Analyze geometric situations using Cartesian coordinates. distance, midpoint coordinates, and slope using coordinate geometry. Common Learning Activities 9C/I2 Develop a formal proof for a given geometric situation on the plane. Algebra essentials review Discuss and model basic interactions of points, lines, and planes Make a conjecture and construct a simple proof, or disprove by counterexample Springboard (optional): “Riddle me This” Measure segments and angles using both technology and formulas Algebra pretest and posttest Discuss and model special angle pairs Discuss and model coordinate linear analysis Springboard (suggested): “Patios by Madeline” Springboard (required): “What’s my Name?” Products/Assessments Review for MidSemester Exam Daily bell-ringers Mid-Semester Exam Proof sets (in groups) Daily bell ringers Mid-chapter quizzes Mid-chapter quizzes Chapter test Chapter test Daily bell ringers Mid-chapter quizzes Chapter test Notebooks/journals Springboard embedded assessment 2nd Quarter Essential Questions Major Content Common Focus/Skills Unit 4 (Weeks 11-13) How can we identify and prove relationships between congruent triangles? Classification and properties of triangles by angles and sides; triangle congruence properties. 1. Classify triangles by angles and sides. 2. Apply Angle Sum and Exterior Angle Theorems 3. Identify congruence transformations involving triangles. 4. Use SSS, SAS, ASA, and AAS properties of triangle congruence. 5. Use properties of isosceles and equilateral triangles. IL Standards/ Performance Descriptors 6. Set up and write coordinate proofs involving triangles. 9A/H3 Identify possible types of two- or threedimensional figures that would match a set of given conditions. 9A/I1 Describe and apply properties of a polygon or a circle in a problem-solving situation. 9A/I4 Represent transformations of an object in the plane using sketches, coordinates, and vectors. Unit 5 (Weeks 14-16) How can we indirectly compare measurements? Unit 6 (Weeks 17-19) How can ratios and proportions be used in geometric analysis? Special segments in a triangle, inequality, and indirect proof. Proportional relationships among similar figures 1. Identify and use perpendicular bisectors, angle bisectors, medians, and altitudes in triangles. 1. Solve problems involving ratios and proportions. 2. Recognize and apply properties of inequalities in triangles. 3. Construct indirect algebraic and geometric proofs. 4. Apply the Triangle Inequality Theorem. 5. Apply the SAS Inequality and SSS Inequality Theorems. 9A/I10 Identify and apply properties of medians , altitudes, perpendicular bisectors, and midlines of triangles. 9A/I1 Describe and apply properties of a polygon or a circle in a problem-solving situation. 9C/I6 Describe the difference between an inductive argument and a deductive argument. 2. Solve problems involving scale factor of similar polygons. 3. Identify similar triangles and solve problems involving proportionality of their corresponding parts, including sides, angle bisectors, altitudes, medians, and perimeters. 4. Recognize and describe characteristics of fractals (optional) 6D/IH1 Develop, use, analyze, and explain methods for solving number sentences or word problems involving proportions with rational numbers. 9B/I1 Solve problems using triangle congruence and similarity of figures. 9C/I1 Create and critique arguments concerning geometric ideas and relationships such as properties of circles, triangles and quadrilaterals. Common Learning Activities 9C/J1 Prove conjectures about geometric figures on the plane using coordinate geometry. Discuss and model triangle classifications and transformations Model triangle congruence proofs Springboard (required): “Truss Your Judgment” 9A/H4 Determine if a triangle is possible using side lengths and the triangle inequality. 9C/I2 Develop a formal proof for a given geometric situation on the plane. Discuss and model use of special segments in triangles Student examples of real-life indirect proof used to introduce mathematical ones Discuss and model inequality theorems Springboard (optional): “What’s the Point” Review for Semester 1 Exam Review ratios and proportions: model and discuss their use in geometric situations Springboard (suggested): “The Sagging Gate” 3rd Quarter Unit 7 (Weeks 20-22) How can side length affect angle measure in a triangle? Unit 8 (Weeks 23-25) How can we classify and use the properties of specific quadrilaterals? Major Content Special properties of right triangles and trigonometry. Common Focus/Skills 1. Use geometric mean to solve problems involving the altitude to the hypotenuse of a right triangle. Interior and exterior angle sums; properties of and coordinate proofs involving quadrilaterals. 1. Find the interior and exterior angle sums of a polygon. Essential Questions 2. Use the Pythagorean Theorem. 3. Use properties of 45-45-90 and 30-60-90 triangles. 4. Solve problems involving basic trigonometric ratios, including ones involving angle of elevation or depression. IL Standards /Performance Descriptors 5. Use the Law of Sines and Law of Cosines to solve triangles (optional). 9A/H5 Solve pictorial or word problems that involve geometric relationships within a single geometric shape or figure, 2. Recognize and apply properties of parallelograms (including special properties of rectangles, rhombi, and squares) and trapezoids. 3. Use coordinates to prove theorems involving quadrilaterals. Unit 9 (Weeks 2627) How can we view geometric relationships in terms of movement within the plane? Transformations, tessellations, dilations, vectors, and matrices. 1. Use transformational analysis to identify reflection, rotation, translation, and symmetry in congruent figures. 2. Identify and create specific tessellations 3. Classify dilations and determine their scale factors. 4. Find magnitude and direction of, and perform translations with, vectors (optional). Unit 10 (Weeks 28-30) What are the relationships among circles and their parts? Circumference and equation of a circle; angle, arc, chord, secant, and tangent relationships. 1. Identify parts of a circle and use to find its circumference. 2. Recognize and use relationships between angles, arcs, chords, tangents, and secants. 3. Find measures of intersecting segments inside and outside of a circle. 4. Write the equation of a circle and graph in the coordinate plane. 5. Use matrices to determine transformational coordinates (optional). 7C/I6 Calculate by an appropriate method the length, width, height, perimeter, . . . angle measures or sums of angle measures 9A/I4 Represent transformations of an object in the plane using sketches, coordinates, and vectors. 9A/I1 Describe and apply properties of a polygon or a circle in a problemsolving situation. 9B/I3 Identify including the Pythagorean Theorem. 9D/I2 Solve problems involving 45-4590 and 30-60-90 triangles. 9D/H3 Solve for missing side lengths using the trigonometric ratios in right triangles. Common Learning Activities 9D/J1 Solve problems using the Laws of Sines/Cosines. Discuss and model use of right triangle properties Introduce use of SOHCAHTOA 9A/I1 Describe and apply properties of a polygon or a circle. 9B/I5 Analyze and describe the transformations that lead to successful tessellations of one or more figures. 6B/J9 Solve problems using matrices. relationships among circles, arcs, chords, tangents, and secants. 9A/I3 Analyze geometric situations using Cartesian coordinates. 9A/I3 Analyze geometric situations using Cartesian coordinates. Discuss and model use of angle sum properties Model transformational and algebraic comparison of figures Confirm special quadrilateral properties through measurement Display studentcreated tessellations Daily bell ringers Springboard (optional): “Miror, Mirror on the Floor” Daily bell ringers Springboard (required): “Community Quilting Project” Daily bell ringers Mid-chapter quizzes Mid-chapter quizzes Mid-chapter quizzes Chapter test Chapter test Chapter test Springboard (suggested): “Picture This” Products/Assessments of common geometric figures, or combinations of common geometric figures. Springboard embedded assessment Review for MidSemester Exam Confirm circle properties by measurement using ruler and protractor Mid-Semester Exam Daily bell ringers Mid-chapter quizzes Chapter test Notebooks/journals 4th Quarter Essential Questions Unit 11 (Weeks 31-33) How are the areas of two-dimensional figures determined? Major Content Perimeter/circumference and area of polygons and circles; geometric probability; segments and sectors of circles. Common Focus/Skills 1. Use formulas and measurements to find perimeter/circumference and area of parallelograms, triangles, trapezoids, rhombi, regular polygons, irregular figures, and circles. 2. Solve problems involving geometric probability. Unit 12 (Weeks 34-36) How are the surface areas of threedimensional figures determined? Nets and surface area of prisms, cylinders, pyramids, cones, and spheres. 1. Use nets to find surface area of a threedimensional figure. 2. Use formulas and measurements to find lateral and total surface areas of prisms, cylinders, pyramids, and cones. 3. Use formulas and measurements to find surface area of a sphere. 3. Solve problems involving segments and sectors of circles. IL Standards /Performance Descriptors 7C/I6 Calculate by an appropriate method the length, width, height, perimeter, area, volume, surface area, angle measures or sums of angle measures of common geometric figures, or combinations of common geometric figures. 10C/I1 Determine geometric probability based on area. 9A/I5 Design a net that will create a given figure when folded. 7C/I6 Calculate by an appropriate method the length, width, height, perimeter, area, volume, surface area, angle measures or sums of angle measures of common geometric figures, or combinations of common geometric figures. Unit 13 (Weeks 37-38) How are the volumes of three-dimensional figures determined? Volume of prisms, cylinders, pyramids, cones, and spheres; congruence and similarity of solids; coordinates in space. 1. Use formulas and measurements to find volume of prisms, cylinders, pyramids, and cones. 2. Use formulas and measurements to find volume of a sphere. 3. Identify and use the properties of congruent or similar solids. 4. Graph and determine measurements of solids in space (optional). 7C/I6 Calculate by an appropriate method the length, width, height, perimeter, area, volume, surface area, angle measures or sums of angle measures of common geometric figures, or combinations of common geometric figures. 7C/H8 Determine the volume of a sphere. 7C/I5 Determine the ratio of similar figure perimeters, areas, and volumes using the ratio of similitude. 9A/I3 Analyze Common Learning Activities Products/Assessments Measure polygons and circles and use results in length and area formulas Build Sierpinski’s Pyramid geometric situations using Cartesian coordinates. Review for Final Exam Use polyhedral models to illustrate determination and comparison of volume Use classroom to set up and solve probability problems involving area Measure nets and fold into polyhedra: use results to determine surface area Springboard (required): “Coming Full Circle” Daily bell ringers Springboard (optional): “Plenty of Polygons” Daily bell ringers Springboard (suggested): “Crystal Globe” Final Exam Mid-chapter quizzes Mid-chapter quizzes Daily bell ringers Chapter test Chapter test Mid-chapter quizzes Springboard embedded assessment Chapter test Notebooks/journals