* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Regional Integrated Geometry Curriculum
Survey
Document related concepts
Surface (topology) wikipedia , lookup
Lie sphere geometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Euler angles wikipedia , lookup
Analytic geometry wikipedia , lookup
History of geometry wikipedia , lookup
Map projection wikipedia , lookup
Rational trigonometry wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
Plane of rotation wikipedia , lookup
Riemannian connection on a surface wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Projective plane wikipedia , lookup
Euclidean geometry wikipedia , lookup
Transcript
Regional Integrated Geometry Curriculum UNIT: Geometric Relationships TOPIC: Lines and Planes Time frame for unit: 9 days Time for topic: 2 days Prior Knowledge 8.G.1 8.G.2 8.G.3 8.G.4 Identify pairs of vertical angles as congruent Identify pairs of supplementary and complementary angles Calculate the missing angle in a supplementary or complementary pair Determine angle pair relationships when given two parallel lines cut by a transversal 8.G.5 Calculate the missing angle measurements when given two parallel lines cut by a transversal 8.G.6 Calculate the missing angle measurements when given two intersecting lines and an angle Content G.G.1 Know and apply that if a line is perpendicular to each of two intersecting lines at their point of intersection, then the line is perpendicular to the plane determined by them G.G.2 Know and apply that through a given point there passes one and only one plane perpendicular to a given line G.G.3 Know and apply that through a given point there passes one and only one line perpendicular to a given plane G.G.4 Know and apply that two lines perpendicular to the same plane are coplanar G.G.5 Know and apply that two planes are perpendicular to each other if and only if one plane contains a line perpendicular to the second plane G.G.6 Know and apply that if a line is perpendicular to a plane, then any line perpendicular to the given line at its point of intersection with the given plane is in the given plane G.G.7 Know and apply that if a line is perpendicular to a plane, then every plane containing the line is perpendicular to the given plane G.G.8 Know and apply that if a plane intersects two parallel planes, then the intersection is two parallel lines G.G.9 Know and apply that if two planes are perpendicular to the same line, they are parallel G.G.35 Determine if two lines cut by a transversal are parallel, based on the measure of given pairs of angles formed by the transversal and the lines Concepts Undefined terms: point, line, plane Notation for point, line, plane, parallel, perpendicular Parallel Planes Identify parts of postulate: hypothesis, conclusion Collinear, coplanar Vertical angles, complementary, supplementary Application of line perpendicular to plane Essential Questions How do points, lines and planes relate to describe our world? How do we know if lines, planes are parallel or perpendicular? Process/skills G.PS.1 Use a variety of problem solving strategies to understand new mathematical content G.RP.2 Recognize and verify, where appropriate, geometric relationships of perpendicularity, parallelism, congruence, and similarity, using algebraic strategies G.CM.11 Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and geometric diagrams G.CN.6 Recognize and apply mathematics to situations in the outside world G.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts Vocabulary Alternate Interior Angle Alternate Exterior Angle Axiom Collinear Coplanar Corresponding angles Line Linear Pair Parallel Perpendicular Plane Point Postulate Ray Same side interior Segment Skew Lines Straight angles Supplementary angles Transversal Undefined terms Vertical angles Suggested assessments Pre-assessment Regents/State exams Projects Participation Q-A Responses Oral responses Conversations Resources On-spot checks of class work Homework Observations of students’ work/behaviors Students’ explanations Draw a picture Tests and Quizzes T/F Multiple Choice Written Response Ticket out the door See Blackboard for specific Assessments* Regional Integrated Geometry Curriculum UNIT: Geometric Relationships TOPIC: Geometric Solids Prior Knowledge Time frame for unit: 9 days Time frame for topic: 5 days A.G.1 Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle A.G.2 Use formulas to calculate volume and surface area of rectangular solids and cylinders. Content G.G.10 Know and apply that the lateral edges of a prism are congruent and parallel G.G.11 Know and apply that two prisms have equal volumes if their bases have equal areas and their altitudes are equal G.G.12 Know and apply that the volume of a prism is the product of the area of the base and the altitude G.G.13 Apply the properties of a regular pyramid, including: lateral edges are congruent lateral faces are congruent isosceles triangles volume of a pyramid equals one-third the product of the area of the base and the altitude G.G.14 Apply the properties of a cylinder, including: bases are congruent volume equals the product of the area of the base and the altitude lateral area of a right circular cylinder equals the product of an altitude and the circumference of the base G.G.15 Apply the properties of a right circular cone, including: lateral area equals one-half the product of the slant height and the circumference of its base volume is one-third the product of the area of its base and its altitude G.G.16 Apply the properties of a sphere, including: the intersection of a plane and a sphere is a circle a great circle is the largest circle that can be drawn on a sphere two planes equidistant from the center of the sphere and intersecting the sphere do so in congruent circles surface area is 4 r 2 4 volume is r 3 3 Concepts Analyze and solve verbal problems Analysis of 2 and 3 dimensional units of measure Use nets to describe prisms, pyramids and cones. Properties, area, volume, surface area, lateral area of: Cone Cylinder Prisms Pyramids Sphere Essential Questions How would you determine the least and greatest sum of the angles of a triangle in spherical geometry? How would you describe the process used to calculate the greater of the height of a container of 3 tennis balls or the circumference of the container? How are the volume formulas for cone and pyramid related? How are the volume formulas for cylinder and prism related? How would you verify the formula for the volume of a pyramid? Process/skills G.PS.3 Use multiple representations to represent and explain problem situations (e.g., spatial, geometric, verbal, numeric, algebraic, and graphical representations) G.RP.2 Recognize and verify, where appropriate, geometric relationships of perpendicularity, parallelism, congruence, and similarity, using algebraic strategies G.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams G.CN.6 Recognize and apply mathematics to situations in the outside world G.R.6 Use mathematics to show and understand physical phenomena (e.g., determine the number of gallons of water in a fish tank) Vocabulary Altitude Bases Circumference Cone Cube Cylinder Equator Equidistant Great circle Lateral area Lateral edges Lateral faces Nets Prime meridian Prism Regular pyramid Slant height Solid Sphere Surface Area Symmetry plane Suggested assessments Pre-assessment Regents/State exams Projects Participation Q-A Responses Oral responses Conversations Resources On-spot checks of class work Homework Observations of students’ work/behaviors Students’ explanations Draw a picture Tests and Quizzes T/F Multiple Choice Written Response Ticket out the door See Blackboard for specific Assessments*