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Harrison County Schools Curriculum Guide for Math Department Course Name: Geometry Essential Questions toward Course Objectives Kentucky Core Content Version 4.1 Grade Level Targeted: 10 - 11 Key Vocabulary Activities and Assessments Measuring Physical Attributes What is surface area/volume? How does it differ from perimeter/area of two dimensional figure? MA-11-2.1.1 Students will determine the surface area and volume of right rectangular prisms, pyramids, cylinders, cones, and spheres in real-world problems. Surface area, lateral area, volume, right rectangular prisms, pyramids, cylinders, cones, spheres, hemisphere How does a change in shape affect the perimeter, area, and volume of a figure? What shape maximizes perimeter, area, and volume? MA-11-2.1.2 DOK 3 Experiment Volume & Cat Litter Open Response The Silo DOK – 3 Perimeter, area, Students will describe and volume how a change in one or more dimensions of a geometric figure affects the perimeter, area, and volume of Unit (s): Project Construction Project Essential Questions toward Course Objectives How do you recognize a right triangle? When should you use the Pythagorean Theorem ? trig ratios? When can the right triangle theorems be used to solve real world situations? Kentucky Core Content Version 4.1 the figure. MA-11-2.1.3 Students will apply definitions and properties of right triangle relationships (right triangle trigonometry and the Pythagorean theorem) to determine length and angle measures to solve real-world problems. DOK – 3 MA-11-2.1.3a Students will apply special right triangles and the converse of the Pythagorean theorem to solve real-world problems. Systems of Measurements Key Vocabulary Right triangle trigonometry and Pythagorean theorem Sine, Cosine, Tangent, angle of elevation, vectors, magnitude, direction 45-45-90 Triangle Theorem 30-60-90 Triangle Theorem Activities and Assessments Project Measure the Flagpole Using shadows Using clinometers Essential Questions toward Course Objectives What units of measure are appropriate for the situation? How do you make a conversion of units within a system of measurement? Kentucky Core Content Version 4.1 Key Vocabulary Activities and Assessments MA-11-2.2.1a Supporting Students will continue to apply to both real world and mathematical situations U.S. customary and metric systems of measurement. Shapes and Relationships Identify relationships between and among points, lines, and planes. Define, describe properties of, give examples of, and apply to both real world and mathematical situations spatial relationships such as betweenness, parallelism, and perpendicularity. Find the intersection of lines, planes, and solids. MA-11-3.1.1 Students will analyze and apply spatial relationships (not using Cartesian coordinates) among points, lines, and planes (e.g., betweenness of points, midpoint, segment length, collinear, coplanar, parallel, perpendicular, skew). DOK – 2 MA-11-3.1.1a Students will use spatial relationships to prove Point, line, plane, collinear, coplanar, betweeness, segment, ray, parallel, perpendicular, skew, intersection, midpoint Segment Addition Postulate Hands on Activities MIRA Patty Paper Essential Questions toward Course Objectives Kentucky Core Content Version 4.1 Key Vocabulary Activities and Assessments basic theorems. Draw, name, analyze, and apply the different types of angle relationships. Describe, draw, and construct two-dimensional figures. Classify according to characteristics. MA-11-3.1.2 Students will analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, supplementary, corresponding, and alternate interior angles) in real-world or mathematical situations. DOK – 2 MA-11-3.1.2a Students will use angle relationships to prove basic theorems. MA-11-3.1.3 Students will classify and apply properties of two-dimensional geometric figures (e.g., number of sides, vertices, length of sides, sum of interior and exterior angle Angle, degrees, ray, sides, vertex, vertical angles, linear pair, straight, right, acute, obtuse, complementary, supplementary, transversal, corresponding, alternate interior, alternate exterior, same-side interior Angle Addition Postulate Triangle, scalene, isosceles, equilateral, equiangular, acute, obtuse, right, legs, hypotenuse, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, dodecagon, interior Hands on Activities Golden Rectangle Construction Geometry Scavenger Hunt Essential Questions toward Course Objectives Kentucky Core Content Version 4.1 measures). DOK – 2 MA-11-3.1.3a Students will know the definitions and basic properties of a circle and will use them to prove basic theorems and solve problems. What properties of triangles can be used to find missing sides and/or angles? Can this info be applied to real world situations? MA-11-3.1.4 DOK 3 Students will solve real world problems by applying properties of triangles (e.g., Triangle Sum Theorem and Isosceles Triangle Theorems) Describe, draw, and construct threedimensional figures. Classify according to characteristics. MA-11-3.1.5 Students will classify and apply properties of three-dimensional geometric figures (e.g., number of edges, faces, vertices). DOK - 2 MA-11-3.1.5a Students will describe the intersection of a plane Key Vocabulary angles, exterior angles, regular, parallelogram, rhombus, rectangle, square, kite, trapezoid, isosceles trapezoid, base angles Triangle Sum Theorem, Exterior Angle Theorem Edges, faces, vertices, polyhedron, regular, convex, cross section, Platonic solids, tetrahedron, octahedron,, dodecahedron, icosahedron, , prism, bases, lateral faces, right prism, oblique Activities and Assessments Discovery Lesson Hands on Activities Constructions MIRA Patty Paper Essential Questions toward Course Objectives Kentucky Core Content Version 4.1 with a three-dimensional figure Determine height and distance using methods of indirect measurement Apply concepts of congruence to solve realworld and mathematical problems (not including proofs) Apply concepts of similarity to solve realworld and mathematical problems (not including proofs) Use to solve real-world problems Key Vocabulary Activities and Assessments prism, MA-11-3.1.5b Students will visualize solids and surfaces in three-dimensional space when given twodimensional representations (e.g., nets, multiple views) and create two-dimensional representations for the surfaces of threedimensional objects. MA-11-3.1.6 Students will apply the concepts of congruence and similarity to solve real-world problems. Open Response The Obelisk DOK – 3 MA-11-3.1.6a Students will prove triangles congruent and similar. SSS Postulate SAS, ASA, AAS Theorems HL Theorem AA-Similarity Theorem Essential Questions toward Course Objectives Reflect two-dimensional figures across the x-axis, the y-axis, or any given lines. Describe properties of and give examples of geometric transformations and apply geometric transformations, with and without a coordinate plane, to both real-world and mathematical situations. Perform transformations on figures. Interpret how figures in a coordinate plane and their resulting images under a transformation are algebraically and geometrically related. Kentucky Core Content Version 4.1 Transformations of Shapes Key Vocabulary MA-11-3.2.1 Students will describe properties of and apply geometric transformations within a plane to solve realworld problems. DOK - 3 Transformations, isometry, image, preimage, reflection, line of reflection, line of symmetry, rotation, translation, glide reflection Coordinate Geometry Represent geometric figures and properties using coordinates Connect these concepts to MA-11-3.3.1 Students will apply algebra or graphing in the coordinate plane to analyze and Distance Formula Midpoint Formula Slope Slope-Intercept Form Pythagorean Activities and Assessments Essential Questions toward Course Objectives algebraic representations. Describe properties of, define, give examples of, and apply to both real-world and mathematical situations ratio measures including slope and rate Apply formulas for the slope of a line, distance between two points, and midpoint of a segment to solve problems. Kentucky Core Content Version 4.1 solve problems (e.g., finding the final coordinates for a specified polygon, finding midpoints, finding the distance between two points, finding the slope of a segment). Key Vocabulary Theorem DOK - 2 Foundational Statements Students will be able to apply geometric definitions, axioms, and theorems as they continue throughout the course. MA-11-3.4.1a ADP Students will identify, explain the necessity of, and give examples of definitions, axioms, and theorems. MA-11-3.4.1b ADP Students will recognize that there are geometries, other than Euclidean geometry, in Theorem, Corollary, Postulate, Proof Activities and Assessments Essential Questions toward Course Objectives Kentucky Core Content Version 4.1 Key Vocabulary which the parallel postulate is not true. MA-11-3.4.1c ADP Students will be able to perform constructions such as a line parallel to a given line through a point not on an a line, the perpendicular bisector of a line, and a bisector of an angle. Construction, Compass, Protractor, Straightedge Congruent segments Congruent angles, Angle Bisector Midpoint, Perpendicular Bisector Perpendicular and Parallel Lines Median, Altitude, Points of Concurrency Activities and Assessments