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Transcript
Secondary Mathematics Curriculum Map Grade Level/Course:_____Geometry_______________ Grading Period 1 Grading Period 1 1st 3-weeks 2nd 3-weeks Concept: 1.2 Construct 1.3 Understand and Standard(s): congruent segments use the relationships and angles, angle between special pairs bisectors, and parallel of angles formed by and perpendicular parallel lines and lines transversals Concept: 8.9 Perform basic 2.1 Identify and Standard(s): constructions, describe convex, describing and concave, and regular justifying the polygons procedures used. Concept: 1.1 Find the lengths 2.5/3.3 Find and use Standard(s): and midpoints of line measures of sides, segments in one- or perimeters, and areas two- dimensional of polygons and coordinate system quadrilaterals. Grading Period 1 3rd 3-weeks 8.3 Make conjectures about geometric ideas. Distinguish between info that supports a conjecture and proof of conjecture. 8.4 Write and interpret statements of the form “if – then” and “if and only if” Grading Period 2 1st 3-weeks 4.2 Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors 4.3 Construct triangles congruent to given triangles 4.5 Prove and apply theorems involving segments divided proportionally. 8.5 State, use and examine the validity of the converse, inverse, and contrapositive of “if – then” statements. 4.6 Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles. 8.6 Identify and give examples of undefined terms, axioms, and theorems, and inductive and deductive proofs. 8.7 Construct logical arguments, judge their validity, and give counterexamples. 8.8 Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. 4.8 Prove and apply the inequality theorems: triangle inequality, inequality in one triangle, and hinge theorem. 4.2 Locate orthocenter, incenter, circumcenter, and centroid. Concept: Standard(s): 1.4 Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines Concept: Standard(s): 4.7 Solve problems by relating the measures of the sides and perimeters of triangles. Undefined terms, point, line, plane, collinear, coplanar, two-dimensional, three-dimensional, line segment, ray, angle, degree, vertex, postulate (axiom), theorem, corollary, midpoint, bisect, acute angle, right angle, obtuse angle, straight angle, congruent, construction, compass, straight edge, protractor, complementary, supplementary, adjacent, linear pair, vertical angles, convex, concave, conjecture, inductive reasoning, deductive reasoning, counterexample, conditional statement, biconditional statement, converse, inverse, contrapositive, truth value, proof( paragraph, flow, two-column), skew, transversal, corresponding angles Vocabulary 4.1 Identify triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular. First Semester Grading Period 2 2nd 3-weeks 4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas. 8.9 Perform basic constructions, describing and justifying the procedures used. Grading Period 2 3rd 3-weeks 4.1 Define scalene, isosceles, equilateral, right, obtuse, acute, and equiangular. Classify triangles by their sides and angles. 4.2 Define altitudes, medians, angle bisectors, and perpendicular bisectors. 4.7 Find and use the measures of sides, perimeters, and areas of triangles. Relate these measures to each other using formulas. 4.8 Solve problems by applying triangle inequality theorem, theorems involving inequalities, and hinge theorem. 4.9 Use coordinate geometry to prove properties of triangles. Scalene, isosceles, equilateral, equiangular, acute, obtuse, and right triangles, interior and exterior angles of a triangle, corresponding parts, congruent triangles, opposite side, opposite angle, included angle, included side, hypotenuse and legs of right triangle, base angles and vertex angle of isosceles triangle, base and legs of an isosceles triangle, midsegment, altitude, median, angle bisector, perpendicular bisector, point of concurrency, orthocenter, centroid, incenter, circumcenter, coordinate proof, ratio, proportion, scale, similar Secondary Mathematics Curriculum Map Grade Level/Course:________Geometry_______ Grading Period 3 Grading Period 3 st 1 3-weeks 2nd 3-weeks Concept: 5.1 Prove and use the 3.4 Use coordinate Standard(s): Pythagorean geometry to prove Theorem properties of quadrilateral. Concept: Standard(s): Concept: Standard(s): 5.2 State/apply relationships when altitude is drawn to hypotenuse of right triangle 5.3 Use special right triangles to solve problems 2.2 Find measures of interior and exterior angles of polygons. 2.3 Use properties of congruent and similar polygons to solve problems. 3.1 Describe relationships among the quadrilaterals. Grading Period 3 3rd 3-weeks 3.3 Find, use measures of sides, perimeters, and areas of quadrilaterals. 4.4 Use properties of congruent triangles to solve problems involving lengths and areas. 4.7 Recall formula for perimeter and area of triangles. Concept: Standard(s): 5.4 Define and use trig functions in terms of angles of right triangles Concept: Standard(s): 5.5 Know the 3.2 Use properties of relationship congruent and similar quadrilaterals to solve sin + cos = 1 5.6 Solve word problems. problems involving right triangles Pythagorean Theorem, Pythagorean triple, geometric mean, isosceles right triangle, trigonometric ratio, sine, cosine, tangent, cosecant, secant, cotangent, arcsine, arccosine, arctangent, angle of elevation, angle of depression, parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid, midsegment of a trapezoid, bases and legs of a trapezoid, kite, apothem, central angle Vocabulary 4.7 Solve problems by relating measures of sides, perimeters, and areas of triangles. Grading Period 4 st 1 3-weeks 2.4 Apply transformations to polygons to determine congruence, similarity, symmetry and tessellations. 6.1 Find the center of a given circle. Construct circle through 3 given points. 6.4 Construct tangents to circles and circumscribe and inscribe circles. 7.6 Identify and know properties of congruent and similar solids. 6.2 Define relationships among: radius, diameter, arc, measure of arc, chord, secant, and tangent. Second Semester Grading Period 4 Grading Period 4 2nd 3-weeks 3rd 3-weeks 6.3 Prove theorems 7.1 Describe and make related to circles. regular and non regular polyhedral 6.5 Define arcs and related angles (central, inscribed, and intersections of secants and tangents). 6.6 Define and identify congruent and concentric circles. 7.2 Describe the polyhedron that can be made from a given net. Describe the net for a given problem. 7.3 Describe relationships between the faces, edges, and vertices of polyhedra. 6.7 Define/find/use measure of circumference, are length, and areas of circles and sectors. 6.8 Find the equation of a circle in the coordinate plane in terms of its center and radius. 7.4 Describe symmetries of geometric solids. 7.5 Describe sets of points on spheres: chords, tangents, and great circles. 7.7 Find/use measures of sides, volumes of solids, and surface areas of solids. Polyhedron, face, edge, Platonic solid, tetrahedron, hexahedron, octahedron, dodecahedron, icosahedrons, cross section, prism, pyramid, cylinder, cone, sphere, great circle, slant height, lateral face, lateral edge, lateral area, right/oblique, Cavalieri’s principle, chord, major arc, minor arc, arc length, sector, tangent line, secant line, inscribed angle, intercepted arc, circumscribe, inscribe, standard equation of a circle, transformation, congruence transformation, image, preimage, translation, reflection, rotation, dilation, symmetry, tessellation