Discovering Geometry: 1 st Quarter. California Geometry Standard Resources

Transcription

1 Discovering Geometry: 1 st Quarter 1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, Ch. 1,2, 1,2,3, 2.0 Students write geometric proofs, including proofs by contradiction. On-going year round 1,2,3, 3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a Ch. 1,2 1,2,3, 6.0 Students know and are able to use the triangle inequality theorem. Ch. X Bmk 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties 12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems..0 Students prove relationships between angles in polygons by using properties of complementary, 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the 1,2,3, Ch. 2 1,2,3, Ch. 1, 1,2,3, Ch. X Bmk 1,2,3, Ch. 3 1,2,3, Ch. 1,2,3, Ch. 1 Ch. 2 Ch. 3 Ch days days 1 days days Discovering Geometry: 2 nd Quarter 1 7/16/2012

2 1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms,, 5, 6 2,3, 2.0 Students write geometric proofs, including proofs by contradiction., 5, 6 2,3, 3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a 5 2,3,.0 Students prove basic theorems involving congruence and similarity., 5 X Bmk 2,3, 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding X Bmk 2,3, 6.0 Students know and are able to use the triangle inequality theorem. X Bmk 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures..0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems..0 Students prove relationships between angles in polygons by using properties of complementary, Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the 21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. 2,3, 5, 6 2,3, 6, 8 2,3, 8 2,3,, 5 2,3,, 5 X Bmk 2,3, 5 2,3, 6 2,3, Ch...8 days Ch. 5 days Ch days Ch days Discovering Geometry: 3 rd Quarter 2 7/16/2012

3 Students write geometric proofs, including proofs by contradiction. Ch., 11, 12 3, Students construct and judge the validity of a logical argument and give counterexamples to disprove a Ch. 11, 12 3,.0 Students prove basic theorems involving congruence and similarity. Ch. 11, 12 3, 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding Ch. X Bmk, 11, 12 3, 1.0 Students prove the Pythagorean theorem. Ch. 3, 15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right Ch. X Bmk triangles. 3, 17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the Ch. 3, 1.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an Ch. angle and a length of a side. 12 3, 20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such Ch. X0 Bmk as 30, 60, and 0 triangles and 5, 5, and 0 triangles. 3, Ch. Ch. 12 Ch days 1 days 1 days Discovering Geometry: th Quarter 3 7/16/2012

4 1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, Ch. 2.0 Students write geometric proofs, including proofs by contradiction. Ch. 3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a Ch.,.0 Students prove basic theorems involving congruence and similarity. Ch. 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding Ch. X Bmk 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties Ch. 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral Ch. area, and surface area of common geometric figures..0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and Ch. X Bmk students commit to memory the formulas for prisms, pyramids, and cylinders Students determine how changes in dimensions affect the perimeter, area, and volume of common Ch. geometric figures and solids..0 Students prove relationships between angles in polygons by using properties of complementary, Ch. X Bmk 21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed Ch. angles, and inscribed and circumscribed polygons of circles Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, Ch. translations, and reflections. 7 Alg 1 After testing, teachers need to review key Algebra 1 standards as indicated on the next page in order to Bmk Stds help students prepare for Algebra 2 Ch. 1 days Ch days Ch. 1 days Discovering Geometry Quarter 7/16/2012

5 Algebra Review Standards: 3,5-7,11,1,1, Students solve equations and inequalities involving absolute values. 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = ). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < ). 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. 1.0 Students solve a quadratic equation by factoring or completing the square. 1.0 Students know the quadratic formula and are familiar with its proof by completing the square Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. 5 7/16/2012