Geometry District Benchmark
| Starting Dates | Block Spr | None | Mar 16th | Nov 12th | May 18th | Notes |
| Block Fall | None | Oct 13th | Mar 16th | Jan 5th | ||
| Traditional | Oct 13th | Jan 5th | Bmk 3 | May 18th | ||
| Geometry | Star | Bmk 1 | Bmk 2 | Bmk 4 | ||
| Logic and Geometric Proofs | 22.67 | 17 | 24 | 20 | 19 | |
| 1.0* Students demonstrate understanding by
identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning |
2 | 3 | 1 | 1 | 1 | |
| 2.0* Students write geometric proofs, including proofs by contradiction. | 3 | 4 | 3 | 2 | 2 | |
| 3.0* Students construct and judge the validity of
a logical argument and give counterexamples to disprove a statement. |
4 | 4 | 4 | 3 | 3 | |
| 4.0* Students prove basic theorems involving congruence and similarity. | 5 | 6 | 5 | 4 | ||
| 5.0 Students prove that triangles are congruent
or similar, and they are able to use the concept of corresponding parts of congruent triangles. |
2 | 3 | 3 | 3 | 2: no Similar | |
| 6.0 Students know and are able to use the triangle inequality theorem. | 1 | 2 | 2 | 1 | ||
| 7.0* Students prove and use theorems involving
the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. |
5.67 | 6 | 5 | 4 | 5 | 1/2: No Circles or Quads |
| Total Items | 22.67 | 17 | 24 | 20 | 19 | |
| Percent | 35% | 77% | 59% | 45% | 32% | |
| Volume and Area Formulas | 11 | 0 | 0 | 0 | 10 | |
| 8.0* Students know, derive, and solve problems
involving perimeter, circumference, area, volume, lateral area, and surface area of common geometric |
4 | 2 | ||||
| 10.0* Students compute areas of polygons,
including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. |
4 | 3 | ||||
| 9.0 Students compute the volumes and surface
areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. |
2 | 3 | ||||
| 11.0 Students determine how changes in dimensions
affect the perimeter, area, and volume of common geometric figures and solids. |
1 | 2 | ||||
| Total Items | 11 | 0 | 0 | 0 | 10 | |
| Percent | 17% | 0% | 0% | 0% | 17% | |
| Angle relationships, constructions and lines | 16.33 | 5 | 12 | 13 | 14 | |
| 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. |
5 | 5 | 5 | 4 | ||
| 13.0 Students prove relationships between angles
in polygons by using properties of complementary, supplementary, vertical, and exterior angles. |
2 | 3 | 2 | 3 | ||
| 14.0* Students prove the Pythagorean theorem. | 0.33 | |||||
| 15.0 Students use the Pythagorean theorem to
determine distance and find missing lengths of sides of right triangles. |
2 | 0 | 2 | 3 | ||
| 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. |
4 | 5 | 2 | 2 | 2 | 1: No Perp Bisect or line par to pts |
| 17.0* Students prove theorems by using coordinate
geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. |
3 | 2 | 2 | 2 | 2:No Circles | |
| Total Items | 16.33 | 5 | 12 | 13 | 14 | |
| Percent | 25% | 23% | 29% | 30% | 23% | |
| Trigonometry | 15 | 0 | 5 | 11 | 17 | |
| 18.0* Students know the definitions of the basic
trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x ) = sin(x )/cos(x ), (sin (x ))2 + (cos (x ))2 = 1 |
3 | 3 | 3 | |||
| 19.0* Students use trigonometric functions to
solve for an unknown length of a side of a right triangle, given an angle and a length of a side. |
3 | 3 | 3 | Cluster: TRIG | ||
| 20.0 Students know and are able to use angle and
side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles. |
1 | 3 | 3 | |||
| 21.0* Students prove and solve problems regarding
relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. |
5 | 5 | ||||
| 22.0* Students know the effect of rigid motions
on figures in the coordinate plane and space, including rotations, translations, and reflections. |
3 | 5 | 2 | 3 | ||
| Total Items | 15 | 0 | 5 | 11 | 17 | |
| Percent | 23% | 0% | 12% | 25% | 28% | |
| TOTAL | 65 | 22 | 41 | 44 | 60 |
