# Accelerated 8th Grade

This class covers High School Geometry topics in greater depth and at a faster pace than regular Geometry courses.

Topics include the foundations of geometry, geometric reasoning, parallel and perpendicular lines, triangle congruence, properties and attributes of triangles, polygons and quadrilaterals, similarity, right triangles and trigonometry, perimeter, circumference, and area, spatial reasoning, circles, transformational geometry.

While these topics are similar to those offered in most classes, more emphasis is placed on theory and application in this advanced version. The class moves at an accelerated pace.

The text used in this class is: Geometry. Holt McDougal 2011.

Students have access to an online textbook.

To remain in this class a student must maintain a B (86%) trimester average.

#### Minnesota Department of Education Geometry Standards

 Standard Benchmark Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations. Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate. For example: Measure the height and radius of a cone and then use a formula to find its volume. Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations. Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures. For example: Find the volume of a regular hexagonal prism by decomposing it into six equal triangular prisms. Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems. For example: 60 miles/hour = 60 miles/hour × 5280 feet/mile × 1 hour/3600 seconds = 88 feet/second. Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations. Understand and apply the fact that the effect of a scale factor k on length, area and volume is to multiply each by k, k^2, k^3, respectively. Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations. Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements. For example: Suppose the sides of a rectangle are measured to the nearest tenth of a centimeter at 2.6 cm and 9.8 cm. Because of measurement errors, the width could be as small as 2.55 cm or as large as 2.65 cm, with similar errors for the height. These errors affect calculations. Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry. Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments. Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry. Accurately interpret and use words and phrases such as “if…then,” “if and only if,” “all,” and “not.” Recognize the logical relationships between an “if…then” statement and its inverse, converse and contrapositive. Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry. Assess the validity of a logical argument and give counterexamples to disprove a statement. Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry. Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations. Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry. Use technology tools to examine theorems, make and test conjectures, perform constructions and develop mathematical reasoning skills in multi-step problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets. Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry. Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results. For example: Prove that the perpendicular bisector of a line segment is the set of all points equidistant from the two endpoints, and use this fact to solve problems and justify other results. Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry. Know and apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve problems and logically justify results. For example: Prove that two triangles formed by a pair of intersecting lines and a pair of parallel lines (an “X” trapped between two parallel lines) are similar. Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry. Know and apply properties of equilateral, isosceles and scalene triangles to solve problems and logically justify results. For example: Use the triangle inequality to prove that the perimeter of a quadrilateral is larger than the sum of the lengths of its diagonals. Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry. Apply the Pythagorean Theorem and its converse to solve problems and logically justify results. Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry. Know and apply properties of right triangles, including properties of 45- 45-90 and 30-60-90 triangles, to solve problems and logically justify results. Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry. Know and apply properties of congruent and similar figures to solve problems and logically justify results. Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry. Use properties of polygons—including quadrilaterals and regular polygons—to define them, classify them, solve problems and logically justify results. Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry Know and apply properties of a circle to solve problems and logically justify results. Solve real-world and mathematical geometric problems using algebraic methods. Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle. Solve real-world and mathematical geometric problems using algebraic methods. Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios. Solve real-world and mathematical geometric problems using algebraic methods. Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts. Solve real-world and mathematical geometric problems using algebraic methods. Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments. Solve real-world and mathematical geometric problems using algebraic methods. Know the equation for the graph of a circle with radius = r, and center (h,k),  (x-h)^2  +  (y-k)^2 = r^2  and justify this equation using the Pythagorean Theorem and properties of translations. Solve real-world and mathematical geometric problems using algebraic methods. Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90˚, to solve problems involving figures on a coordinate grid. Solve real-world and mathematical geometric problems using algebraic methods. Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.