Below you will find the outcomes that will be assessed throughout the course of the year. Next to each outcome is the criteria I will use to determine your final rating of that outcome. Please refer to this list when you are interested in fixing a "not-yet" rating. (Bear in mind that the criteria list is not a complete list of vocabulary and skills you will need to know!)
#01: Argues with different types of reasoning in order to prove or disprove a statement
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Differentiates between inductive and deductive reasoning and can work with examples of each; uses correct notation and terminology to accurately complete a proof in paragraph, two-column, or flow chart form
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#02: Discerns information about points, lines, and planes including parallel, perpendicular, intersecting or skew and uses appropriate notation and terminology
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Knows relationships of corresponding, alternate interior/exterior, same-side interior/exterior angles and what that means for parallel lines; given a diagram or description of a space can determine which planes or lines are parallel, perpendicular, or skew and use given information to make conclusions about other lines and planes within that given space (e.g. if two planes are parallel to the same plane, then they must be parallel to each other.); uses algebra to determine measures of angles; knows when points are collinear or when points and lines are coplanar; knows relationships of supplementary, complementary and vertical angles
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#03: Uses a straightedge and a compass to make preciseconstructions and can arguethe validity of the construction
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Constructs an angle bisector, perpendicular bisector, parallel line through a given point, perpendicular line through a given point on a line, perpendicular line through a given point off a line, equilateral/isosceles triangle; using knowledge of circles, triangles, properties of parallel lines can prove each construction
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#04: Be precise in calculating and applying the length and midpoint of a segment
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Knows the midpoint formula, uses the midpoint formula to find the midpoint of a segment or given the midpoint and one endpoint can determine the other endpoint, knows and derives the distance formula; uses the distance formula to find the length of a segment and can write the answer in simplest radical form
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#05: Concludes the conditions under which a compound statement is true and can write the inverse, converse, and contrapositive of a given statement
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Identifies the hypothesis and conclusion of a conditional; knows if a conditional is true or false (and its converse, inverse, and contrapositive); finds the converse, inverse and contrapositive of a statement; identifies compound statements ("and", "or") and determines and justifies their truth value
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#06: Graphically and algebraically discerns if lines are parallel or perpendicular on a coordinate plane and can identify the point of intersection of intersecting lines
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Can determine the slope of linear equations and uses this information to determine if they're parallel or perendicular (or neither); if neither, can determine the point(s) of intersection (including with a parabola and line); can write the equation of a line knowing certain given information
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#07: Identifies polygons precisely and can determine angle sums and missing angle measures
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Knows the names of polygons, and correct vocabulary for different types of triangles (acute, obtuse,right, scalene, isosceles, equilateral) and quadrilaterals (kite, trapezoid, parallelogram, rectangle, rhombus, square) based on properties; can determine the missing interior or exterior angle in any polygon; knows the general formula for determining the sum of all the angles in any polygon (interior and exterior); Triangle exterior Angle Theorem
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#08: Concludes if two triangles are congruent and identifies corresponding parts
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Uses SSS, SAS, ASA, AAS, and HL to determine the congruence of two triangles and can justify it; accurately names the corresponding parts in two triangles
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#09: Discerns and applies theorems and relationships within triangles andcommunicates those relationships
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Knows the relationships within triangles such as Midsegment Theorem, Angle bisector theorem, Proportional side lengths when a line cuts the sides of a triangle and is parallel to the other side, points of concurrency (orthocenter, circumcenter, incenter, centroid) and their properties; Triangle Inequality theorem;
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#10: Discerns and applies theorems and relationships about quadrilaterals and communicates those relationships
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Differentiates between different quadrilaterals based on their properties (quadrilateral, parallelogram, rhombus, rectangle, square, kite, trapezoid, isosceles trapezoid) and uses this information to determine side lengths and angle measurements; knows the trapezoid midsegment theorem
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#11: Discerns and applies concepts of similarity in two triangles or polygons
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Uses SAS~, SSS~, and AA~ similarity theorems; finds side lengths and angle measurements; understands the proportional relationships that exist within a right triangle when the altitude is drawn from the right angle to the hypotenuse and can use this relationship to determine missing side lengths
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#12: Discerns and applies concepts of perimeter, area, surface area, and volume for two and three dimensional figures
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Knows formulas for area, perimeter, surface area and volume for two and three dimensional shapes (not needed for formulas that are provided on the Regents); knows the similarity ratio among similar figures and the information this provides for their perimeters, areas, surface areas and volume
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#13: Applies the Pythagorean Theorem and investigates relationships in special right triangles
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Uses the Pythagorean Theorem to find missing side lengths in right triangles (including non-obvious scenarios such as when the triangles appear in circles); uses the Pythagorean Theorem to determine if triangles are right, acute or obtuse
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#14: Applies and argues properties of transformations and concepts of symmetry
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Can perform translations, rotations, reflections, glide reflections, and dilations on a coordinate plane and knows the notation for each including composition of transformations; knows when a transformation is an isometry; identifies which parts of a figure are preserved under a certain transformation
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#15: Identifies parts and properties of circles and preciselydetermines measurements of area, circumference, arc length, angles, tangents and secants
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Determines measurements of angles and segments formed by intersecting chords, a tangent and a chord, a tangent and a radius (or diameter), a tangent and secant, two secants; determines arc length; justifies relationships
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#16: Writes, graphs and communicates equations of circles
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Knows the general equation for a circle and can use the equation to determine the coordinates of the center and the length of the radius
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#17: Graphs, solves and communicates problems using compound loci, including on a coordinate plane
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Determine the locus of points (graphically and as a drawing) for a given situation; can graph vertical and horizontal lines; uses a ruler and a compass to create accurate drawings; uses the given information to create an appropriate sketch
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