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Penn-Trafford School District |
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Penn-Trafford Secondary Mathematics |
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Mathematics - Geometry |
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Algebraic Concepts: Problem Scenarios
The learner will be able to
create expressions, equations, inequalities, systems of equations and inequalities, and matrices to represent routine and non-routine problem scenarios.
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Patterns: Analyze
The learner will be able to
study a given set of data for the existence of a pattern and illustrate the pattern algebraically and graphically.
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Equations: Illustrate Curves
The learner will be able to
represent curves using equations.
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Equality/Inequality/Expression
The learner will be able to
interpret equations, expressions, and inequalities using graphs and tables.
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Polynomials: Multiplying
The learner will be able to
multiply 2 binomials to make a trinomial as a skill and within application problems.
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Quadratic Formula
The learner will be able to
describe the discriminant, identify the quadratic formula and solve an equation using the quadratic formula.
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Algebraic Concepts: Relationship
The learner will be able to
show the relationship between algebraic equations and inequalities and the geometry of relations in the coordinate plane.
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Graphing/2 Variables
The learner will be able to
graph a linear equation in two variables: including equations in slope intercept form and standard form.
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Linear Equations: Solve
The learner will be able to
obtain solutions to linear equations.
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Inequalities: Algebraic/Solve
The learner will be able to
obtain solutions to algebraic inequalities and graph them on a number line.
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Equations: Choose/Apply
The learner will be able to
choose and apply a method to solve an equation or inequality, describe the solution and check the solution for accuracy.
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Equations: Unknown Quantities
The learner will be able to
apply the inverse relationship that exists between addition and subtraction and between multiplication and division, and exponentiation and root extraction to find unknown quantities in equations.
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Algebraic Concepts: Create/Solve
The learner will be able to
create and solve expressions, equations, or inequalities that illustrate problem scenarios.
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Algebraic Concepts: Manipulatives
The learner will be able to
use manipulatives to represent algebraic concepts.
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Variable: Solving For
The learner will be able to
manipulate a given formula to solve for a specific variable.
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Computation: Develop/Apply
The learner will be able to
develop and apply computation ideas, operations and procedures with real numbers in problem-solving situations.
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Equations: Solve/Graph
The learner will be able to
use scientific and graphing calculators, computers, and pencil and paper to solve and graph equations and inequalities.
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Circle Graphs: Construct
The learner will be able to
use compasses and protractors to construct circle graphs.
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Graping Functions: Table
The learner will be able to
create a table from a function.
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Graphing: Linear Functions
The learner will be able to
choose, account for, and use a suitable method (such as, slope-intercept, x and y intercepts, graphing calculators, and the use of transformations) to create a graph of a linear function with two variables.
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Arc, Chord, Angle
The learner will be able to
apply knowledge of chords, vertical angles, arcs, and circle relationships to determine an unknown angle between intersecting chords or arc measure created by the endpoints of chords.
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Angle: Construct
The learner will be able to
construct an angle using a protractor when given the angle measure.
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Angle: Missing/Measure
The learner will be able to
determine the missing angle.
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Angles/Triangles
The learner will be able to
identify and define various triangles and angles.
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Angles/Triangles
The learner will be able to
calculate the length of the missing side of a given triangle, know both the meaning and relationship between complementary and supplementary angles, and apply the triangle sum property to find the value of the third angle.
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Angles: Acute/Obtuse/Right
The learner will be able to
identify acute, obtuse, and right angles.
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Angles: Adjacent/Apply
The learner will be able to
use the properties of adjacent angles in solving problems.
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Angles: Alternate Interior
The learner will be able to
identify alternate interior angles.
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Angles: Bisect
The learner will be able to
d efine thenbisect a given angle.
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Angles: Complementary
The learner will be able to
identify and define angles which are complementary.
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Angles: Complementary/Solve Problems
The learner will be able to
find solutions to problems involving complementary angles.
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Angles: Congruent
The learner will be able to
identify congruent angles.
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Angles: Congruent/Solve Problems
The learner will be able to
find the solutions to problems involving congruent angles.
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Angles: Congruent/Supplementary
The learner will be able to
determine the congruent and supplementary relationships of the angles created by cutting parallel lines by a transversal.
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Angles: Construct/Bisector
The learner will be able to
use a compass and a straightedge to construct angle bisectors.
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Angles: Determine/Label
The learner will be able to
determine and name the vertex, rays, interior and exterior of an angle.
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Angles: Interior
The learner will be able to
identify and calculate the interior angles of a given figure.
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Angles: Investigate/Measures
The learner will be able to
explore angle measures applying models and manipulatives for the common angles of 45, 90, and 180 degrees.
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Angles: Label/Corresponding
The learner will be able to
label angles that are corresponding.
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Angles: Linear Pairs
The learner will be able to
identify and define angles which are linear pairs.
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Angles: Measurements
The learner will be able to
apply knowledge of angles, angle bisectors, perpendicular bisectors, and congruent angles to solve geometry problems.
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Angles: Naming
The learner will be able to
identify the different ways to name an angle.
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Angles: Problem Solve/Real World
The learner will be able to
obtain solutions to real world problems involving measurement of right, acute, obtuse, and straight angles.
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Angles: Right/Real-World
The learner will be able to
identify right angles within real-world situations.
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Angles: Solve Problems
The learner will be able to
obtain solutions to problems with complementary, supplementary, and congruent angles, including vertical angles, angles formed when parallel lines are cut by a transversal, and angles in polygons.
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Angles: Straight
The learner will be able to
identify angles of 180 degrees as straight.
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Angles: Sum of Angles of a Polygon
The learner will be able to
identify how to calculate the sum of the angles of a polygon.
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Angles: Supplementary
The learner will be able to
identify and define angles which are supplementary.
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Angles: Supplementaty/Solve Problems
The learner will be able to
find the solutions to problems involving supplementary angles.
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Angles: Vertical/Application
The learner will be able to
apply knowledge of vertical angles in solving for the value of a variable in an equation given for the opposite vertical angle.
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Building 3 Dimensional Models: Pattern
The learner will be able to
recognize the appropriate pattern, in 2 dimensions, that is needed to build a 3 dimensional model.
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Circle Parts: Arcs/Angles
The learner will be able to
use circle parts of chords, arcs, secants, and tangents to find various arc and angle measures.
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Circle Parts: Pi
The learner will be able to
understand the relationship which pi represents.
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Circle: Arc Length
The learner will be able to
calculate arc length.
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Circle: Construct/Non-Collinear Points
The learner will be able to
construct a circle which contains three non-collinear points.
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Circle: Determine
The learner will be able to
determine that the irrational number pi is the ratio of circumference to diameter of any circle.
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Circle: Diameter/Radius
The learner will be able to
determine a circle's diameter or radius given the value of the other.
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Circle: Draw/Label
The learner will be able to
display proficiency in drawing and labeling circle parts.
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Circle: Equation
The learner will be able to
determine the correct equation of a circle given its center point and radius.
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Circle: Identify/Center/Radius
The learner will be able to
recognize the center and radius of a circle when given the equation of a circle in standard form.
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Circle: Parts/Identify
The learner will be able to
identify the center, radius, diameter, chords, secants , tangents, circumference, and a semi-circle on a circle.
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Circle: Relationships
The learner will be able to
determine the relationships among the radius, diameter, chord, center, and circumference.
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Circle: Sphere/Terms
The learner will be able to
recognize terms associated with circles and spheres.
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Circles: Problem Solving
The learner will be able to
obtain solutions to problems involving circles using the properties of angles, arcs, chords, radii, daimeter, tangents, and secants.
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Circles: Proving
The learner will be able to
prove and/or apply theorems involving the properties of circles.
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Combine Figures: Union/Intersection
The learner will be able to
identify the intersection or union of familiar geometric figures.
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Combine/Partition/Transform Figures
The learner will be able to
accurately combine, partition, and transform geometric figures.
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Communicate: Standard Notation
The learner will be able to
understand standard geometric notations.
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Communication: Notation/Symbols
The learner will be able to
use mathematical notation and appropriate symbols to communicate ideas involving geometry.
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Congruence/Similarity: Identify
The learner will be able to
identify the properties and concepts of congruence and similarity.
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Congruence: Identify
The learner will be able to
recognize congruent figures that are created through the translation and/or reflection of geometric figures.
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Congruence: Prove Theorems
The learner will be able to
prove elementary theorems involving congruence.
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Congruency/Similarity/Symmetry: Designs
The learner will be able to
apply knowledge of congruency, similarity, and symmetry in describing and creating designs with geometric figures.
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Congruency/Similarity: Polygons
The learner will be able to
apply algebraic and coordinate as well as deductive proofs to prove two polygons are congruent or similar.
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Congruency: Applying
The learner will be able to
solve problems by applying concepts of congruency.
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Congruency: Congruent Figures/Apply
The learner will be able to
analyze how geometric principles related to congruency are applied in real-world problem solving.
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Congruency: Triangles/Construct
The learner will be able to
apply congruency theorems and postulates in order to construct congruent triangles.
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Congruency: Triangle Postulates
The learner will be able to
determine triangle congruence postulates by constructing congruent triangles.
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Construct: 2-D Representation/3-D
The learner will be able to
draw two-dimensional representations that illustrate different perspectives of three-dimensional objects.
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Constructions: 2 and 3-D
The learner will be able to
accurately create two- and three-dimensional figures.
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Constructions: Check
The learner will be able to
use proof as a check on the validity of geometric constructions.
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Constructions: Instruments
The learner will be able to
use a straightedge and compass in completing given constructions.
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Diagonals: Polygon/Draw and Identify
The learner will be able to
identify and draw diagonals of polygons.
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Diagonals: Rectangle and Square
The learner will be able to
determine the length of diagonals of a given rectangle or square.
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Figures: Characteristics/Solve Problems
The learner will be able to
use characteristics of basic figures to solve problems.
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Figures: Classify/Properties
The learner will be able to
classify figures according to their geometric properties.
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Figures: Edges/Faces/Vertices
The learner will be able to
identify the edges, faces, and vertices of geometric solids and determine their number.
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Figures: Geometric Names
The learner will be able to
use appropriate mathematical names for geometric figures.
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Figures: Identifying Open/Closed
The learner will be able to
identify open and closed figures.
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Figures: Parallelogram/Properties/Apply
The learner will be able to
apply the properties of a parallelogram.
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Figures: Terms
The learner will be able to
apply geometric terms in discussing and comparing figures and shapes.
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Figures: Trapezoid/Properties/Apply
The learner will be able to
apply the properties of a trapezoid.
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Geometric Concepts: Formulas
The learner will be able to
indicate comprehension of various geometric formulas, (including those for perimeter, circumference, area, and volume).
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Geometric Concepts: Problem Solving
The learner will be able to
solve problems with relationships between geometric concepts and real-world situations.
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Geometry: Appreciate
The learner will be able to
recognize the value of geometry in his/her environment, to include applications in science, art, and architecture.
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Grids: Locate Points
The learner will be able to
locate points on a grid using ordered pairs.
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Line Segment: Length
The learner will be able to
determine line segment lengths.
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Line Segment: Midpoint
The learner will be able to
determine the midpoint of a line segment.
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Line Segments: Midpoint/Construct
The learner will be able to
use a compass and a straightedge to identify and/or construct midpoints of line segments.
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