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Norwin School District |
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Norwin High School Mathematics |
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Mathematics - Grade 9-12 Cognitive Tutor Geometry |
Patterns: Problem Solving/Recognize
The learner will be able to
use pattern recognition to solve problems.
| Strand |
Source |
Activities |
| Patterns: Problem Solving |
PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.C |
Classroom
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Planes/Points/Lines: Understand/Concepts
The learner will be able to
understand the concepts of planes, points, lines, and rays.
| Strand |
Source |
Activities |
| Planes/Points/Lines |
Norwin School District 8-04 |
Classroom
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Parallel/Perpendicular/Skew: Classify
The learner will be able to
make classifications of lines as being either parallel, perpendicular, or skew.
| Strand |
Source |
Activities |
| Lines: Parallel/Perpendicular |
Norwin School District 8-04 |
Classroom
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Real Numbers and the Coordinate Plane
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Coordinate Plane: Distance/Midpoint
The learner will be able to
find the midpoint and the distance between two ordered pairs.
| Strand |
Source |
Activities |
| Coordinate Geometry |
Norwin School District 8-04 |
Classroom
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Logic: Write/Interpret/Conditional
The learner will be able to
write conditional statements and interpret them, including converse, inverse, and contrapositive.
| Strand |
Source |
Activities |
| Logic |
Norwin School District 8-04 |
Classroom
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Deductive Reasoning: Proof
The learner will be able to
apply deductive reasoning techniques to prove a statement.
| Strand |
Source |
Activities |
| Reasoning |
Norwin School District 8-04 |
Classroom
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Properties: Equality
The learner will be able to
use the reflexive, transitive or symmetric properties of equality.
| Strand |
Source |
Activities |
| Properties |
Norwin School District 8-04 |
Classroom
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Angles: Congruent/Solve Problems
The learner will be able to
find the solutions to problems involving congruent angles.
| Strand |
Source |
Activities |
| Angles |
Norwin School District 8-04 |
Classroom
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Angles/Lines: Problem Solving
The learner will be able to
apply the properties and definitions of angles and lines to obtain solutions to problems associated with special pairs of angles formed by parallel lines and a transversal.
| Strand |
Source |
Activities |
| Lines/Angles/Polygons |
Norwin School District 8-04 |
Classroom
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Proofs: Parallel Lines
The learner will be able to
compose formal proofs with regards to parallel lines.
| Strand |
Source |
Activities |
| Proofs |
Norwin School District 8-04 |
Classroom
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Triangles: Solve/Basic Problem/Angle Sum
The learner will be able to
obtain solutions to basic triangle problems by applying the triangle sum property.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Triangles: Recognize/Explain
The learner will be able to
recognize and explain triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Polygons: Classify
The learner will be able to
classify polygons as being concave, convex, regular.
| Strand |
Source |
Activities |
| Polygons |
Norwin School District 8-04 |
Classroom
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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.
| Strand |
Source |
Activities |
| Angles |
Norwin School District 8-04 |
Classroom
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Real Numbers and the Coordinate Plane
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Slope: Define/Identify/Use
The learner will be able to
define, identify, and use the slope of a line.
| Strand |
Source |
Activities |
| Slope |
Norwin School District 8-04 |
Classroom
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Congruency: Congruent Figures
The learner will be able to
identify congruent figures by determining that they are the same size and shape.
| Strand |
Source |
Activities |
| Congruence |
Norwin School District 8-04 |
Classroom
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Triangles: Recognize/Congruent/Theorems
The learner will be able to
recognize congruent triangles and right triangles by applying elementary congruence theorems and postulates (SSS, SAS, ASA, AAS).
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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CPCTC triangle congruence
The learner will be able to
to use triangle congruence and CPCTC to prove that parts of two triangles are congruent.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Triangles: Isosceles
The learner will be able to
identify an isosceles triangle.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Triangles: Equiangular
The learner will be able to
identify and define an equiangular triangle.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Right Triangle: Identify Parts
The learner will be able to
recognize the various parts of a right triangle.
| Strand |
Source |
Activities |
| Right Triangles |
Norwin School District 8-04 |
Classroom
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Congruence in right triangles
The learner will be able to
prove triangles congruent using the HL Theorem.
| Strand |
Source |
Activities |
| Right Triangles |
Norwin School District 8-04 |
Classroom
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Triangles: Analyzing
The learner will be able to
define and draw conclusions regarding the altitudes, medians, mid-segments, and bisectors of triangles.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Logic: Inverse
The learner will be able to
write the inverse of a given logic statement.
| Strand |
Source |
Activities |
| Logic |
Norwin School District 8-04 |
Classroom
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Logic: Write/Contrapositive
The learner will be able to
write the contrapositive of a conditional statement.
| Strand |
Source |
Activities |
| Logic |
Norwin School District 8-04 |
Classroom
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Logic: Indirect/Deductive
The learner will be able to
apply indirect and deductive reasoning to draw a conclusion.
| Strand |
Source |
Activities |
| Logic |
Norwin School District 8-04 |
Classroom
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Triangle Inequality: Apply/Arrange
The learner will be able to
use the triangle inequality property to determine if a triangle exists and arrange the sides and angles according to size.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Quadrilaterals: Explore
The learner will be able to
explore quadrilaterals to include classification and properties of parallelograms, rectangles, rhombi, squares, trapezoids, and kites.
| Strand |
Source |
Activities |
| Quadrilaterals |
Norwin School District 8-04 |
Classroom
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Diagonals: Parallelogram/Angles
The learner will be able to
find the interior angle measure of the diagonals of a parallelogram given an interior corner angle measures and two side lengths.
| Strand |
Source |
Activities |
| Diagonals |
Norwin School District 8-04 |
Classroom
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Quadrilaterals: Problem Solve/Proofs
The learner will be able to
apply the properties, definitions, and theorems associated to quadrilaterals (parallelograms, rectangles, rhombi, squares, trapezoids, kites) to obtain solutions to problems and/or write proofs.
| Strand |
Source |
Activities |
| Quadrilaterals |
Norwin School District 8-04 |
Classroom
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Quadrilaterals: Prove/Properties
The learner will be able to
prove properties of quadrilaterals using coordinate geometry.
| Strand |
Source |
Activities |
| Quadrilaterals |
Norwin School District 8-04 |
Classroom
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Pythagorean Theorem
The learner will be able to
use the Pythagorean Theorem to determine an unknown side length of a right triangle.
| Strand |
Source |
Activities |
| Pythagorean Theorem |
Norwin School District 8-04 |
Classroom
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Pythagorean Theorem: Use/Converse/Solve
The learner will be able to
apply the Pythagorean Theorem and its converse in problem solving scenarios.
| Strand |
Source |
Activities |
| Pythagorean Theorem |
Norwin School District 8-04 |
Classroom
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Right Triangles: Apply Relationships
The learner will be able to
apply a knowledge of side and angle relationships in special right triangles (30-60-90 & 45-45-90).
| Strand |
Source |
Activities |
| Right Triangles |
Norwin School District 8-04 |
Classroom
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Circles: Problem Solving
The learner will be able to
obtain solutions to problems involving circles using the properties of angles.
| Strand |
Source |
Activities |
| Circles |
PA: Academic Standards, January 16, 1999, Grade 11, p.16,2.9.11.F |
Classroom
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Circle Parts: Sector/Area
The learner will be able to
compute the area of a sector or segment of a circle when given a diagram.
| Strand |
Source |
Activities |
| Circles |
Norwin School District 8-04 |
Classroom
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Problem Solving: Geometric Probability
The learner will be able to
solve problems involving geometric probability by using areas and segments.
| Strand |
Source |
Activities |
| Problem Solving |
Norwin School District 8-04 |
Classroom
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Ratio/Proportion: Apply/Real World
The learner will be able to
apply ratio and proportion concepts to solve real world scenario problems.
| Strand |
Source |
Activities |
| Ratio/Proportion |
PA: System of School Assessment, 1997, Grade 11, p.11,#1 week tested: 27. |
Classroom
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Ratio: Similarity/Polygons
The learner will be able to
use the ideas of ratio and similarity in polygons, and include real world problem situations.
| Strand |
Source |
Activities |
| Ratio/Proportion |
Norwin School District 8-04 |
Classroom
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Similarity: Similar Figures/Apply
The learner will be able to
understand and apply the concepts related to similar figures and properties of similar figures.
| Strand |
Source |
Activities |
| Similarity |
PA: System of School Assessment, 1997, Grade 11, p.11,#3 week tested: 27. |
Classroom
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Similarity: Triangles
The learner will be able to
recognize similar triangles (and other polygons) through the application of their properties.
| Strand |
Source |
Activities |
| Similarity |
Norwin School District 8-04 |
Classroom
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Triangles: Similarity
The learner will be able to
use indirect measurement with similar triangles to make judgments about similar figures.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Triangles: Manipulatives/Geometric Mean
The learner will be able to
utilize manipulatives to investigate the geometric mean of similar triangles.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Triangles: Similar/Proportion
The learner will be able to
determine the length of an unknown side of a triangle using proportion and the concepts of similar triangles.
| Strand |
Source |
Activities |
| Triangles |
Norwin School District 8-04 |
Classroom
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Similarity: Compare/Area and Perimeter
The learner will be able to
make comparisons of the areas and dimensions of similar polygons.
| Strand |
Source |
Activities |
| Similarity |
Norwin School District 8-04 |
Classroom
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Right Triangles: Sine/Cosine/Tangent
The learner will be able to
use the definitions for the ratios of sine, cosine, and/or tangent in solving right triangles.
| Strand |
Source |
Activities |
| Right Triangles |
Norwin School District 8-04 |
Classroom
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Problem Solving: Right Triangles
The learner will be able to
recognize, create, and solve practical right triangle problems by applying trigonometric functions and the Pythagorean Theorem.
| Strand |
Source |
Activities |
| Problem Solving |
PA: Academic Standards, January 16, 1999, Grade 11, p.18,2.10.11.B |
Classroom
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Real Numbers and the Coordinate Plane
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Slope: Angle of Elevation/Depression
The learner will be able to
make comparisons of slope and angle of elevation/depression as steepness measures.
| Strand |
Source |
Activities |
| Slope |
Norwin School District 8-04 |
Classroom
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Calculus and Pre-Calculus
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Vectors
The learner will be able to
investigate vectors as line segments with direction and magnitude in a plane, including real world applications.
| Strand |
Source |
Activities |
| Vectors |
Norwin School District 8-04 |
Classroom
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Figures: create nets
The learner will be able to
recongize and use nets to create space figures.
| Strand |
Source |
Activities |
| Figures: Construct |
Norwin School District 8-04 |
Classroom
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Figures: Identify/3D/2D Drawings
The learner will be able to
identify the three-dimensional figure illustrated by a two-dimensional drawing.
| Strand |
Source |
Activities |
| Figures: Identify |
Norwin School District 8-04 |
Classroom
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Three-Dimensional Solids: Volumes
The learner will be able to
determine the volume of solid figures composed of prisms, pyramids, cylinders, cones.
| Strand |
Source |
Activities |
| Three-Dimensional Solids |
Norwin School District 8-04 |
Classroom
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Circles/Spheres: Applying Concepts
The learner will be able to
apply geometric concepts of circles and spheres, such as secants, arcs, chords, tangents, angles, circumscribed figures, etc., in problem solving situations.
| Strand |
Source |
Activities |
| Circles |
Norwin School District 8-04 |
Classroom
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Circle: 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, tangents, and secants.
| Strand |
Source |
Activities |
| Circles |
Norwin School District 8-04 |
Classroom
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Circles: Equation/Coordinate Points
The learner will be able to
find the equation of a circle from its given coordinates.
| Strand |
Source |
Activities |
| Circles |
Norwin School District 8-04 |
Classroom
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Computer Software: Practice/Master
The learner will be able to
apply suitable software to practice and master instructional objectives in Conceptual Mathematics.
| Strand |
Source |
Activities |
| Computers |
Norwin School District 8/04 |
Classroom
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Computer Software: Practice/Master
The learner will be able to
apply suitable software to practice and master appropriate mathematical grade level instructional objectives.
| Strand |
Source |
Activities |
| Computers |
Norwin School District 8/04 |
Classroom
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Computer Software: Create/Tables/Graphs
The learner will be able to
apply computer graphing software to create tables and bar graphs.
| Strand |
Source |
Activities |
| Computers |
Norwin School District 8-04 |
Classroom
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