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Westmoreland County Public Schools |
| Geometry |
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Logic: Mathematical Deduction
The learner will be able to construct formal geometric proofs by applying deductive reasoning (G.1.d).
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Logic: Deductive Arguments
The learner will be able to incorporate definitions, postulates, theorems, and logical reasoning techniques to develop deductive arguments in paragraph form, flow chart form, or formal proofs to solve real-world scenario problems and class problems. (G.1.d).
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Constructions: 3-D from 2-D
The learner will be able to create a three-dimensional model of a two-dimensional drawing and a two dimensional illustration of a three-dimensional shape, using blueprints and other representations in this process (G.12).
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Solids: Construct
The learner will be able to use manipulatives to reproduce a three-dimensional object given in a pictorial representation (G.12).
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Solids: Draw/Dot Paper
The learner will be able to draw three-dimensional solids using isometric dot paper (G.12).
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Solids: Drawing
The learner will be able to draw the following three-dimensional objects: cubes, cylinders, cones, and rectangular prisms (G.12).
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Solids: Drawing/Multiple Perspectives
The learner will be able to draw three-dimensional solids from multiple perspectives (G.12).
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Solids: Construct/Drawing
The learner will be able to construct familiar three-dimensional solids from a drawing using the necessary materials (G.12).
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Deductive Reasoning
The learner will be able to use deductive reasoning to solve problems (G.1.d).
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| Measurement |
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Area/Per: Relationships Holding Constant
The learner will be able to analyze the relationships, either between figures with a specific perimeter and their possible area measurements, or between figures with a specific area and their possible perimeters (G.13; G.14).
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Area/Volume: Comparing Plane - Solid
The learner will be able to compare and explore the relationship of perimeter and area of plane figures to the relationship of area and volume of solid figures (G.13; G.14).
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Area/Volume: Comparing
The learner will be able to compare area and volume measurements by exploring, questioning, and discussing how area and volume measurements change as the linear dimensions of an object change (G.13; G.14).
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Perimeter/Area/Volume: Relating
The learner will be able to analyze the perimeter, area, and volume of figures to determine not only how they are related, but also how changes in one attribute will affect the other attributes (G.14; G.13).
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Scale Drawing: Problem Solving
The learner will be able to solve real-world problems using ratio concepts with scale drawings (G.12).
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Length/Perimeter/Area: Relating
The learner will be able to use formulas to determine how the side length, perimeter, and area of quadrilaterals are related (G.13).
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Surface Area/Cylinder: Calculate/Formula
The learner will be able to use the appropriate formula to calculate the surface area of a cylinder (G.13).
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Surface Area/Cone and Pyramid Calculate
The learner will be able to use the appropriate formula to calculate the surface area of a cone and a pyramid. (G.13).
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Surface Area/Sphere: Calculate/Formula
The learner will be able to use the appropriate formula to calculate the surface area of a sphere (G.13).
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Surface Area: Appropriate Formula
The learner will be able to calculate surface area for a given figure using the appropriate formula (G.13).
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Surface Area: Application
The learner will be able to solve real-world application problems involving surface area measurements (G.13).
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Volume: Rectangular Solid/Formula
The learner will be able to calculate the volume of a rectangular solid using the correct formula. (G.13).
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Volume of a Cylinder: Calculate/Formula
The learner will be able to use the appropriate formula to calculate the volume of a cylinder (G.13).
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Volume of a Sphere: Calculate/Formula
The learner will be able to use the appropriate formula to calculate the volume of a sphere (G.13).
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Volume: Calc./Formula With Technology
The learner will be able to apply the correct formula to calculate the volume of a geometric solid using technology when necessary (G.13).
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Volume: Application
The learner will be able to solve real-world application problems involving volume measurements (G.13).
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Scale Drawing
The learner will be able to use proportional relationships to determine actual measurements from a diagram or map drawn to scale (G.12; G.14).
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Scale Models: 2- and 3-Dimensions
The learner will be able to construct two- and three-dimensional scale models of common objects (G.12).
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Scale Drawing: Problem Solving
The learner will be able to solve real-world problem situations by applying ratio concepts with scale drawings, using technology when necessary (G.14).
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| Technology |
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Calculator: Approximations
The learner will be able to apply approximations suitably in computations made with calculators and identify errors occurring as a result (G.7; G.13).
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