EAST LONGMEADOW PUBLIC SCHOOLS
2006 - 2007 DISTRICT CURRICULUM GUIDES

Mathematics - Geometry: All Levels

Mathematics

The Massachusetts Mathematics Curriculum Framework envisions all students in the Commonwealth achieving mathematical competence through a strong mathematics program that emphasizes problem solving, communicating, reasoning and proof, making connections, and using representations. Acquiring such competence depends in large part on a clear, comprehensive, coherent, and developmentally appropriate set of standards to guide curriculum expectations.

Geometry: All Levels

The Massachusetts Mathematics Curriculum Framework provides learning standards for students in Geometry.


Geometry
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. The Geometry Unit includes properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving.

    Congruence/Similarity: Apply/Justify
The learner will be able to apply congruent and similar correspondences and properties of figures to determine missing parts of shapes, and provide a logical justification.
Strand Scope Source
Congruence/Similarity/Symmetry Master MA: Curriculum Framework, 2000, Geometry, G.G.5
  
    Triangles: Inequalities/Problems/Proofs
The learner will be able to obtain problem solutions and prove theorems by applying the triangle inequality and other inequalities related to triangles.
Strand Scope Source
Triangles Master MA: Curriculum Framework, 2000, Geometry, G.G.10
  
    Points: Set/Draw/Label
The learner will be able to draw and label a set of points.
Strand Scope Source
Planes/Points/Lines Master MA: Curriculum Framework, 2000, Geometry, G.G.1
  
    Polygons: Special
The learner will be able to apply the properties of sides, diagonals, and angles in special polygons, and recognize their parts and special segments.
Strand Scope Source
Polygons Master MA: Curriculum Framework, 2000, Geometry, G.G.1
  
    Solids: Identify/Projections
The learner will be able to identify the projections of solid shapes.
Strand Scope Source
Three-Dimensional Solids Master MA: Curriculum Framework, 2000, Geometry, G.G.16
  
    Solids: Identify/Cross Sections
The learner will be able to identify the cross sections of solid shapes.
Strand Scope Source
Three-Dimensional Solids Master MA: Curriculum Framework, 2000, Geometry, G.G.16
  
    Congruence/Similarity: Draw/Instruments
The learner will be able to draw congruent and similar shapes using a compass, a straightedge, a protractor, or computer software.
Strand Scope Source
Congruence/Similarity/Symmetry Master MA: Curriculum Framework, 2000, Geometry, G.G.4
  
    Lines: Parallel/Apply/Solve Problems
The learner will be able to apply the properties of parallel lines to obtain problem solutions.
Strand Scope Source
Lines: Parallel/Perpendicular Master MA: Curriculum Framework, 2000, Geometry, G.G.6
  
    Angles: Solve/Properties
The learner will be able to obtain solutions to problems by applying the properties of angles.
Strand Scope Source
Angles Master MA: Curriculum Framework, 2000, Geometry, G.G.6
  
    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 Scope Source
Triangles Master MA: Curriculum Framework, 2000, Geometry, G.G.7
  
    Triangles: Solve Problems/Pythagorean
The learner will be able to obtain solutions to basic triangle problems by applying the Pythagorean Theorem.
Strand Scope Source
Pythagorean Theorem Master MA: Curriculum Framework, 2000, Geometry, G.G.7
  
    Triangles: Solve Problems/Special
The learner will be able to obtain problem solutions by applying the properties of special triangles.
Strand Scope Source
Triangles Master MA: Curriculum Framework, 2000, Geometry, G.G.8
  
    Circles: Apply/Properties/Solve Problems
The learner will be able to apply the properties of arcs, radii, chords, tangents, and secants to obtain problem solutions.
Strand Scope Source
Circles Master MA: Curriculum Framework, 2000, Geometry, G.G.6
  
    Transformation: Interpret
The learner will be able to develop interpretations of transformations of figures in the coordinate plane.
Strand Scope Source
Transformations Master MA: Curriculum Framework, 2000, Geometry, G.G.15
  
    Transformation: Problem Solving
The learner will be able to solve problems using transformations.
Strand Scope Source
Transformations Master MA: Curriculum Framework, 2000, Geometry, G.G.15
  
    Transformations: Draw/Coordinate Plane
The learner will be able to draw the results of a transformation of a figure on the coordinate plane.
Strand Scope Source
Transformations Master MA: Curriculum Framework, 2000, Geometry, G.G.15
  
    Proofs: Write/Basic/Theorems
The learner will be able to write basic proofs for theorems in geometry.
Strand Scope Source
Proofs Master MA: Curriculum Framework, 2000, Geometry, G.G.2
  
    Proofs: Apply/Contradiction
The learner will be able to apply proof by contradiction.
Strand Scope Source
Proofs Master MA: Curriculum Framework, 2000, Geometry, G.G.2
  
    Logic: Write/Inverse
The learner will be able to write the inverse of a conditional statement.
Strand Scope Source
Logic Master MA: Curriculum Framework, 2000, Geometry, G.G.2
  
    Logic: Write/Converse
The learner will be able to write the converse of a conditional statement.
Strand Scope Source
Logic Master MA: Curriculum Framework, 2000, Geometry, G.G.2
  
    Logic: Write/Contrapositive
The learner will be able to write the contrapositive of a conditional statement.
Strand Scope Source
Logic Master MA: Curriculum Framework, 2000, Geometry, G.G.2
  
    Symmetry
The learner will be able to determine if a given shape is symmetrical.
Strand Scope Source
Symmetry Master MA: Curriculum Framework, 2000, Geometry, G.G.1
  
    Connecting: Geometry/Algebra/Circles
The learner will be able to illustrate an understanding of the connection between algebraic and geometric representations of circles.
Strand Scope Source
Connecting Master MA: Curriculum Framework, 2000, Geometry, G.G.14
  
    Constructions: Formulate/Conjectures
The learner will be able to formulate conjectures about construction techniques.
Strand Scope Source
Constructions Master MA: Curriculum Framework, 2000, Geometry, G.G.4
  
    Problem Solving: Apply
The learner will be able to apply vertex-edge graphs in order to model problems.
Strand Scope Source
Problem Solving Master MA: Curriculum Framework, 2000, Geometry, G.G.17
  
    Problem Solving: Apply
The learner will be able to apply vertex-edge graphs in order to obtain solutions to problems.
Strand Scope Source
Problem Solving Master MA: Curriculum Framework, 2000, Geometry, G.G.17
  
    Spatial Thinking: 3D
The learner will be able to visualize a three dimensional object.
Strand Scope Source
Spatial Thinking Master MA: Curriculum Framework, 2000, Geometry, G.G.16
  
    Polygons: Identify/Special
The learner will be able to identify special polygons.
Strand Scope Source
Polygons Master MA: Curriculum Framework, 2000, Geometry, G.G.1
  
    Polygons: Regular/Find/Interior/Angles
The learner will be able to find the interior angles for regular polygons.
Strand Scope Source
Polygons Master MA: Curriculum Framework, 2000, Geometry, G.G.1
  

Mathematics Processes
The Mathematics Processes Unit focuses on mathematical connections, communication, modeling, concepts and procedures.

    Mathematical Concepts: Theorem/Postulate
The learner will be able to differentiate between a theorem and a postulate.
Strand Scope Source
Mathematical Concepts Master MA: Curriculum Framework, 2000, Geometry, G.G.2
  
    Reasoning: Apply/Inductive
The learner will be able to apply inductive reasoning.
Strand Scope Source
Reasoning Master MA: Curriculum Framework, 2000, Geometry, G.G.2
  
    Reasoning: Apply/Deductive
The learner will be able to apply deductive reasoning.
Strand Scope Source
Reasoning Master MA: Curriculum Framework, 2000, Geometry, G.G.2
  
    Conjectures: Verify/Logical Arguments
The learner will be able to apply logical arguments to verify conjectures.
Strand Scope Source
Conjecture/Argument Master MA: Curriculum Framework, 2000, Geometry, G.G.4
  

Measurement
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. The Measurement Unit includes concepts of length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns and problem solving.

    Perimeter: Compute/Basic Shapes
The learner will be able to compute the perimeter of basic shapes.
Strand Scope Source
Perimeter Master MA: Curriculum Framework, 2000, Geometry, G.M.1
  
    Area: Compute/Basic Shapes
The learner will be able to compute the area of basic shapes.
Strand Scope Source
Area Master MA: Curriculum Framework, 2000, Geometry, G.M.1
  
    Area: Determine/Lateral/Formula
The learner will be able to determine the lateral area of a prism, pyramid, sphere, cylinder, and cone when presented with the formula.
Strand Scope Source
Area Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Circumference: Compute/Basic Shapes
The learner will be able to compute the circumference of basic shapes.
Strand Scope Source
Circumference Master MA: Curriculum Framework, 2000, Geometry, G.M.1
  
    Surface Area/Cone: Calculate Formula
The learner will be able to use the appropriate formula to calculate the surface area of a cone.
Strand Scope Source
Surface Area Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Volume of a Prism: Calculate/Formula
The learner will be able to determine the volume of prisms using a given formula.
Strand Scope Source
Volume Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Measurement: Changes
The learner will be able to describe how changes in the measure of one attribute of an object may affect the other measures.
Strand Scope Source
Measurement: Analysis Master MA: Curriculum Framework, 2000, Geometry, G.M.3
  
    Measurement Analysis: Dimensional
The learner will be able to verify the reasonableness of expressions and equations by applying dimensional analysis.
Strand Scope Source
Measurement: Analysis Master MA: Curriculum Framework, 2000, Geometry, G.M.5
  
    Measurement Analysis: Unit Conversion
The learner will be able to apply dimensional analysis for unit conversion.
Strand Scope Source
Measurement: Analysis Master MA: Curriculum Framework, 2000, Geometry, G.M.5
  
    Accuracy: Explain/Error/Effects/Measure
The learner will be able to explain the effects of estimated error in measurements.
Strand Scope Source
Accuracy Master MA: Curriculum Framework, 2000, Geometry, G.M.4
  
    Accuracy: Explain/Error/Effects/Rounding
The learner will be able to explain the effects of estimated error when rounding measurements.
Strand Scope Source
Accuracy Master MA: Curriculum Framework, 2000, Geometry, G.M.4
  
    Accuracy: Explain/Error/Effects
The learner will be able to explain the effects of estimated error on calculated measurement values.
Strand Scope Source
Accuracy Master MA: Curriculum Framework, 2000, Geometry, G.M.4
  
    Formula: Volume/Cylinders
The learner will be able to apply the formula for the volume of a cylinder.
Strand Scope Source
Formulas Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Formulas: Surface Area/Prism
The learner will be able to use a formula to determine the surface area of a prism.
Strand Scope Source
Formulas Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Formulas: Surface Area/Cylinder
The learner will be able to use a formula to determine the surface area of a cylinder.
Strand Scope Source
Formulas Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Formulas: Surface Area/Sphere
The learner will be able to use a formula to determine the surface area of a sphere.
Strand Scope Source
Formulas Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Formulas: Volume/Sphere
The learner will be able to use a formula to determine the volume of a sphere.
Strand Scope Source
Formulas Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Formula: Find/Surface Area/Pyramid
The learner will be able to find the surface area of a pyramid when presented with the formula.
Strand Scope Source
Formulas Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Formula: Find/Volume/Pyramid
The learner will be able to find the volume of a pyramid when presented with a formula.
Strand Scope Source
Formulas Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  
    Formula: Find/Volume/Cone
The learner will be able to find the volume of a cone when presented with a formula.
Strand Scope Source
Formulas Master MA: Curriculum Framework, 2000, Geometry, G.M.2
  

Real Numbers and the Coordinate Plane
The Real Numbers and the Coordinate Plane Unit includes graphing equations, and making connections between algebraic concepts and their geometric correspondences.

    Coordinate Geometry: Compute
The learner will be able to compute the midpoints of segments, the distance between two points, and the slope of lines and line segments using rectangular coordinates, as well as applying the results to obtaining problem solutions.
Strand Scope Source
Coordinate Geometry Master MA: Curriculum Framework, 2000, Geometry, G.G.12
  
    Slope: Describe/Significance
The learner will be able to describe the significance of a positive, negative, zero, or undefined slope.
Strand Scope Source
Slope Master MA: Curriculum Framework, 2000, Geometry, G.G.11
  
    Slope: Determine From Graph
The learner will be able to use the graph of a linear equation to determine the slope.
Strand Scope Source
Slope Master MA: Curriculum Framework, 2000, Geometry, G.G.11
  
    Coordinate Geometry: Apply/Formulas
The learner will be able to apply formulas of a rectangular coordinate system to obtain proofs of theorems.
Strand Scope Source
Coordinate Geometry Master MA: Curriculum Framework, 2000, Geometry, G.G.3
  
    Linear Equations: Graph
The learner will be able to find the equation of a line when given its graph.
Strand Scope Source
Linear Equations Master MA: Curriculum Framework, 2000, Geometry, G.G.11
  
    Linear Equations: Understand/Forms
The learner will be able to illustrate an understanding of the relationships between the various presentation forms of lines.
Strand Scope Source
Linear Equations Master MA: Curriculum Framework, 2000, Geometry, G.G.11
  
    Linear Equations: Intercepts
The learner will be able to find the intercepts of a linear equation.
Strand Scope Source
Linear Equations Master MA: Curriculum Framework, 2000, Geometry, G.G.11
  
    Linear Equations: Slope
The learner will be able to find the slope of a linear equation.
Strand Scope Source
Linear Equations Master MA: Curriculum Framework, 2000, Geometry, G.G.11
  
    Linear Equations: Geometric Explanation
The learner will be able to determine the linear equation when presented with a geometric description of the line.
Strand Scope Source
Linear Equations Master MA: Curriculum Framework, 2000, Geometry, G.G.11
  
    Linear Equations: Determine/Equation
The learner will be able to determine the equation of the line through a point that is either perpendicular or parallel to a particular line.
Strand Scope Source
Linear Equations Master MA: Curriculum Framework, 2000, Geometry, G.G.13
  
    Linear Equations: X-/Y-Intercepts
The learner will be able to find the x- and y-intercepts of a line when given the graph of a linear relationship.
Strand Scope Source
Linear Equations Master MA: Curriculum Framework, 2000, Geometry, G.G.11
  

Trigonometry
The Trigonometry Unit includes studying triangles, trigonometric ratios, and triangle measurements, applying triangle properties, and solving right triangle problems.

    Problem Solving: Apply/Sin/Cos/Tan
The learner will be able to apply the sine, cosine, and tangent of an acute angle to obtain problem solutions.
Strand Scope Source
Problem Solving Master MA: Curriculum Framework, 2000, Geometry, G.G.9
  
    Trigonometric Concepts: Define/Sine
The learner will be able to define the sine of an acute angle.
Strand Scope Source
Trigonometric Concepts Master MA: Curriculum Framework, 2000, Geometry, G.G.9
  
    Trigonometric Concepts: Define/Cosine
The learner will be able to define the cosine of an acute angle.
Strand Scope Source
Trigonometric Concepts Master MA: Curriculum Framework, 2000, Geometry, G.G.9
  
    Trigonometric Concepts: Define/Tangent
The learner will be able to define the tangent of an acute angle.
Strand Scope Source
Trigonometric Concepts Master MA: Curriculum Framework, 2000, Geometry, G.G.9
  

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