Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 2.0 Knowledge of Geometry

 

A1  Analyze properties of plane geometric figures

Grades 3 & 5

·          Identify polygons within a composite figure

Grades 5 & 6

·          Identify and describe relationships of lines and line segments

Grades 3 – 6

·          Identify, describe, and label points, lines, rays, vertices, angles, and planes using correct symbolic notation

Grade 7

·          Identify and describe the angles formed by intersecting lines, line segments, and rays including vertical, adjacent, complementary, and supplementary angles

Grades 7 & 8

·          Identify and describe the relationships between angles formed when parallel lines are cut by a transversal including alternate interior, alternate exterior, and corresponding angles

Grades 7 & 8

·          Identify and describe the relationship among the parts of a right triangle

 

A2  Analyze geometric relationships

Grade 4

·          Compare and classify angles in geometric figures and pictures 

Grade 5

·          Compare and classify quadrilaterals by length of sides and measures of angles

Grade 6

·          Compare and classify triangles by sides and angle measures

·          Identify and compare the relationship between parts of a circle

Grades 6 & 7

·          Determine a missing angle measure using the sum of the interior angles of a polygon

Grade 7

·          Determine the measure of angles formed by intersecting lines, line segments, and rays

Grade 8

·          Determine the measure of angles formed by parallel lines cut by a transversal

 

B1  Analyze the properties of solid geometric figures

Grades 3 – 5

·          Identify and describe solid geometric figures using the number of edges, faces, vertices, or shape of base

 

2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

 

2.1.1 The student will analyze the properties of geometric figures.

 

Assessment Limits

Ř       Essential properties, relationships, and geometric models include the following:

·          congruence and similarity

·          line/segment/plane relationships (parallel, perpendicular, intersecting, bisecting, midpoint, median, altitude)

·          point relationships (collinear, coplanar)

·          angles and angle relationships (vertical, adjacent, complementary, supplementary, obtuse, acute, right, interior, exterior)

·          angle relationships with parallel lines

·          polygons (regular, non-regular, composite, equilateral, equiangular)

·          geometric solids (cones, cylinders, prisms, pyramids, composite figures)

·          circle/sphere (tangent, radius, diameter, chord, secant, central/inscribed angle, inscribed, circumscribed).

 

Skill Statement

The student describes and analyzes geometric figures.

 

 

 

 

 

Solid Geometric Figures

·          The student will analyze the properties and relationships of geometric solids with bases other than rectangles, triangles, or circles.

·          The student will analyze the properties and relationships of oblique solids.

·          The student will analyze the properties and relationships of truncated three-dimensional solids.

 

Radians

·          The student will explore the relationship between the measure of the central angle and the arc length in a circle.

·          The student will explore the relationship between radian measure and the corresponding degree measure from 0 to 2π.

 

Perspective Drawings

·          The student will analyze the properties of perspective drawings including vanishing points, lines of sight, and hidden lines.

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

B2  Analyze the relationship between plane geometric figures and surfaces of solid geometric figures

Grades 3 – 5

·          Compare plane figure to surfaces of solid geometric figures

 

C1  Represent plane geometric figures

Objective Grades 3 – 8

·          Sketch or draw plane geometric figures

 

D1  Analyze and apply the properties of congruent and/or similar polygons

Grades 3 – 7

·          Analyze and apply the properties of congruent polygons

Grades 5 – 8

·          Analyze and apply the properties of similar polygons

 

2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

 

2.1.1 The student will analyze the properties of geometric figures.

 

Assessment Limits

Ř       Essential properties, relationships, and geometric models include the following:

·       congruence and similarity

·       line/segment/plane relationships (parallel, perpendicular, intersecting, bisecting, midpoint, median, altitude)

·       point relationships (collinear, coplanar)

·       angles and angle relationships (vertical, adjacent, complementary, supplementary, obtuse, acute, right, interior, exterior)

·       angle relationships with parallel lines

·       polygons (regular, non-regular, composite, equilateral, equiangular)

·       geometric solids (cones, cylinders, prisms, pyramids, composite figures)

·       circle/sphere (tangent, radius, diameter, chord, secant, central/inscribed angle, inscribed, circumscribed).

 

Skill Statement

The student describes and analyzes geometric figures.

 

 

 

 

 

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 1.0 Knowledge of Algebra, Patterns, or Functions

 

B2  Identify, write, solve, and apply equations and inequalities

Grades 3 – 8 and Algebra/Data Analysis CLG 1.2.1

·          Solve linear equations from one-step to variables on both sides

 

C1  Locate points on a number line and in a coordinate graph

Grades 4 – 8

·          Graph ordered pairs in the coordinate plane

 

C2  Analyze linear relationships

Grades 7 & 8 and Algebra/Data Analysis CLG 1.2.1

·          Graph linear equations in a coordinate plane

·          Determine the slope of a line

 

Standard 2.0 Knowledge of Geometry

 

A1  Analyze properties of plane geometric figures

Grades 3 &  5

·          Identify polygons within a composite figure

Grades 5 & 6

·          Identify and describe relationships of lines and line segments

Grades 3 – 6

·          Identify, describe, and label points, lines, rays, vertices, angles, and planes using correct symbolic notation

Grade 7

·          Identify and describe the angles formed by intersecting lines, line segments, and rays including vertical, adjacent, complementary, and supplementary angles

Grades 7 & 8

·          Identify and describe the relationships between angles formed when parallel lines are cut by a transversal including alternate interior, alternate exterior, and corresponding angles

Grades 7 & 8

·          Identify and describe the relationship among the parts of a right triangle

 

A2  Analyze geometric relationships

Grade 4

·          Compare and classify angles in geometric figures and pictures 

 

2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

 

2.1.2 The student will identify and/or verify properties of geometric figures using the coordinate plane and concepts from algebra.

 

Assessment Limits

Ř       “Verify properties” means to justify solutions using definitions and/or mathematical principles.

Ř       Properties, relationships, and geometric models include the following:

·          congruence and similarity

·          line/segment relationships (parallel, perpendicular, intersecting, bisecting, midpoint, median, altitude)

·          point relationships (collinear)

·          angles and angle relationships (obtuse, acute, right)

·          polygons (regular, non-regular, equilateral, equiangular)

·          circle (tangent, radius, diameter, chord).

Ř       Items for this indicator may be set on the coordinate plane or may just have coordinates identified with no grid.

Ř       Concepts from algebra include applications of the distance, midpoint, and slope formulas.

 

 

 

 

 

 

 

Polar Coordinates *

·          The student will locate points on the polar coordinate system including points with rotation greater than 360°.

·          The student will explore the relationship between a point on the coordinate plane with the same point on the polar coordinate system.

 

Three-dimensional Coordinate Plane

·          The student will represent a point in space as an ordered triple.

·          The student will use the distance and midpoint formulas for segments in three-dimensional space.

·          The student will explore relationships given a set of points in space such as collinear, coplanar, and relative placement inside or outside a figure.

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Grade 5

·          Compare and classify quadrilaterals by length of sides and measures of angles

Grade 6 

·          Compare and classify triangles by sides and angle measures

·          Identify and compare the relationship between parts of a circle

Grades 6 & 7

·          Determine a missing angle measure using the sum of the interior angles of a polygons

Grade 7

·          Determine the measure of angles formed by intersecting lines, line segments, and rays

Grade 8

·          Determine the measure of angles formed by parallel lines cut by a transversal

 

C1  Represent plane geometric figures

Grades 3 – 8

·          Sketch or draw plane geometric figures

Grade 6

·          Identify, describe, or draw a polygon on a coordinate plane

 

D1  Analyze and apply the properties of congruent and/or similar polygons

Grades 3 – 7

·          Analyze and apply the properties of congruent polygons

Grades 5 – 8

·          Analyze and apply the properties of similar polygons

 

Standard 7.0  Processes of Mathematics

 

B1  Justify ideas or solutions with mathematical concepts or proofs

 

 

 

2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

 

2.1.2 The student will identify and/or verify properties of geometric figures using the coordinate plane and concepts from algebra.

 

Assessment Limits

Ř       “Verify properties” means to justify solutions using definitions and/or mathematical principles.

Ř       Properties, relationships, and geometric models include the following:

·          congruence and similarity

·          line/segment relationships (parallel, perpendicular, intersecting, bisecting, midpoint, median, altitude)

·          point relationships (collinear)

·          angles and angle relationships (obtuse, acute, right)

·          polygons (regular, non-regular, equilateral, equiangular)

·          circle (tangent, radius, diameter, chord).

Ř       Items for this indicator may be set on the coordinate plane or may just have coordinates identified with no grid.

Ř       Concepts from algebra include applications of the distance, midpoint, and slope formulas.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Voluntary State Curriculum – Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 1.0 Knowledge of Algebra, Patterns, or Functions

 

C1  Locate points on a number line and in a coordinate graph

Grades 4 – 8

·          Graph ordered pairs in the coordinate plane

 

Standard 2.0 Knowledge of Geometry

 

A1  Analyze properties of plane geometric figures

Grades 3 & 5

·          Identify polygons within a composite figure

Grades 5 & 6

·          Identify and describe relationships of lines and line segments

Grades 3 – 6  

·          Identify, describe, and label points, lines, rays, vertices, angles, and planes using correct symbolic notation

Grade 7

·          Identify and describe the angles formed by intersecting lines, line segments, and rays including vertical, adjacent, complementary, and supplementary angles

 

A2  Analyze geometric relationships

Grade 4

·          Compare and classify angles in geometric figures and pictures

Grade 5 

·          Compare and classify quadrilaterals by length of sides and measures of angles

Grade 6

·          Compare and classify triangles by sides and angle measures

 

C1  Represent plane geometric figures

Grades 3 – 8

·          Sketch or draw plane geometric figures

Grades 7 & 8

·          Construct geometric figures using a variety of construction tools

 

 

 

 

2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

 

2.1.3 The student will use transformations to move figures, create designs, and/or demonstrate geometric properties.

 

Assessment Limits

Ř       Transformations include reflections, rotations, translations, and dilations.

Ř       Items should go beyond the identification of transformations.

Ř       Essential properties and relationships include the following: congruence, similarity, and symmetry.

Ř       The student’s explanation of a transformation must include the following:

·          translation – distance and direction

·          reflection – line of reflection

·          rotation – center of rotation, angle measure, direction (clockwise or counterclockwise)

·          dilation – center and scale factor.

Ř       Paper folding and the use of Mirasä and mirrors are appropriate methods for performing transformations, and their use must be referenced.

 

Skill Statement

Given one or more transformations, the student sketches the result of the transformation(s) and/or explains the geometric effect of the transformation(s) on the figure.

 

 

 

 

 

Matrices

·          The student will write and plot ordered pairs from matrix notation.

·          The student will find transformation images, including rotations, reflections, dilations and translations, using matrices.

 

Vectors

·          The student will identify the distance and direction of a given vector.

·          The student will find resultant vectors.

·          The student will describe translations using vectors.

·          The student will find translation images using vector sums.


Voluntary State Curriculum – Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

D1  Analyze and apply the properties of congruence and/or similar polygons

Grades 3 – 7 

·          Analyze and apply the properties of congruent polygons

Grades 5 – 8

·          Analyze and apply the properties of similar polygons

 

E1  Analyze a transformation

Grades 3 – 5

·          Identify and describe the results of translations, reflections, and rotations

Grades 6 – 8

·          Identify, describe, and plot transformations on a coordinate plane

Grade 7

·          Identify and describe transformations that result in rotational and reflectional symmetry

 

Standard 3.0 Knowledge of Measurement

 

B1  Measure in customary and metric units

Grades 3 – 6 

·          Measure length in customary and metric unit

 

B2  Measure angles in polygons

Grades 5 & 6

·          Measure angles in a polygon

 

Standard 7.0 Processes of Mathematics

 

B1 Justify ideas or solutions with mathematical concepts or proofs

 

2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

 

2.1.3 The student will use transformations to move figures, create designs, and/or demonstrate geometric properties.

 

Assessment Limits

Ř       Transformations include reflections, rotations, translations, and dilations.

Ř       Items should go beyond the identification of transformations.

Ř       Essential properties and relationships include the following: congruence, similarity, and symmetry.

Ř       The student’s explanation of a transformation must include the following:

·          translation – distance and direction

·          reflection – line of reflection

·          rotation – center of rotation, angle measure, direction (clockwise or counterclockwise)

·          dilation – center and scale factor.

Ř       Paper folding and the use of Mirasä and mirrors are appropriate methods for performing transformations, and their use must be referenced.

 

Skill Statement

Given one or more transformations, the student sketches the result of the transformation(s) and/or explains the geometric effect of the transformation(s) on the figure.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 2.0 Knowledge of Geometry

 

A1  Analyze properties of plane geometric figures

Grades 3 & 5

·          Identify polygons within a composite figure

Grades 5 & 6 

·          Identify and describe relationships of lines and line segments

Grades 3 – 6  

·          Identify, describe, and label points, lines, rays, vertices, angles, and planes using correct symbolic notation

Grade 7

·          Identify and describe the angles formed by intersecting lines, line segments, and rays including vertical, adjacent, complementary, and supplementary angles

Grades 7 & 8

·          Identify and describe the relationships between angles formed when parallel lines are cut by a transversal including alternate interior, alternate exterior, and corresponding angles

Grades 7 & 8

·          Identify and describe the relationship among the parts of a right triangle

 

A2  Analyze geometric relationships

Grade 4

·          Compare and classify angles in geometric figures and pictures

Grade 5

·          Compare and classify quadrilaterals by length of sides and measures of angles

Grade 6

·          Compare and classify triangles by sides and angle measures

·          Identify and compare the relationship between parts of a circle

Grades 6 & 7

·          Determine a missing angle measure using the sum of the interior angles of a polygons

Grade 7

·          Determine the measure of angles formed by intersecting lines, line segments, and rays

Grade 8

·          Determine the measure of angles formed by parallel lines cut by a transversal

 

 

 

 

 

2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

 

2.1.4 The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.

 

Assessment Limits

Ř       “Validate properties” in this indicator, means justifying solutions using definitions, mathematical principles and/or measurement.

Ř       Students may use a compass, straightedge, patty paper, a Mira™, and/or a mirror as construction tools. Using a ruler or protractor cannot be part of the strategy.

Ř       Students may use a compass, ruler, patty paper, a Mira™, a mirror and/or a protractor as drawing tools.

Ř       It is acceptable to do a construction when the item asks for a drawing.

Ř       Paper folding and the use of Miras™ and mirrors are appropriate methods for representing, constructing, and/or analyzing figures, and their use must be referenced.

Ř       Constructions and drawings are limited to the two-dimensional relationships listed in 2.1.1.

 

Skill Statement

The student draws and/or constructs geometric figures and/or justifies the solution.

 

 

 

 

 

Perspective Drawings

·          The student will use the properties of perspective drawings to draw two-dimensional or three-dimensional shapes using vanishing points, lines of sight, and hidden lines.

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

B1  Analyze the properties of solid geometric figures

Grades 3 – 5

·          Identify and describe solid geometric figures using the number of edges, faces, vertices, or shape of base

 

B2  Analyze the relationship between plane geometric figures and surfaces of solid geometric figures

Grades 3 – 5

·          Compare plane figures to surfaces of solid geometric figures

 

C1  Represent plane geometric figures

Grades 3 – 8

·          Sketch or draw plane geometric figures

Grades 7 & 8

·          Construct geometric figures using a variety of construction tools

 

D1  Analyze and apply the properties of congruent and/or similar polygons

Grades 3 – 7

·          Analyze and apply the properties of congruent polygons

Grades 5 – 8

·          Analyze and apply the properties of similar polygons

 

Standard 3.0 Knowledge of Measurement

 

B1  Measure in customary and metric units

Grades 3 – 6

·          Measure length in customary and metric units

 

B2  Measure angles in polygons

Grades 5 & 6

·          Measure angles in a polygon

 

Standard 7.0 Processes of Mathematics

 

B1 Justify ideas or solutions with mathematical concepts or proofs

 

2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

 

2.1.4 The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.

 

Assessment Limits

Ř       “Validate properties” in this indicator, means justifying solutions using definitions, mathematical principles and/or measurement.

Ř       Students may use a compass, straightedge, patty paper, a Mira™, and/or a mirror as construction tools. Using a ruler or protractor cannot be part of the strategy.

Ř       Students may use a compass, ruler, patty paper, a Mira™, a mirror and/or a protractor as drawing tools.

Ř       It is acceptable to do a construction when the item asks for a drawing.

Ř       Paper folding and the use of Miras™ and mirrors are appropriate methods for representing, constructing, and/or analyzing figures, and their use must be referenced.

Ř       Constructions and drawings are limited to the two-dimensional relationships listed in 2.1.1.

 

Skill Statement

The student draws and/or constructs geometric figures and/or justifies the solution.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Voluntary State Curriculum – Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 1.0 Knowledge of Algebra, Patterns and Functions.

 

B2  Identify, write, solve, and apply equations and inequalities

Grades 3 – 8 and Algebra/Data Analysis CLG 1.2.1

·          Solve linear equations from one-step to variables on both sides

 

Standard 2.0 Knowledge of Geometry

 

A1  Analyze properties of plane geometric figures

Grades 3 & 5

·Identify polygons within a composite figure

Grades 5 & 6

·Identify and describe relationships of lines and line segments

Grades 3 – 6

·Identify, describe, and label points, lines, rays, vertices, angles, and planes using correct symbolic notation

Grades 7

·Identify and describe the angles formed by intersecting lines, line segments, and rays including vertical, adjacent, complementary, and supplementary angles

Grades 7 & 8

·Identify and describe the relationships between angles formed when parallel lines are cut by a transversal including alternate interior, alternate exterior, and corresponding angles

Grades 7 & 8

·Identify and describe the relationship among the parts of a right triangle

 

A2  Analyze geometric relationships

Grade 4

·Compare and classify angles in geometric figures and pictures 

Grade 5

·Compare and classify quadrilaterals by length of sides and measures of angles

Grade 6 

·          Compare and classify triangles by sides and angle measures

·          Identify and compare the relationship between parts of a circle

Grades 6 & 7 

·          Determine a missing angle measure using the sum of the interior angles of polygons

Grade 7

·          Determine the measure of angles formed by intersecting lines, line segments, and rays

 

2.2 The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

 

2.2.1 The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts.

 

Assessment Limits

Ř       Students will demonstrate geometric reasoning and justify conclusions.  Although the focus is on geometric theory, answers to some items may include a numeric answer.

Ř       Corresponding measurements include length, angle measure, perimeter, circumference, area, volume, surface area and lateral area.

 

Skill Statement

Ř       The student recognizes shapes as congruent or similar, calculates corresponding measurements, and/or justifies conclusions.

Ř       The student uses congruency and similarity statements to identify corresponding parts of figures.

 

 

 

 

 

 

 


Voluntary State Curriculum – Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Grade 8

·          Determine the measure of angles formed by parallel lines cut by a transversal

 

D1  Analyze and apply the properties of congruent and/or  similar polygons

Grades 3 – 7

·Analyze and apply the properties of congruent polygons

Grades 5 – 8

·Analyze and apply the properties of similar polygons

 

Standard 3.0 Knowledge of measurement

 

C1  Estimate and apply measurement formulas

Grades 3 – 7

·Estimate and determine area and perimeter of geometric figures

Grade 6

·          Determine the missing dimension of  rectangles

Grades 6 – 8

·Estimate and determine the surface area and volume of geometric solids including prisms, cylinders, cones, pyramids, and spheres

Grade 8

·          Estimate and determine the area and circumference of a circle

 

C2  Analyze measurement relationships

Grade 7 

·          Determine the missing dimension for a figure using a scale

Grade 8

·          Use proportional reasoning to solve measurement problems

 

 

2.2 The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

 

2.2.1 The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts.

 

Assessment Limits

Ř       Students will demonstrate geometric reasoning and justify conclusions.  Although the focus is on geometric theory, answers to some items may include a numeric answer.

Ř       Corresponding measurements include length, angle measure, perimeter, circumference, area, volume, surface area and lateral area.

 

Skill Statement

Ř       The student recognizes shapes as congruent or similar, calculates corresponding measurements, and/or justifies conclusions.

Ř       The student uses congruency and similarity statements to identify corresponding parts of figures.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Voluntary State Curriculum – Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 6.0 Knowledge of Number Relationships or Computation

 

C3  Analyze ratios, proportions, or percents

Grades 6 – 8

·Determine or use ratios, unit rates, and percents, in the context of the problem

Grade 8

·          Solve problems using proportional reasoning

 

Standard 7.0 Processes of Mathematics

 

B1 Justify ideas or solutions with mathematical concepts or proofs

 

2.2 The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

 

2.2.1 The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts.

 

Assessment Limits

Ř       Students will demonstrate geometric reasoning and justify conclusions.  Although the focus is on geometric theory, answers to some items may include a numeric answer.

Ř       Corresponding measurements include length, angle measure, perimeter, circumference, area, volume, surface area and lateral area.

 

Skill Statement

Ř       The student recognizes shapes as congruent or similar, calculates corresponding measurements, and/or justifies conclusions.

Ř       The student uses congruency and similarity statements to identify corresponding parts of figures.

 

 

 

 

 

 

 

 

 

 

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 1.0 Knowledge of Algebra, Patterns and Functions

 

B2  Identify, write, solve, and apply equations and inequalities

Grades 3 – 8 and Algebra/Data Analysis CLG 1.2.1

·          Solve linear equations from one-step to variables on both sides

 

Standard 2.0 Knowledge of Geometry

 

A2  Analyze geometric relationships

Grade 4

·          Compare and classify angles in geometric figures and pictures 

Grade 5

·          Compare and classify quadrilaterals by length of sides and measures of angles

Grade 6

·          Compare and classify triangles by sides and angle measures

·          Identify and compare the relationship between parts of a circle

Grades 6 & 7

·          Determine a missing angle measure using the sum of the interior angles of a polygon

Grade 7

·          Determine the measure of angles formed by intersecting lines, line segments, and rays

Grade 8

·          Determine the measure of angles formed by parallel lines cut by a transversal

·          Use the Pythagorean Theorem to solve problems

 

Standard 6.0 Knowledge of Number Relationships or Computation

 

C1  Analyze number relationships and compute

Grades 7 & 8

·          Calculate powers of integers and square roots of perfect square whole numbers

 

 

 

2.2 The student will apply geometric properties and relationships to solve problems using tools and technology.

 

2.2.2 The student will solve problems using two-dimensional figures and/or right-triangle trigonometry.

 

Assessment Limits

Ř       Students will demonstrate geometric reasoning and justify conclusions.

Ř       Trigonometric functions may be used to find sides or angles.

Ř       Trigonometric functions will be limited to sine, cosine, and tangent and their inverses.

 

Skill Statement

The student solves a problem involving missing parts of two-dimensional figures, which may require the use of right-triangle trigonometry, the Pythagorean theorem, or special right triangle relationships.

 

Trigonometry

·          The student will apply the Law of Sines and the Law of Cosines to solve problems involving oblique triangles.

·          The student will solve problems using the secant, cosecant, and cotangent functions.

 

Similarity/Right Triangles

·          The student will use geometric mean and relationships between parts of a right triangle and the altitude drawn to the hypotenuse to find missing parts of right triangles.

 

 

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 2.0 Knowledge of Geometry

 
A1  Analyze properties of plane geometric figures

Grades 5 & 6

·          Identify and describe relationships of lines and line segments

Grade 7

·          Identify and describe the angles formed by intersecting lines, line segments, and rays including vertical, adjacent, complementary, and supplementary angles

Grades 7 & 8

·          Identify and describe the relationships between angles formed when parallel lines are cut by a transversal including alternate interior, alternate exterior, and corresponding angles

Grades 7 & 8

·          Identify and describe the relationship among the parts of a right triangle

 

A2  Analyze geometric relationships

Grade 4

·          Compare and classify angles in geometric figures and pictures 

Grade 5

·          Compare and classify quadrilaterals by length of sides and measures of angles

Grade 6

·          Compare and classify triangles by sides and angle measures

·          Identify and compare the relationship between parts of a circle

Grades 6 & 7

·          Determine a missing angle measure using the sum of the interior angles of a polygon

Grade 7

·          Determine the measure of angles formed by intersecting lines, line segments, and rays

Grade 8

·          Determine the measure of angles formed by parallel lines cut by a transversal

·          Use the Pythagorean Theorem to solve problems

 

B1  Analyze the properties of solid geometric figures

Grades 3 – 5

·            Identify and describe solid geometric figures using the number of edges, faces, vertices, or shape of base

 

 

 

 

2.2 The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

 

2.2.3 The student will use inductive or deductive reasoning.

 

 

Assessment Limits

Ř       Students are expected to demonstrate their geometric reasoning and justify conclusions.  Although the focus is on geometric theory, answers to some questions may include a numeric answer.

Ř       Items may include geometric applications, patterns, and logic, including syllogisms.

Ř       Narrative, flow chart, or two-column proof may be used as a valid argument.

 

Skill Statement

Given a situation, the student arrives at or justifies a conclusion using inductive or deductive reasoning.

 

 

 

 

 

 

Algebraic Proofs

·          The student will write algebraic proofs.

Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 
D1  Analyze and apply the properties of congruent and/or similar polygons

Grades 3 – 7

·          Analyze and apply the properties of congruent polygons

Grades 5 – 8

·          Analyze and apply the properties of similar polygons

 

Standard 7.0 Processes of Mathematics

 

B1  Justify ideas or solutions with mathematical concepts or proofs

 

 

 

 

 

 

 

 

2.2 The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

 

2.2.3 The student will use inductive or deductive reasoning.

 

 

Assessment Limits

Ř       Students are expected to demonstrate their geometric reasoning and justify conclusions.  Although the focus is on geometric theory, answers to some questions may include a numeric answer.

Ř       Items may include geometric applications, patterns, and logic, including syllogisms.

Ř       Narrative, flow chart, or two-column proof may be used as a valid argument.

 

Skill Statement

Given a situation, the student arrives at or justifies a conclusion using inductive or deductive reasoning.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 1.0 Knowledge of Algebra, Patterns, or Function

 

B2 Identify, write, solve, and apply equations and inequalities

Grades 3 – 8 and Algebra/Data Analysis CLG 1.2.1

·          Solve linear equations from one-step to variables on both sides

Grades 6 – 8 and Algebra/Data Analysis CLG 1.2.2

·          Solve linear inequalities

Grades 6 – 8 and Algebra/Data Analysis CLG 1.2.5

·          Apply given formulas in a problem-solving situation

 

Standard 2.0 Knowledge of Geometry

 

A2 Analyze geometric relationships

Grades 6 & 7

·          Determine a missing angle measure using the sum of interior angles of a polygon

Grade 8

·          Determine the measure of angles formed by parallel lines cut by a transversal

·          Use the Pythagorean Theorem to solve problems

 

D1 Analyze and apply the properties of congruent and/or similar polygons

Grades 3 – 7

·          Analyze and apply the properties of congruent polygons

Grades 5 – 8

·          Analyze and apply the properties of similar polygons

 

Standard 3.0 Knowledge of Measurement

 

B1 Measure in customary and metric units

Grades 3 – 6

·          Measure length in customary and metric units

 

2.3 The student will apply concepts of measurement using tools and technology when appropriate.

 

2.3.1 The student will use algebraic and/or geometric properties to measure indirectly.

 

Assessment Limits

Ř       “Measure indirectly” means to use mathematical concepts such as congruence, similarity, and ratio and proportion to calculate measurements.

Ř       Similarity and congruence will be directly stated or implied (scale drawings, enlargements.)

Ř       Items may require the student to make comparisons.

Ř       This indicator may incorporate measuring.

Ř       This indicator does not include right-triangle trigonometry.

 

Skill Statement

The student calculates measurements indirectly by using mathematical concepts.

Ř           

 

 

 

 

 

 

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

B2 Measure angles in polygons

Grades 5 & 6

·          Measure angles in polygons

 

C1 Estimate and apply measurement formulas

Grades 3 – 7

·          Estimate and determine the area and perimeter of geometric figures

Grades 6 – 8

·          Estimate and determine the surface area and volume of geometric solids including prisms, cylinders, cones, pyramids, and spheres

Grade 8

·          Estimate and determine the area and circumference of a circle

 

C2 Analyze measurement relationships

Grade 7

·          Determine a missing dimension for a figure using a scale

Grade 8

·          Use proportional reasoning to solve measurement problems

 

Standard 6.0 Knowledge of Number Relationships or Computation

 

C3 Analyze ratios, proportions, or percents

Grades 6 – 8

·          Determine or use ratios, unit rates, and percents, in the context of the problem

 

 

2.3 The student will apply concepts of measurement using tools and technology when appropriate.

 

2.3.1 The student will use algebraic and/or geometric properties to measure indirectly.

 

Assessment Limits

Ř                 “Measure indirectly” means to use mathematical concepts such as congruence, similarity, and ratio and proportion to calculate measurements.

Ř                 Similarity and congruence will be directly stated or implied (scale drawings, enlargements.)

Ř                 Items may require the student to make comparisons.

Ř                 This indicator may incorporate measuring.

Ř                 This indicator does not include right-triangle trigonometry.

 

Skill Statement

The student calculates measurements indirectly by using mathematical concepts.

Ř                    

 

 

 

 

 

 

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 1.0 Knowledge of Algebra, Patterns, or Functions

 

B2  Identify, write, solve, and apply equations and inequalities

Grades 3 – 8 and Algebra/Data Analysis CLG 1.2.1

·          Solve linear equations from one-step to variables on both sides

Grades 6 – 8 and Algebra/Data Analysis CLG 1.2.2

·          Solve linear inequalities

Grades 6 – 8 and CLG 1.2.5

·          Apply given formulas in a problem-solving situation

 

Standard 2.0 Knowledge of Geometry

 

A1  Analyze properties of plane geometric figures

Grades 3 & 5

·          Identify polygons within a composite figure

Grades 5 & 6

·          Identify and describe relationships of lines and line segments

Grades 3 – 6

·          Identify, describe, and label points, lines, rays, vertices, angles, and planes using correct symbolic notation

Grade 7

·          Identify and describe the angles formed by intersecting lines, line segments, and rays including vertical, adjacent, complementary, and supplementary angles

Grades 7 & 8

·          Identify and describe the relationships between angles formed when parallel lines are cut by a transversal including alternate interior, alternate exterior, and corresponding angles

Grades 7 & 8

·          Identify and describe the relationship among the parts of a right triangle

 

A2  Analyze geometric relationships

Grade 4

·          Compare and classify angles in geometric figures and pictures 

Grade 5

·          Compare and classify quadrilaterals by length of sides and measures of angles

 

 

 

2.3 The student will apply concepts of measurement using tools and technology when appropriate.

 

 

2.3.2 The student will use techniques of measurement and will estimate, calculate, and/or compare perimeter, circumference, area, volume, and/or surface area of two- and three-dimensional figures and their parts. 

 

Assessment Limits

Ř       Two-dimensional shapes include polygons, circles, and composite figures.

Ř       Three-dimensional shapes include cubes, prisms, pyramids, cylinders, cones, spheres, and composite figures.

Ř       Formulas will be provided. 

Ř       No oblique solids will be used.

Ř       Items may involve applications of geometric properties and relationships.

Ř       Students may be required to make comparisons which do not require calculations.

 

Skill Statement

The student solves a problem involving perimeter, area, surface area, lateral area, circumference, and/or volume expressing solutions with appropriate units.

 

Circles

·          The student will determine the area of a sector.

·          The student will determine the length of an arc.

 

Solid Geometric Figures

·          The student will determine properties of oblique solid geometric figures. *

·          The student will determine properties of pyramids that have non-square bases.


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

Grade 6

·          Compare and classify triangles by sides and angle measures

·          Identify and compare the relationship between parts of a circle

Grades 6 & 7

·          Determine a missing angle measure using the sum of the interior angles of a polygon

Grade 7

·          Determine the measure of angles formed by intersecting lines, line segments, and rays

Grade 8

·          Determine the measure of angles formed by parallel lines cut by a transversal

 

B1  Analyze the properties of solid geometric figures

Grades 3 – 5

·          Identify and describe solid geometric figures using the number of edges, faces, vertices, or shape of base

 

B2  Analyze the relationship between plane geometric figures and surfaces of solid geometric figures

Grades 3 – 5

·          Compare a plane figure to surfaces of solid geometric figures

 

C1  Represent plane geometric figures

Grades 3 – 8

·          Sketch or draw plane geometric figures using a variety of tools

 

Standard 3.0 Knowledge of Measurement

 

C1  Estimate and apply measurement formulas

Grades 3 – 7

·          Estimate and determine the area and perimeter of geometric figures

Grades 6 – 8

·          Estimate and determine the surface area and volume of geometric solids including prisms, cylinders, cones, pyramids, and spheres

Grade 8

  • Estimate and determine the area and circumference of a circle

 

2.3 The student will apply concepts of measurement using tools and technology when appropriate.

 

 

2.3.2 The student will use techniques of measurement and will estimate, calculate, and/or compare perimeter, circumference, area, volume, and/or surface area of two- and three-dimensional figures and their parts. 

 

Assessment Limits

Ř       Two-dimensional shapes include polygons, circles, and composite figures.

Ř       Three-dimensional shapes include cubes, prisms, pyramids, cylinders, cones, spheres, and composite figures.

Ř       Formulas will be provided. 

Ř       No oblique solids will be used.

Ř       Items may involve applications of geometric properties and relationships.

Ř       Students may be required to make comparisons which do not require calculations.

 

Skill Statement

The student solves a problem involving perimeter, area, surface area, lateral area, circumference, and/or volume expressing solutions with appropriate units.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Voluntary State Curriculum Geometry

 

Pre-requisites Summarized from Voluntary State Curriculum

 Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG

Geometry Voluntary State Curriculum (VSC)

CLG 2 The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

Additional Topics for a Complete Course Would Include

 

Standard 6.0 Knowledge of Number Relationships or Computation

 

C2  Apply estimation strategies

Grades 3 – 8

Use estimation to determine the reasonableness of an answer

 

2.3 The student will apply concepts of measurement using tools and technology when appropriate.

 

 

2.3.2 The student will use techniques of measurement and will estimate, calculate, and/or compare perimeter, circumference, area, volume, and/or surface area of two- and three-dimensional figures and their parts. 

 

Assessment Limits

Ř       Two-dimensional shapes include polygons, circles, and composite figures.

Ř       Three-dimensional shapes include cubes, prisms, pyramids, cylinders, cones, spheres, and composite figures.

Ř       Formulas will be provided. 

Ř       No oblique solids will be used.

Ř       Items may involve applications of geometric properties and relationships.

Ř       Students may be required to make comparisons which do not require calculations.

 

Skill Statement

The student solves a problem involving perimeter, area, surface area, lateral area, circumference, and/or volume expressing solutions with appropriate units.