School Improvement in Maryland

Using the Core Learning Goals: Mathematics

View:

Print:

CLG Toolkit

Tools aligned to CLG expectations and/or indicators.

  • Skill Statements
    Describes how a student demonstrates an understanding of an indicator
  • Public Release Items
    HSA items and annotated student responses as appropriate
  • Lesson Plans
    Written by Maryland educators for teaching the concepts

Goal 2: Geometry, Measurement, And Reasoning

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.

Expectation

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

Indicator

  • 2.1.1 The student will analyze the properties of geometric figures.

Assessment limit:

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).

Indicator

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

Assessment limits:
  • “Verify properties” means to justify solutions using definitions and/or mathematical principles.
  • 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).
  • Items for this indicator may be set on the coordinate plane or may just have coordinates identified with no grid.
  • Concepts from algebra include applications of the distance, midpoint, and slope formulas.

Indicator

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

Assessment limits:
  • Transformations include reflections, rotations, translations, and dilations.
  • Items should go beyond the identification of transformations.
  • Essential properties and relationships include the following: congruence, similarity, and symmetry.
  • 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
  • Paper folding and the use of MirasTM and mirrors are appropriate methods for performing transformations, and their use must be referenced.

Indicator

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

Assessment limits:
  • “Validate properties” in this indicator, means justifying solutions using definitions, mathematical principles and/or measurement.
  • Students may use a compass, straightedge, patty paper, a MiraTM, and/or a mirror as construction tools. Using a ruler or protractor cannot be part of the strategy.
  • Students may use a compass, ruler, patty paper, a MiraTM, a mirror and/or a protractor as drawing tools.
  • It is acceptable to do a construction when the item asks for a drawing.
  • Paper folding and the use of MirasTM and mirrors are appropriate methods for representing, constructing, and/or analyzing figures, and their use must be referenced.
  • Constructions and drawings are limited to the two-dimensional relationships listed in 2.1.1.

Expectation

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

Indicator

  • 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:
  • Students will demonstrate geometric reasoning and justify conclusions. Although the focus is on geometric theory, answers to some items may include a numeric answer.
  • Corresponding measurements include length, angle measure, perimeter, circumference, area, volume, surface area and lateral area.

Indicator

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

Assessment limits:
  • Students will demonstrate geometric reasoning and justify conclusions.
  • Trigonometric functions may be used to find sides or angles.
  • Trigonometric functions will be limited to sine, cosine, and tangent and their inverses.

Indicator

  • 2.2.3 The student will use inductive or deductive reasoning.

Assessment limits:
  • 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.
  • Items may include geometric applications, patterns, and logic, including syllogisms.
  • Narrative, flow chart, or two-column proof may be used as a valid argument.

Expectation

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

Indicator

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

Assessment limits:
  • “Measure indirectly” means to use mathematical concepts such as congruence, similarity, and ratio and proportion to calculate measurements.
  • Similarity and congruence will be directly stated or implied (scale drawings, enlargements).
  • Items may require the student to make comparisons.
  • This indicator may incorporate measuring.
  • This indicator does not include right-triangle trigonometry.

Indicator

  • 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:
  • Two-dimensional shapes include polygons, circles, and composite figures.
  • Three-dimensional shapes include cubes, prisms, pyramids, cylinders, cones, spheres, and composite figures.
  • Formulas will be provided.
  • No oblique solids will be used.
  • Items may involve applications of geometric properties and relationships.
  • Students may be required to make comparisons which do not require calculations.