The High School Assessments assess student's knowledge of Core Learning Goals at the indicator level. Some indicators have assessment limits which indicate more specifically what will be assessed. Assessment items and other instructional resources at the indicator level can be viewed in the CLG Toolkit.
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.
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.
- 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).
- 2.1.2 The student will identify and/or verify properties of geometric figures using the coordinate plane and concepts from algebra.
- “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.
- 2.1.3 The student will use transformations to move figures, create designs, and/or demonstrate geometric properties.
- 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.
- 2.1.4 The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.
- “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.
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.
- 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.
- 2.2.2 The student will solve problems using two-dimensional figures and/or right-triangle trigonometry.
- 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.
- 2.2.3 The student will use inductive or deductive reasoning.
- 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.
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.
- “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.
- 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.
- 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.