Wachusett Regional School District
Wachusett Mountain

District Frameworks - Mathematics

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Standard 8

Geometry & Measurements Standards

Grades K-4

Geometry and Spatial Sense (NCTM Standard 9) - shall include two- and three-dimensional geometry so that students will:

  • Describe, model, draw, and classify shapes; 
  • Investigate and predict the results of combining, subdividing, and changing shapes; 
  • Develop spatial sense; 
  • Relate geometric ideas to number and measurement ideas; 
  • Recognize and appreciate geometry in their world. 

Measurement (NCTM Standard 10) - shall include measurement so that students will:

  • Understand the attributes of length, capacity, weight, area, volume, time, temperature, and angle; 
  • Develop the process of measuring and concepts related to units of measurement; 
  • Make and use measurements in problem and everyday situations; 
  • Make and use estimates of measurements.

Grades 5-8

Geometry (NCTM Standard 12) - shall include the study of the geometry on one, two, and three dimensions in a variety of situations so that students will:

  • Identify, describe, compare, and classify geometric figures; 
  • Visualize and represent geometric figures with special attention to developing spatial sense; 
  • Explore transformations of geometric figures; 
  • Represent and solve problems using geometric models; 
  • Understand and apply geometric properties and relationships; 
  • Develop an appreciation of geometry as a means of describing the physical world.

 Measurement (NCTM Standard 13) - shall include extensive concrete experiences using measurement so that students will:

  • Extend their understanding of the process of measurement; 
  • Estimate, make, and use measurements to describe and compare phenomena; 
  • Select appropriate units and tools to measure to the degree of accuracy required in a particular situation; 
  • Understand the structure and use of systems of measurement; 
  • Extend their understanding of the concept of perimeter, area, volume, angle measure, capacity, and weight and mass; 
  • Develop the concepts of rates and other derived and indirect measurements; 
  • Develop formulas and procedures for determining measures to solve problems.

Grades 9-12

Geometry from a Synthetic Perspective (NCTM Standard 7) - shall include the continued study of the geometry of two and three dimensions so that all students will:

  • Interpret and draw three-dimensional objects; 
  • Represent problem situations with geometric models and apply properties of figures; 
  • Classify figures in terms of congruence and similarity and apply these relationships; 
  • Deduce properties of, and relationships between, figures from given assumptions;

and, in addition, college-intending students will:

  • Develop an understanding of an axiomatic system through investigating and comparing various geometries.

Geometry from an Algebraic Perspective (NCTM Standard 8) - shall include the study of the geometry of two and three dimensions from an algebraic point of view so that all students will:

  • Translate between synthetic and coordinate representations; 
  • Deduce properties of figures using transformations and using coordinates; 
  • Identify congruent and similar figures using transformations; 
  • Analyze properties of Euclidean transformations and relate translations to vectors;

and, in addition, college-intending students will:

  • Deduce properties of figures using vectors; 
  • Apply transformations, coordinates, and vectors in problem solving.

ADULT BASIC EDUCATION

Geometry and Spatial Sense (ABE Standard 10) - shall include approaches to teaching geometry and spatial sense which allow the learner to:

  • Use geometry as a means of describing the physical world relative to all the arts and sciences; 
  • Understand and apply geometric properties and relationships to concrete situations; 
  • Visualize and represent geometric figures with special attention to developing spatial sense; 
  • Identify, describe, compare, and classify geometric figures; 
  • Relate geometric ideas to number and measurement ideas, including the concepts of perimeter, area, volume, angle measure, capacity, weight, and mass; 
  • Explore transformations of geometric figures; 
  • Represent and solve problems using geometric models; 
  • Apply the use of appropriate technologies to the study of geometry and spatial sense.

 Measurement (ABE Standard 11) - shall include concrete and experiential approaches to teaching measurements which allow the learner to:

  • Understand the process and concepts of measurement; 
  • Make and use exact and estimated measurements to describe and compare phenomena; 
  • Select appropriate units and tools to measure to the degree of accuracy required in a particular situation; 
  • Understand the structure and use of different systems of measurement.