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Seeing Reason Tool: Bridge the Gap
Content Standards and Objectives
Targeted Content Standards and Benchmarks
NCTM Content Standards:
Geometry Standard for Grades 6-8
In grades 6-8 all students should:
  • Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties
  • Understand relationships among the angles, side lengths, perimeter, areas and volumes of similar objects
  • Draw geometric objects with specified properties, such as side lengths or angle measures
  • Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume
  • Use geometric models to represent and explain numerical and algebraic relationships;
  • Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life
Problem-Solving Standard for Grades 6-8
In grades 6-8 instructional programs should enable all students to:
  • Solve problems that arise in mathematics and in other contexts
  • Build new mathematical knowledge through problem solving
  • Apply and adapt a variety of appropriate strategies to solve problems
  • Monitor and reflect on the process of mathematical problem solving
Connections Standard for Grades 6-8
In grades 6-8 instructional programs should enable all students to:
  • Recognize and use connections among mathematical ideas
  • Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
  • Recognize and apply mathematics in contexts outside of mathematics
Student Objectives
Students will be able to:
  • Learn about triangulation
  • Understand that side lengths determine the exact shape of a triangle (Side-Side-Side Congruence Theorem), as long as the sum of the lengths of any pair of sides is longer than the length of the third side (this is known as the triangle inequality: a+b>c in order for it to make a triangle
  • Understand that for quadrilaterals, side lengths can be arranged in a variety of shapes.
  • Understand that the sum of the lengths of any three sides of a quadrilateral is greater than the length of the fourth side
  • Understand that the triangle is a stable figure and keep their shape under stress, whereas quadrilaterals can wobble into many unstable shapes and become distorted under stress
  • Examine the strengths and weaknesses of structures
  • Create procedures for constructing and testing components of a structure
  • Compare the strengths of different components of a structure
  • Learn about bridge types and their structural design
  • Provide arguments related to principles and to evidence for ideas and choices expressed
  • Use measurement and scale factor to draw accurate scale models
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