Benchmark 9C: The Mathematical World - Shapes

• Some shapes have special properties: Triangular shapes tend to make structures rigid, and found shapes give the least possible boundary for a given amount of interior area. Shapes can match exactly or have the same shape in different sizes. (1 of 6)
• Standard 12-5, page 112, Grades 5-8
Understand and apply geometric properties and relationships
• Lines can be parallel, perpendicular, or oblique. (2 of 6)
• Standard 12-5, page 112, Grades 5-8
Understand and apply geometric properties and relationships
• Shapes on a sphere like the earth cannot be depicted on a flat surface without distortion. (3 of 6)
• Standard 12-6, page 112, Grades 5-8
Develop an appreciation of geometry as a means of describing the physical world

Standard 8-3 page 161, Grades 9-12
Identify congruent and similar figures using transformations

• The graphic display of numbers may help to show patterns such as trends, varying rates of change, gaps, or clusters. Such patterns sometimes can be used to make predictions about the phenomena being graphed. (4 of 6)
• Standard 10-3, page 105, Grades 5-8
Make inferences and convincing arguments that are based on data analysis
• It takes two numbers to locate a point on a map or any other flat surface. The numbers may be two perpendicular distances from a point, or an angle and a distance from a point. (5 of 6)
• Standard 5-5, page 87, Grades 5-8
Represent numerical relationships in one- and two-dimensional graphs

Standard 8-1 page 161, Grades 9-12
Translate between synthetic and coordinate representations

Standard 8-4 page 161, Grades 9-12
Analyze properties of Euclidean transformations and relate translations to vectors and similar figures using transformations

• The scale chosen for a graph or drawing makes a big difference in how useful it is. (6 of 6)
• Standard 5-5, page 87, Grades 5-8
Represent numerical relationships in one- and two-dimensional graphs