Geometry and Measurement
Tennessee Diploma Project
Conceptual StrandGeometry studies geometric shapes and structures and their characteristics and relationships. Understanding what a measurable attribute is and becoming familiar with the units and processes that are used in measuring attributes are the major emphasis of this standard.Guiding QuestionHow can students make and explore conjectures about geometry and reason carefully about geometric ideas while expanding their understanding of precision in measurement?
Grade Level Expectation
Understand and use basic properties of triangles, quadrilaterals, and other polygons.
Use the concepts of translation, rotation, reflection, and symmetry to understand congruence in the plane.
Develop and use formulas to determine the circumference and area of circles, and the area of trapezoids, and develop strategies to find the area of composite shapes.
Develop and use formulas for surface area and volume of 3-dimensional figures.
Check For Understanding
Investigate the sum of the angles in a triangle and a quadrilateral using various methods.
Relate the sum of the angles in a triangle to the sum of the angles in polygons.
Verify the basic properties of triangles and quadrilaterals using a protractor and ruler.
Classify triangles by side lengths (scalene, isosceles, and equilateral) and angle measure (acute, right, obtuse, isosceles and equiangular).
Model and use the Triangle Inequality Theorem.
Use the properties of interior and exterior angles of polygons to solve problems.
Work with transformations in a plane and explore their meanings through drawings and manipulatives.
Understand scaling, dilation and their relation to similarity.
Analyze the differences between congruence and similarity.
Describe the effect of a transformation on a 2-dimensional figure and the resulting symmetry.
Relate the circumference of a circle with the perimeter of a polygonal figure.
Derive the meaning of Pi using concrete models and/or appropriate technology.
Understand the relationships among the radius, diameter, circumference and area of a circle, and that the ratio of the circumference to the diameter is the same…
Relate the area of a trapezoid to the area of a parallelogram.
Find lengths given areas or volumes, and vice versa.
Solve contextual problems involving area and circumference of circles, surface areas and volumes of prisms, pyramids, cones, and cylinders.
Use manipulatives to discover the volume of a pyramid is one-third the volume of the related prism (the heights and base areas are equal).
Use manipulatives to discover the volume of a cone is one-third the volume of the related cylinder (the heights and base areas are equal).
State Performance Indicator
Identify, define or describe geometric shapes given a visual representation or a written description of its properties.
Find a missing angle measure in problems involving interior/exterior angles and/or their sums.
Solve problems using the Triangle Inequality Theorem.
Calculate with circumferences and areas of circles.
Determine the surface area and volume of prisms, pyramids and cylinders.
Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa.