Geometry and Measurement

7.GM.1Determine the scale factor and translate between scale models and actual measurements (e.g., lengths, area) of real-world objects and geometric figures using proportional reasoning.7.GM.2Construct triangles and special quadrilaterals using a variety of tools (e.g., freehand, ruler and protractor, technology).7.GM.2aConstruct triangles given all measurements of either angles or sides.7.GM.2bDecide if the measurements determine a unique triangle, more than one triangle, or no triangle.7.GM.2cConstruct special quadrilaterals (i.e., kite, trapezoid, isosceles trapezoid, rhombus, parallelogram, rectangle) given specific parameters about angles or sides.7.GM.3Describe two-dimensional cross-sections of three-dimensional figures, specifically right rectangular prisms and right rectangular pyramids.7.GM.4Investigate the concept of circles.7.GM.4aDemonstrate an understanding of the proportional relationships between diameter, radius, and circumference of a circle.7.GM.4bUnderstand that the constant of proportionality between the circumference and diameter is equivalent to π.7.GM.4cExplore the relationship between circumference and area using a visual model.7.GM.4dUse the formulas for circumference and area of circles appropriately to solve real-world and mathematical problems.7.GM.5Write equations to solve problems involving the relationships between angles formed by two intersecting lines, including supplementary, complementary, vertical, and adjacent.7.GM.6Apply the concepts of two- and three-dimensional figures to real-world and mathematical situations.7.GM.6aUnderstand that the concept of area is applied to two-dimensional figures such as triangles, quadrilaterals, and polygons.7.GM.6bUnderstand that the concepts of volume and surface area are applied to three-dimensional figures such as cubes, right rectangular prisms, and right triangular prisms.7.GM.6cDecompose cubes, right rectangular prisms, and right triangular prisms into rectangles and triangles to derive the formulas for volume and surface area.7.GM.6dUse the formulas for area, volume, and surface area appropriately.
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