K-12 Geometry Standards for Shape – Sorting Cards

Apply the formulas V = l × w × h and V = b × h for rectangular
prisms to find volumes of right rectangular prisms with whole number edge lengths. / Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. / Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
Describe the 2-D figures that result from slicing 3-D figures, as in plane sections of right rectangular prisms and right rectangular pyramids. / Understand that a cube with side length 1 unit is said to have
“one cubic unit” of volume, and can be used to measure volume.
Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths. / Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. / Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths.
Recognize and draw shapes given specific attributes. / Compose 2-D or 3-D shapes to form a composite shape.
Classify two-dimensional figures in a hierarchy based on properties. / Find the area of a rectangle with whole-number side lengths by
tiling it, and show that the area is the same as would be found by multiplying the side lengths
Classify 2-D figures based on the presence or absence of
parallel or perpendicular lines, or angles of a specified size. / Measure areas by counting unit squares.
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. / Compose simple shapes to form larger shapes.
Identify shapes as 2-D or 3-D. / Represent 3-D figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.
Understand that a square with side length 1 unit is said to have “one square unit” of area and can be used to measure area. / Solve real-world and mathematical problems involving area, volume and surface area of 2-D and 3-D objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. / Partition a rectangle into rows and columns of same-size squares and count to find the total.
Understand that shapes in different categories share attributes. / Identify the shapes of 2-D cross-sections of 3-D objects, and identify 3-D objects generated by rotations of 2-D objects.
Solve real world and mathematical problems involving perimeters of polygons. / Correctly name shapes.
Distinguish between defining and non-defining attributes of shapes.