K-12 Geometry Standards for Shape – Answer Sheet

Condensed versions of the standards were written on the cards. The complete standard is included in the right column below.

Note that within grade levels, the standards are not necessarily in the order that they will be taught. Pacing guides are being developed. Also, for some standards, prior mastery of another standard in that same grade level is not required. The progression you developed should at least follow grade levels.

Kindergarten / Correctly name shapes. / K.G.2
Correctly name shapes regardless of their orientations or overall size.
Kindergarten / Identify shapes as 2-D or 3-D. / K.G.3
Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).
Kindergarten / Compose simple shapes to form larger shapes. / K.G.6
Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”
1st / Distinguish between defining and non-defining attributes of shapes. / 1.G.1
Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
1st / Compose 2-D or 3-D shapes to form a composite shape. / 1.G.2
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
2nd / Recognize and draw shapes given specific attributes. / 2.G.1
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
2nd / Partition a rectangle into rows and columns of same-size squares and count to find the total. / 2.G.2
Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
3rd / Understand that shapes in different categories share attributes. / 3.G.1
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
3rd / 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. / 3.MD.5a
Recognize area as an attribute of plane figures and understand concepts of area measurement.
a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
3rd / Measure areas by counting unit squares. / 3.MD.6
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
3rd / 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. / 3.MD.7a
Relate area to the operations of multiplication and addition.
a. 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.
3rd / Solve real world and mathematical problems involving perimeters of polygons. / 3.MD.8
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
4th / Apply the area and perimeter formulas for rectangles in real world and mathematical problems. / 4.MD.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
4th / Classify 2-D figures based on the presence or absence of
parallel or perpendicular lines, or angles of a specified size. / 4.G.2
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
5th / 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. / 5.MD.3a
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
5th / 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. / 5.MD.5a
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
a. 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, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
5th / 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. / 5.MD.5b
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
b. 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 in the context of solving real world and mathematical problems.
5th / Classify two-dimensional figures in a hierarchy based on properties. / 5.G.4
Classify two-dimensional figures in a hierarchy based on properties.
6th / Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. / 6.G.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
6th / Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths. / 6.G.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
6th / Represent 3-D figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. / 6.G.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
7th / Describe the 2-D figures that result from slicing 3-D figures, as in plane sections of right rectangular prisms and right rectangular pyramids. / 7.G.3
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
7th / 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. / 7.G.4
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.
7th / 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. / 7.G.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
8th / Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. / 8.G.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
High School Geometry Domain / Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. / G-GMD.1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
High School Geometry Domain / Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. / G-GMD.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★
High School Geometry Domain / Identify the shapes of 2-D cross-sections of 3-D objects, and identify 3-D objects generated by rotations of 2-D objects. / G-GMD.4
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
High School Geometry Domain / Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). / G-MG.1
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).★