Geometry & Spatial Reasoning

Understanding shape, space, position, and how objects fit and move in the world.

K–12 objective ladder

• K D05.S3.K.01 Name and match common shapes and use position words (over, under, beside).
• 1 D05.S3.01.01 Compose and take apart two- and three-dimensional shapes and describe their sides, corners, and faces.
• 1 D05.S3.01.02 Measure and compare lengths using non-standard units such as hand spans or paper clips.
• 2 D05.S3.02.01 Identify and draw shapes with given attributes, such as a certain number of angles or equal sides.
• 2 D05.S3.02.02 Partition circles and rectangles into equal shares and describe the shares as halves, thirds, and fourths.
• 3 D05.S3.03.01 Understand the area and perimeter of rectangles and solve problems using them in real contexts.
• 3 D05.S3.03.02 Sort shapes into categories by their attributes and recognize that shapes in a category share common properties.
• 4 D05.S3.04.01 Draw and identify points, lines, line segments, rays, and angles, and classify shapes by their lines and angles.
• 4 D05.S3.04.02 Apply formulas for the area and perimeter of rectangles to solve real-world and mathematical problems.
• 5 D05.S3.05.01 Graph points in the first quadrant of a coordinate grid and use them to solve problems about location and distance.
• 5 D05.S3.05.02 Find the volume of right rectangular prisms using unit cubes and formulas, and explain what volume measures.
• 6 D05.S3.06.01 Find area, surface area, and volume of common figures and use nets to build and analyze three-dimensional shapes.
• 6 D05.S3.06.02 Draw and use polygons on the coordinate plane to solve real problems involving position and length.
• 7 D05.S3.07.01 Construct and describe triangles and other shapes from given conditions, and tell when such a shape is impossible.
• 7 D05.S3.07.02 Solve problems with scale drawings and circles, using the relationship between circumference and diameter.
• 8 D05.S3.08.01 Describe translations, rotations, reflections, and dilations, and use them to show congruence and similarity.
• 8 D05.S3.08.02 Use the Pythagorean theorem to solve problems about right triangles and distances.
• 9 D05.S3.09.01 Use rigid motions and coordinates to prove and reason about geometric relationships such as congruence.
• 9 D05.S3.09.02 Prove and apply theorems about lines, angles, triangles, and parallelograms.
• 10 D05.S3.10.01 Use trigonometric ratios and the Pythagorean theorem to solve right-triangle problems in real contexts such as surveying or navigation.
• 10 D05.S3.10.02 Prove and apply theorems about circles and use coordinate geometry to describe and analyze figures.
• 11 D05.S3.11.01 Use the unit circle and trigonometry of general triangles to model periodic relationships in real phenomena.
• 11 D05.S3.11.02 Reason about three-dimensional shapes, finding the volume and surface area of composite solids in real contexts.
• 12 D05.S3.12.01 Use coordinates and vectors to analyze geometric situations and prove results.
• 12 D05.S3.12.02 Apply geometric reasoning to real-world design, such as architecture, mapping, or the layout of shared spaces, considering access and sustainability.

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