Standards - Mathematics

Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

Correctly name shapes regardless of their orientations or overall sizes.

Identify shapes as two-dimensional (lying in a plane, flat“) or three-dimensional (“solid”).“

Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (number of sides and vertices or corners“) and other attributes.“

Model shapes in the world by building them from sticks, clay balls, or other components and by drawing them.

Use simple shapes to compose larger shapes.

Build and draw shapes which have defining attributes.

Distinguish between defining attributes and non-defining attributes.

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.

Partition circles and rectangles into two and four equal shares and describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.

Describe the whole“ as two of or four of the shares of circles and rectangles partitioned into two or four equal shares.“

Explain that decomposing into more equal shares creates smaller shares of circles and rectangles.

Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Recognize and draw shapes having specified attributes.

Partition a rectangle into rows and columns of same-size squares, and count to find the total number of squares.

Explain that equal shares of identical wholes need not have the same shape.

Recognize and describe polygons (up to 8 sides), triangles, and quadrilaterals (rhombuses, rectangles, and squares) based on the number of sides and the presence or absence of square corners.

Draw examples of quadrilaterals that are and are not rhombuses, rectangles, and squares.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines, and identify these in two-dimensional figures.

Identify 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.

Describe right triangles as a category, and identify right triangles.

Define a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.

Identify line-symmetric figures and draw lines of symmetry.

Classify triangles according to side length (isosceles, equilateral, scalene) and angle measure (acute, obtuse, right, equiangular).

Classify quadrilaterals in a hierarchy based on properties.

Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.