Shapes and Volume

Understand volume as an attribute of solid figures that is measured in cubic units. Find the volume of concrete three-dimensional figures.

Find the volume of pictorial three-dimensional figures.

Find the volume of a right rectangular prism by thinking about its layers.

Find the volume of a right rectangular prism using its side lengths.

Represent volume using expressions related to the formulas $$V = b \times h $$ and $$V = l \times w \times h$$. Use these formulas to find the volume of pictorial rectangular prisms.

Understand standard units for measuring volume, including cubic inches, cubic centimeters, cubic feet, and cubic meters. Solve real-world and mathematical problems involving these various units.

Solve more complex real-world and mathematical problems involving volume.

Solve a three-act task involving volume.

Understand that volume is additive. Find the volume of composite solid figures when all dimensions are given and their decomposition is already shown.

Understand that volume is additive. Find the volume of composite solid figures when not all dimensions are given and/or they must be decomposed.

Classify shapes as polygons versus non-polygons and classify polygons according to their number of sides.

Classify quadrilaterals based on the presence or absence of one pair of parallel sides. Understand trapezoids as quadrilaterals with at least one pair of parallel sides.

Classify trapezoids based on the presence of one or two sets of parallel sides. Understand parallelograms as trapezoids with two sets of parallel sides.

Classify parallelograms based on the presence or absence of right angles or based on the presence or absence of sides of equal length. Understand rectangles as parallelograms with four right angles and rhombuses as parallelograms with four equal sides.

Classify rectangles based on the presence or absence of sides of equal length, and classify rhombuses based on the presence or absence of right angles. Understand squares as quadrilaterals with sides of equal length and all right angles.

Classify triangles based on side and angle measures.