Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures.
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
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.
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.
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Triangles can be classified by the angles that they contain, or the relationship between their side lengths. All triangles have two names: one name that describes their angles, and one name that describes their side lengths.
Classifying by Side Length
Classifying by Angle Measure
The tables below describe the triangle classificaton system.
Quadrilaterals are shapes that have 4 sides. Just like triangles, quadrilaterals can have multiple names. Some categories, like parallelograms, are broad. A parallelogram, for example, is any quadrilateral with two pairs of parallel sides. Rectangles, squares, and rhombuses are all parallelograms, for example. However, other categories are narrow. Squares, for instance, must have two pairs of parallel sides, four equal sides, and four right angles.
All rhombuses are parallelograms.
All rectangles are quadrilaterals and parallelograms.
All squares are quadrilaterals, parallelograms, rectangles, and rhombuses.
Volume is the amount of space that an object takes up.
It can help to think of volume as the number of unit cubes that can fit inside an object.
In this 3-inch cube, think of how many 1-inch cubes would fit on the bottom layer of the cube.