Three-Dimensional Shapes

Three-dimensional shapes, also known as 3D shapes, are objects that have three dimensions - length, width, and height. These shapes are often encountered in everyday life and can be found all around us.

Properties of Three-Dimensional Shapes

Three-dimensional shapes have several properties that distinguish them from two-dimensional shapes:

They have volume, which is the amount of space inside the shape.
They have faces, edges, and vertices.
The faces are flat surfaces that make up the boundary of the shape.
The edges are the line segments where the faces meet.
The vertices are the points where the edges meet.

Examples of Three-Dimensional Shapes

There are many different types of 3D shapes, including:

Study Guide

When studying three-dimensional shapes, it's important to understand the following concepts:

The names and properties of different 3D shapes
Calculating the volume of 3D shapes using appropriate formulas
Identifying and counting the number of faces, edges, and vertices for each shape
Recognizing real-life examples of 3D shapes in the environment

Practice drawing and visualizing 3D shapes from different perspectives to improve your spatial reasoning skills.

Understanding three-dimensional shapes is essential for various fields, including architecture, engineering, and design. Mastery of this topic can also provide a strong foundation for advanced mathematical concepts.

◂Math Worksheets and Study Guides Sixth Grade. Proportions/Equivalent Fractions

Study Guide

Proportions/Equivalent Fractions

Worksheet/Answer key

Proportions/Equivalent Fractions

Worksheet/Answer key

Proportions/Equivalent Fractions

Worksheet/Answer key

Proportions/Equivalent Fractions

Create And Print more Fractions worksheets with Comparing Fractions, Equivalent Fractions, and Simplifying Fractions

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Grade 6 Curriculum Focal Points (NCTM)

Number and Operations: Connecting ratio and rate to multiplication and division

Students use simple reasoning about multiplication and division to solve ratio and rate problems (e.g., 'If 5 items cost $3.75 and all items are the same price, then I can find the cost of 12 items by first dividing $3.75 by 5 to find out how much one item costs and then multiplying the cost of a single item by 12'). By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative sizes of quantities, students extend whole number multiplication and division to ratios and rates. Thus, they expand the repertoire of problems that they can solve by using multiplication and division, and they build on their understanding of fractions to understand ratios. Students solve a wide variety of problems involving ratios and rates.