Students explore cube nets in an effort to understand what properties are common to all nets that form a cube. Students work hands-on with nets and are then pushed to use their experience to visually determine whether other nets will form a given figures.

Kindergarteners love to identify shapes in their environment. In order effectively do that, they must be able to recognize different shapes by their specific attributes. In this lesson kindergartners learn about the attributes of a cube.

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.

To display the results from the previous activity, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. They problem solve and apply their understanding of see-saws and lever systems to create balanced mobiles.

Student pairs are given 10 minutes to create the biggest box possible using one piece of construction paper. Teams use only scissors and tape to each construct a box and determine how much puffed rice it can hold. Then, to meet the challenge, they improve their designs to create bigger boxes. They plot the class data, comparing measured to calculated volumes for each box, seeing the mathematical relationship. They discuss how the concepts of volume and design iteration are important for engineers. Making 3-D shapes also supports the development of spatial visualization skills. This activity and its associated lesson and activity all employ volume and geometry to cultivate seeing patterns and understanding scale models, practices used in engineering design to analyze the effectiveness of proposed design solutions.

This interactive exercise focuses on discovering the relationships between two and three-dimensional shapes.

Demonstrates how to find the cube root of a number that is not a perfect cube. [4:50]

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Students watch a video and attempt practice problems on identifying and naming three dimensional figures.

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What types of 2D and 3D shapes make up the products all around you? This challenge will explore how different shapes can be put together to create a product. All the products that humans design and produce are a combination of different shapes. To design a product, engineers and designers must understand how combining, subtracting and adding shapes can make new and unique objects. This challenge will have students use a 3D design tool to create a new and unique shape.

This is a 60-minute lesson that includes a self-paced interactive module and classroom activities. The teacher guide includes a challenge sequence (timeline), relevance to standards, materials list, assessment, resources like cut-outs template, and learning extensions.

Lesson objectives: (1) Explore and interact with 3D shapes in a design plane. (2) Compose unique 3D shapes by decomposing other shapes. (3) Build a 3D shape from a 2D net.

Brush up on your math skills relating to surface area then try some practice problems to test your understanding.

"The volume of a cube can be developed by considering unit cubes, a single row (longs) of unit cubes or a single layer (flats) of cubes using this applet." This easy software makes it possible to easily construct a cube and take it apart. [Requires Java.]

An interactive game to find number of edges, surfaces and vertices of different geometric shapes.

A guide to support parents as they work with their students in ordering and comparing length measurements as numbers.

In this lesson, students will form cubes and discuss their attributes including edges, faces, vertices, and angles. Media resources and teacher materials are included.

Surface Area and Volume

Type of Unit: Conceptual

Prior Knowledge

Students should be able to:

Identify rectangles, parallelograms, trapezoids, and triangles and their bases and heights.
Identify cubes, rectangular prisms, and pyramids and their faces, edges, and vertices.
Understand that area of a 2-D figure is a measure of the figure's surface and that it is measured in square units.
Understand volume of a 3-D figure is a measure of the space the figure occupies and is measured in cubic units.

Lesson Flow

The unit begins with an exploratory lesson about the volumes of containers. Then in Lessons 2–5, students investigate areas of 2-D figures. To find the area of a parallelogram, students consider how it can be rearranged to form a rectangle. To find the area of a trapezoid, students think about how two copies of the trapezoid can be put together to form a parallelogram. To find the area of a triangle, students consider how two copies of the triangle can be put together to form a parallelogram. By sketching and analyzing several parallelograms, trapezoids, and triangles, students develop area formulas for these figures. Students then find areas of composite figures by decomposing them into familiar figures. In the last lesson on area, students estimate the area of an irregular figure by overlaying it with a grid. In Lesson 6, the focus shifts to 3-D figures. Students build rectangular prisms from unit cubes and develop a formula for finding the volume of any rectangular prism. In Lesson 7, students analyze and create nets for prisms. In Lesson 8, students compare a cube to a square pyramid with the same base and height as the cube. They consider the number of faces, edges, and vertices, as well as the surface area and volume. In Lesson 9, students use their knowledge of volume, area, and linear measurements to solve a packing problem.

Lesson OverviewStudents use scissors to transform a net for a unit cube into a net for a square pyramid. They then investigate how changing a figure from a cube to a square pyramid affects the number of faces, edges, and vertices and how it changes the surface area and volume.Key ConceptsA square pyramid is a 3-D figure with a square base and four triangular faces.In this lesson, the net for a cube is transformed into a net for a square pyramid. This requires cutting off one square completely and changing four others into isosceles triangles.It is easy to see that the surface area of the pyramid is less than the surface area of the cube, because part of the cube's surface is cut off to create the pyramid. Specifically, the surface area of the pyramid is 3 square units, and the surface area of the cube is 6 square units. Students will be able to see visually that the volume of the pyramid is less than that of the cube.Students consider the number of faces, vertices, and edges of the two figures. A face is a flat side of a figure. An edge is a segment where 2 faces meet. A vertex is the point where three or more faces meet. A cube has 6 faces, 8 vertices, and 12 edges. A square pyramid has 5 faces, 5 vertices, and 8 edges.Goals and Learning ObjectivesChange the net of a cube into the net of a pyramid.Find the surface area of the pyramid. 

A complete reference guide to solid geometry. The mathematics resource provides definitions and interactive activities that enhance further explanation.

Learn to measure the volume of rectangular prisms with cube units by watching this video lesson. [2:12]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

On this one page website sharpen your logic, geometry, spatial thinking, and problem solving skills while working on this challenge. The solution is available to double check your solution.