Building a Box
This lesson uses a real-world situation to help develop students' spatial visualization skills and geometric understanding. Emma, a new employee at a box factory, is supposed to make cube?shaped jewelry boxes. Students help Emma determine how many different nets are possible and then analyze the resulting cubes. This activity is a good way for students to visualize surface area.
- Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge...
- Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures....
- Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between...
- Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles,...
- Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- GLE 0606.1.3
- Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
- GLE 0606.4.3
- Develop and use formulas to determine the circumference and area of circles, and the area of trapezoids, and develop strategies to find the area of composite shapes.
- GLE 0606.4.4
- Develop and use formulas for surface area and volume of 3-dimensional figures.
- SPI 0606.4.4
- Calculate with circumferences and areas of circles.
- SPI 0606.4.5
- Determine the surface area and volume of prisms, pyramids and cylinders.
- SPI 0606.4.6
- Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa.
- Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and...
- Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these...
- Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the...
- Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles,...
- Know and understand the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems.
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- Create, compare and describe different two-dimensional nets that can be folded into a three-dimensional cube.
- Examine the properties of the nets and resulting cubes, including surface area.
- Use rotations and flips to compare various nets.
Questions for Students:
- What properties are common to all nets that will form a cube?
- What type of nets will not work? Why not?
- Without folding, is there a quick way to determine whether or not a net will fold into a cube?
- How can you determine if two nets are identical?
- What sort of properties does your final cube have? How do these compare to the properties of the nets?
- Have students determine the net for a typical cereal box. Draw a sketch, and then cut it out and fold it. See if they can design nets for other boxes they have seen. Also, you might have them use the Patch Tool to create nets for other three dimensional objects using triangles, hexagons, and rhombi.
- Give students the following challenge problem:
- The ACME box company wants to make these jewelry boxes as efficiently as possible. They can save money by fitting as many nets as possible on one piece of cardboard. If the company use a piece of cardboard that measures 20 cm × 20 cm, how many nets (of any type) can you arrange to fit on one piece of cardboard? You may use any of the working net designs you created and you may arrange them in any way on your piece of cardboard.
- As an alternative, allow students to use the drawing area of the Patch Tool to represent the cardboard, and see how many different nets they can fit into this region.
- Draw a net on a single sheet of 8½" × 11" piece of paper that will result in the largest cube possible. Which net will you use? What is its volume?
- Computer with internet connection
- Building a Bod Activity Sheet
- Square Polydron or Geofix pieces, or centimeter grid paper to cut and fold