In this activity, you will use graph paper to design a small box.

Question

Create the net for a small box on a piece of graph paper. Label the dimensions of each face of your box.
Find the surface area of your box. Explain how the surface area of your box relates to the net on your graph paper.
Cut out your net and fold it up to create your box. Did your box turn out like you expected? Would you make any changes to your design based on how it turned out?

Answer 1

Here is an example of how to complete this activity:

1. Designing the net for a small box on graph paper:
- Using a piece of graph paper, draw out the net for a small box by creating six rectangles that represent each face of the box.
- Label the dimensions of each face. For example, if you make a box with sides of 2 units, the dimensions could be:
- Top and bottom faces: 2 units by 2 units
- Front and back faces: 2 units by 1 unit
- Side faces: 1 unit by 2 units

2. Finding the surface area of the box:
- To find the surface area of the box, calculate the area of each face separately and then add them together.
- In this example, the surface area would be:
- Top and bottom faces: 2 x 2 = 4 units squared x 2 = 8 units squared
- Front and back faces: 2 x 1 = 2 units squared x 2 = 4 units squared
- Side faces: 1 x 2 = 2 units squared x 4 = 8 units squared
- Total surface area = 8 + 4 + 8 = 20 units squared

3. Relationship between surface area and net:
- The surface area of the box is related to the net on the graph paper by the dimensions of each face. The net represents the different faces of the box, and the dimensions on the graph paper help calculate the surface area.

4. Cutting out and folding the net:
- Cut out the net you designed on the graph paper and fold it along the lines to create the box.
- By folding the net, you should be able to see how the box will turn out based on your design.

5. Evaluating the box:
- Once you fold up the net to create the box, assess if it turned out as expected.
- If the box did not turn out as expected, consider making changes to your design for future iterations. This could include adjusting the dimensions of the faces or the overall size of the box.

Overall, this activity allows you to visually see how the net of a box translates into the actual box and helps you understand the relationship between the surface area calculation and the dimensions of the box.