When it comes to learning about surface area and volume in math, one of the best ways to help students grasp the concepts is by using activities that involve changes in scale. These activities can help students better understand the relationship between surface area, volume, and the dimensions of an object, and how changes in one area affect the others.

There are a variety of activities you can use to teach this topic, depending on the age and skill level of your students, as well as the resources you have available. Here are a few examples:

1. Building Blocks: One simple activity involves using building blocks of different sizes to help students visualize changes in scale. Start by having students build a tower using several blocks of one size. Then, have them build a similar tower using blocks that are half the size. Ask them to compare the two towers in terms of their surface area and volume. You can also experiment with other objects, such as spheres or cylinders, to help students see the changes in scale more clearly.

2. Water Displacement: Another activity involves using water displacement to measure the volume of an object. Have students fill a graduated cylinder with a known amount of water, then carefully drop the object into the cylinder. The amount of water that is displaced will give you the volume of the object. You can then repeat this process with different-sized objects to help students see how changes in scale affect the volume of an object.

3. Box Project: For a more in-depth activity, have students design and build a box using cardboard or other materials. Ask them to calculate the surface area and volume of the box, then challenge them to create a second box that is twice as large in all dimensions. Have them calculate the surface area and volume of the new box, and then compare the results to see how the changes in scale affected the box.

4. Candy Corn: Another fun activity involves using candy corn to teach surface area and volume. Start by having students count the number of candy corns in a row, then stack them to create a pyramid. Help students calculate the surface area and volume of the pyramid, then challenge them to make a larger pyramid using twice as much candy corn. This activity can be done with other types of candy or small objects as well.

5. Digital Tools: For a more high-tech approach, there are a variety of digital tools available that can help students explore changes in scale and surface area/volume. Websites such as GeoGebra and Desmos offer interactive tools that allow students to manipulate objects and see how changes in scale affect their dimensions. There are also apps such as Skyscraper that allow students to design and build structures using virtual blocks.

No matter which activities you choose to use, incorporating changes in scale is a great way to help students understand surface area and volume in a more concrete way. By seeing how changes in one area affect the others, students can better grasp these fundamental mathematical concepts.