Can’t solve it? Sketch it first!
When learning how to calculate surface area and volume of 3D shapes, students are often given a list of formulas without any explanation of the formulas. So when given the following problem,
Find the total volume of a rectangular prism with base side lengths of 6 cm and whose height is 8 cm.
Knowing the formula is V=BxH, students will often solve this by simply multiplying 6×8. Even if they multiply correctly, this shows that they do not understand what volume is measuring, or that they have to find the area of the base. Therefore, I prefer to teach “Volume = any end area x length.” But first, use the following steps to work towards a solution (highlight key terms–>find shape (or equation, etc.)–>put in values–>use formula (or equations steps) –> solution (add units if required). This is what it might look like for the earlier volume problem:
Hint: When you have the correct shape (Google it if not sure) and have added the dimensions, shade the ‘end area’ that has two measurements for finding the area, then times by the height (or length). Your diagram with shaded end might look like this:
Try this: Assuming your classroom is also a rectangular prism (aka ‘box’) you can find the volume by using the area of one end and ‘pushing it through’ the length of the room. That is, ‘End Area x Length.’ Or, you could find the area of the ceiling and ‘drop it down’ the height of the room – again this is ‘End Area x Height.’ So, the rule of ‘End Area x Length‘ is a really good formula to find volumes.
