A rectangle has an area of 20cm^2. Its length and width are enlarged by a factor of 3. Find the area of the enlarged rectangle.

I'd start by drawing out any rectangle with an area of 20cm^2 and labelling the length and width. Any correct combination will do (i.e. 2 X 10, 4 X 5, 20 X 1 etc.). In this example, I will use 4 X 5 Then multiply each side by 3 (4 X 3 = 12 & 5 X 3 = 15). Now you have your new length and width. Multiply the new length and width together to get the area of the new shape: 12 X 15 = 180. 180cm^2 is your answer.

When you get more confident with this technique and wish to do the calculations more quickly, you can multiply the original area (20) by the factor squared (3^2). I.e. 20 X 9 = 180. The reason the factor is squared is because we are looking at the area of a 2D shape. If we were looking at the volume of a 3D shape we would raise the factor to the power of three.