Permittivity and Permeability
Firstly, I get these the right way round by remembering that permeaBility applies to B-fields.
Secondly, if you've never asked a class who've come across both the permittivity of free space (ε₀ = 8.85 x 10⁻¹² Fm⁻¹) and the permeability of free space (μ₀ = 4π x 10⁻⁷ Hm⁻¹) to calculate the value of
[1/sqrt(E0 x u0)]
and seen the look of amazement on their faces when they realise it's equal to the speed of light, then you really must. For an explanation, good pupils might spot that, since ε₀ relates to how electric fields transmit their effects through a vacuum, and μ₀ relates to how magnetic fields transmit their effects through a vacuum, it really shouldn't be surprising that some mathematical combination of the two will relate to how easily electromagnetic waves transmit their effects through a vacuum.
Thirdly, it can be really easy not to appreciate a fundamental difference between ε₀ and μ₀, namely that one is a quantity like resistance but the other is more like conductance. Permittivity (ε) is like resistance - a higher value means that electric fields find it harder to propagate through a substance. Permeability (μ), on the other hand, is like conductance - a higher value means that magnetic fields find it easier to propagate through a substance. This explains why ε₀ is on the denominator of the electric field equations studied in school, but is in the numerator of many magnetic field equations.