Matter can be changed into energy. The famous scientist Albert Einstein created the mathematical formula that explains this. It is: E = mc²

E [energy] equals m [mass] times c² [c stands for the speed of light. c² means c times c, or the speed of light raised to the second power -- or c-squared.]

[Energy (in joules) = Mass (in kilograms) X The Speed of Light Squared (in meters squared per second squared)

This equation has become an icon, or a trade mark for science, and is not really viewed as the equation by the majority of people. It seems to be viewed in the same light as a company logo like Nike, Almost everyone recognises it and are vaguely aware of it's connection with Albert Einstein and may know it has something to do with mass and energy, even though they have never seen the formula as it is shown above.

In his article "Astrophysics for a Ten-Year-Old Mind" Michael Chabin explained that the formula could be understood by a 10 year old, providing the basics were explained, especially that one of the remarkable findings of the century is that matter and energy are two forms of the same thing. Neither can be destroyed but, under special circumstances, either can be turned into the other. This is important. All the matter in the universe condensed out of pure energy over a period of about 700,000 years shortly after the Big Bang, and today, stars shine because matter at their centers is being slowly converted back into energy. Both annihilation of matter into energy and condensation of matter out of energy have been demonstrated in the laboratory. One of the most amazing things about all this is that a simple equation will tell you exactly how much energy a given amount of mass contains.

His method was to write e=mc² at the top of a piece of paper. Then take a moment or two for her to tell you what she knows about the equation.
Then ask her to write the following just below the first equation.

Energy (in joules) = Mass (in kilograms) X The Speed of Light Squared (in metres squared per second squared)

You need to be sure she knows what a metre is and then explain that you want her to figure out how much energy is contained in a one-litre bottle of water if the entire mass is converted to energy.

Begin with the speed of light.
Light travels three hundred million meters in a second so now she can write:

energy = mass X (300,000,000)², or e = m (3 x 10⁸)²

You can leave the units for now, but we cannot forget them at the end. The next step, of course, is to square the speed of light. That produces an even bigger number and makes the need for scientific notation clear. Once that is done, however, the result is a constant that simplifies the equation to:

e = m (90,000,000,000,000,000), or e = m (9 X 10¹⁶)

Mass is next. It is given in kilograms, and, since a litre of water is defined to have a mass of one kilogram, most kids have no trouble with this unit. Because you want to know how much energy is in one litre of water, the mass term is equal to 1 and the equation becomes:

e = 1 (9 X 10¹⁶), or e = 9 X 10¹⁶ joules

That's it. That's the answer. And that is all there is to it. Square the speed of light in meters per second, and you get the energy provided by a kilogram of mass. Swapping values for mass will let kids calculate the energy equivalence for everything from the Sun to a hot dog.

The problem is, of course, understanding what your answer means. Energy is given in joules and not many kids know what a joule is. But they should; it is an extremely intuitive unit. A joule is the effort required to push one kilogram over a metre at an acceleration of one metre per second squared. To get a feel for it, pick up a litre bottle of water and toss it ten centimetres into the air. You've just expended about a joule. Here are some others:

On (very) tiny scales...
Breaking a single bond in human DNA requires just 10-20 joule
A firing neuron needs only 10-9 joule
For a hop, a flea requires about 10-7 joule

On human scales...
A Netball shot from within the goal circle takes about 15 joules
Bowling a fast ball requires 120 joules
Rolling a strike with a bowling ball will cost you 230 joules

On planetary scales...
The largest hydrogen bomb ever tested produced 2.4 X 1017 joules
A typical hurricane amounts to about 3.8 X 1019 joules

On astronomical scales...
A supernova releases around 1044 joules
One estimate gives the energy yield of the Big Bang as 1068 joules

A joule expended continuously for one second is a watt, which means a litre of water, converted to energy could power a 1 watt light bulb for 9<<1016 seconds, or 2.5<<1013 hours. Of course if it were a 100 watt bulb it would only burn for 2.5 x 1011 hours, and you might find it more interesting to burn 1011 light bulbs for two and a half hours instead. It is then reasonable to ask how large an area that many light bulbs would cover.She will find, after a little work (especially if she hasn't seen square roots yet), that if she allows an area of about 10 cm by 10 cm for each bulb, she can tile a square roughly thirty-one kilometres on a side with 1011 light bulbs.

What you've just done is arithmetic. Now for the science.

What would happen if you turned all those light bulbs on for two and a half hours?
Would it explode? The amount of energy released would be a little less than a tenth of the energy released in the enormous hydrogen bomb tests of the early 1960s, but the area over which you are releasing it is larger, and you are releasing it over a longer time.
Or would it generate tornadoes? You are releasing less than one one-hundredth of the energy in a typical hurricane, but hurricanes form over vast stretches of the ocean and typically take a week or so to blow themselves out. You are releasing the energy over a comparatively tiny area in less than three hours.
Or would most of the energy escape through the clear sky as a brilliant beacon? Wondering about such possibilities are the roots of science and very appropriate for ten-year olds and curious adults.
Incidentally, the average ten-year old uses about the same amount of energy as a 100 watt bulb, which is why classrooms can warm up so readily. In fact, there is a direct equivalence to food calories which makes a broad range of interesting and silly calculations possible. One joule is equal to about four food calories.
Of course, the calculations can also be serious and scientific. A little bit of algebra that is very appropriate to introduce to fifth graders will allow you to find the mass you need to meet any particular energy requirement. The equation now looks like m = e/c². For example, given that the Sun emits 4 X 1026 joules per second, how much mass does it convert each second in order to burn? If the Sun is 5 X 109 years (or 1.6 X 1017 seconds) old, how much mass has it used so far?
It doesn't matter very much what the calculations are. It doesn't matter if the distances or quantities are accurate. What does matter is that students will be exercising the maths appropriate to their grade level on one of the most remarkable equations known. Without a refresher from time to time it is unlikely that they will remember the details into adulthood. They don't need to.

What is important is that having played with the equation once, they will know that it is tractable, accessible, and so much more than a trademark of science.