Here is a short video that might change the way you look at equations and your understanding of the equals sign. =
This symbols never lies. = means same. Here is what many consider a novel approach to problem solving. Hero zero makes an appearance and over time problem solving this way will be second nature. You job is to get them to understand equals means SAME and introduce the concept of hero zero and sometimes same is NOT visually obvious and we have to get help from our hero zero.
In the problem 5x + 16 = 4x +12 we are going to end up with NOTHING on one side. We have a symbol for nothing ZERO.
We start off with a low degree of difficulty like this:
3x + 2 = 2x + 6
5x + 16 = 4x +12
2x - 3 = x + 5
a few more and these kinds of problems won't be scary at all.
Find out more about the best ways to use your base ten blocks at Crewton Ramone's house of math.
Get my book on subtraction, Crewton Ramone's Supremely Simple Subtraction it also covers the basics of this kind of problem solving. These concepts can be taught to and understood by even very young students. Hopefully you begin to see how it all goes together...check out this what's under the cup video and you can see problem solving introduced in the most basic way with what's under the cup. When we bust out hero zero we have moved down the road a little. But 5 + x = 10 and 8 + x = 10 and 3 + x = 8 are great ways to start with the CONCEPT of making same and then finding same on both sides is a natural progression. Moving from whats under the cup to seeing 8 + x = 10 = 8 + 2 therefore x must be two is just another more complicated way of playing what's under the cup, but to kids who have played what's under the cup at an early age the symbols make sense because they have SEEN what the symbols represent from an early age.
"Sometimes it is useful to know how large your zero is." ~Anon
"The hardest arithmetic to master is that which enables us to count our blessings." ~Eric Hoffer, Reflections On The Human Condition