An explanation

One of the coolest things in a classroom is when a student comes up to me and asks how something works, knowing that the student has been pondering an answer or a mistake, and then seeing the leap of learning in his mind after my explanation.

The photo below shows a math problem with the wrong answer that a ten year old was pondering because he kept getting it slightly wrong. My students are learning to divide decimal numbers, so he was doing the problem of
.15 ÷ .3 = 5 (the answer is really .5). He couldn't quite understand why the answer wasn't just the whole number of 5. I showed him 1.5 ÷ .3 = 5 and that .15 ÷ .03 = 5 by using the drawing to demonstrate the distances on a number line. There was a bit more to it than that, but the drawing helped make the problem concrete rather than just a procedure that was confusing. He could envision what the numbers stood for, so he got it! This all happened during a transition and took less than a minute to discuss...and we got an AHA! moment out of it. Excellent work young man!

Now, I know for some readers that sounds wordy and like a bunch of jibberish, but I guarantee if you heard the explanation you would have gotten it too. That's what I truly believe for my students too.