The concept is simple: numbers are made up of other numbers. Here we practice the single digit combinations past ten...what you will find with any student of the mathematics is their knowledge has some gaps or holes in it. So occasionally it's good to go through and fill in some of the holes and gaps with fun practice.
Note that this is quite different from just memorizing facts or formula...they learn to figure out the formulas themselves, and if they forget the facts they have algorithms or tools to figure out the answers quickly for themselves if it is not part of their instant recall memory...and the more you practice the better the chance of it getting into the instant recall memory.
Adding some symbols to go along with the blocks certainly doesn't hurt anything. Notice it's just for keeping track and that he doesn't write out all the combinations, the blocks give a quick visual for that, especially with the colors for added instant recognition...we also did subtraction which is basically going "backwards and forwards."
If I have 15 and take away 8 I am left with 7 which is just the addend. You can also each them to just add 2 which is the 10 compliment for 8 to the 5 for a total of 7, or you could take five out of the 8 which leaves 3 and know that the 10 compliment for 3 is 7 or (leaste preferred) you could count backwards from 15, 8 places...students HATE the number line for a reason. It is ineffectual and can be confusing even when presented well. Knowing all 45 addends with emphasis on 9's and 10's will solve many problems later, in fact you won't just solve them you will avoid them altogether. I have had countless students who were failing algebra come to me unable to do simple addition and subtraction in their heads without aid of fingers or toes, not to mention multiplication...these addends lead to multiplication which makes all the math easy because it allows you to count very, very quickly....
Parents always ask me why don't you just cover the blocks why does it have to be a math bag (and why go to all the trouble to decorate the bag)? BECAUSE IT'S FUN. WHAT'S MORE FUN? COVERING THE BLOCKS WITH A PIECE OF PAPER OR GETTING INSIDE YOUR VERY OWN MATH BAG? Seriously: some adults are a sad shadow of the bright, fun loving, energetic, curious, infinitely inquisitive children they used to be.
Here as you can see is a youtube vid, with apologies to all my public school teacher friends who have to go home to view it. It's just a short (less than 3 min) vid where the unknown mathematician shows he knows some of the combinations without looking, without blocks or symbols (or fingers) just his imagination.
Find me on Facebook or Youtube. I'm told there are benefits to subscribing to youtube because sometimes I put videos up and then go back and un-list them as I put them on password protected pages. BTW lots more video has been added to the password protected pages...