The older boy stumbled at 21 + 7 (we were counting by 7's) he wasn't sure what to do when he already had a one for the units but not enough to make a ten...adding seven more didn't automatically mean 28 for him. He is careful, thoughtful, literal and meticulous...
Once I was playing fractions and I said "this is one to two" and he heard one two two and asked where the other 2 was...
More than once over the years the young ones have taught me they take you at your word, literally.
Anyway, here is a quick 5 minute lesson showing place value is well understood and they are well on their way to mastery of number naming. Soon I will begin correcting to one hundred seventeen, no AND. Then adding thousands and ten thousands and hundred thousands...just saying 137,596 is fun for them. As we start naming numbers we also talk about what the words mean just like you would when introducing any new vocabulary. How many is 100,000? How many is a trillion? (We'll get there later, but we will get there.)
Turns out most Americans can't conceive of that number.
What I didn't catch in the video was showing having two tens and a one and a seven, or two tens and a five and a three etc...we talked about doing the addition without worrying about what the tens were doing...the sad thing is there are plenty of parents and educators that take these powerful blocks and teach addition and subtraction and place value and then stop there...look over this blog for algebra, fractions and more...
Again note that there are barely any symbols being used...but when we do use them they know what they mean. Later a fun math activity is to write the numbers and then get out the pieces...the fun part is writing with the markers. Other than that don't be slowed down with making symbols because the little kids don't have the fine motor skills to write quickly. Do that after they have played blocks and named lots of numbers.
I used manipulatives once they didn't really seem to work. I shot a gun once: missed the target, the gun didn't work. Same reasoning.
Here is a fun vid showing how scarily innumerate the average American is...only 21% get the answer right. We are now growing the deficit at 2 trillion a year. People say I need to keep the politics off the blog; however, those people miss the whole point of why it is I do mathematics.