Session 1: I have them count the beads on every row of this little abacus, confirming that every row has ten.  If an abacus isn't available this step could be skipped and go straight to some other manipulative like my magnetic marbles a few steps down. 

Session 2: Again with the abacus we begin dividing the "tens" in each row into "different kinds of tens" We count them, counting the two parts of each ten and then recounting that the whole row is indeed still ten.  When this has been verified, we then do a little chant as she touches the groups of beads,

Chant:

9,1:10;

8,2:10;

7,3:10;

6, 4: 10;

5,5: 10;

5,5: 10;

4,6: 10;

3,7: 10;

2,8: 10;

1, 9: 10; 

Session 3:

Substituting magnetic marbles for the abacus we again make groups to match our chant.

Session 4: As a child points to each section of each ten, we do the chant again, going faster each time to make it a game.  Sometimes I say it and demonstrate, sometimes I have one of the children chant solo, and sometimes we go through the list in unison.   

 Session 5:  (The wee ones are feeling mathish so we have several sessions in a day.)   This time they help set up the groups.   I get out 9 and ask, "What does this need to be a 10?" Keianna (or maybe Keegan) answers, "1".  Then they may get out a contrasting marble.

Once we've formed the tens by adding up, we will do our chant.  The chant changes this time though, and we add in addition termonology!   Instead of just saying, "9,1; 10" we change to "9 plus 1 equals 10" and so on...

 
Session 6: Again I have them count to verify that each set is ten.  (Easier to count if break the circles into rows.)  They count, and then break the groups into the two parts.  They will now touch each part as they say the chant, touching the 9 marbles as they say, "nine" then touching the single marble and saying, "plus one", then touching both togher and saying "ten".  We continue through all the groups.

Session 7: At this point I introduce numeral symbols instead of just the concrete numbers. I simply have them match up numerals to the dot values.  Somehow they knew the numerals already, so it was a short lesson.

Session 8: Now it is time for subtraction.  we separate the contrasting marbles, but keep them near their partners and again do our chant, but this time saying, "10 minus 9 is one; 10 minus 8 is 2; 10 minus 7 is 3" and so on first with the larger number first, then back the other way touching (and saying) the smaller number first.

Session 9:  Now for the chalkboard!  I write a chart of our chant.  I tap the chart while we go through it backward and  forward.  Sometimes we just say the numbers (like the first chant), sometimes with "plus" for addition, sometimes with tapping the 10 on top first, and doing subtraction.  We go through it until it is firmly set, usually just 10 minutes or so because really it is the same thing we'd drilled with abacus and marbles already.

Session 10: Finally I begin erasing numerals and drilling the children on "what was here?" as I erase a single numeral.  Then we run the chart with that numeral missing.  When it is solid, I erase another, tapping all the empty  holes saying, "What goes here?"  Again, we then run the chant with my tapping the chart.  Then we erase another numeral and so on until the chart is a blank tree.  I then drill them tapping just the blank tree a few times a day for a week or two to make sure it is set. 

Additonally, I'll tap the chart as I call out the random facts, calling "10-8" and then tapping the place the "2" would go, I wait for a child to call out, "two!".   

After that, we move on and do the same thing for the 9 chart, 8 chart, 7 chart and on down to 2.  We go through the same steps--marbles and all. (Except after the 10 chart, we skip the abacus in steps 1& 2 and the numeral cards in step 7.).  Usually long before we get to the two chart the child has predicted, "I know what the 2 chart will be, Mommy!  One, One Two!"  They catch on to the pattern pretty quickly.

Once they know all the charts (hence all the addition and subtraction facts up through sums of 10), they are ready to zip through a first grade math text--mostly just doing the text to acquaint themselves with written math.

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*Note: The abacus and marble adaptations are my own, but the chart idea came from the Professor B Math Curriculum.  I used Professor B with Kaira for several years, and retained a few aspects in my teaching for the youngers.