Hi - just to add to what maree1 has suggested. Yes use coins for real money addition/ subtraction but be careful not to use coins to count different amounts (so using 5 p pieces where you're counting each one as just one). This can ultimately lead to a bit of confusion. Stick to unnumbered items like m&ms, smarties, grapes, raisins, buttons, etc...
Now airedailleurs in terms of partitioning - what your DD needs to visualise is that 1 ten = ten units.
So first off have her look at a two digit number - say forty-five (45).
Explain that there is a units columns (the '5' column in this example) and a tens column (the '4' in this example). Each column is counting up different things (first column by ones and second column by tens - if you went to larger numbers third column [hundreds' column] by hundreds and fourth column [thousands' column] by thousands etc...).
It's really important to explain that there is only room for a single digit in each column so once you get over 9 units, you have to make tens - same applies to over 10 tens (need to make hundreds), over 100 hundreds (need to make thousands), etc... You can show this fairly easily by just writing out the numbers - it's clear that after 9 there are two columns and after 99 there are three columns, etc...
Now start having her read numbers through with you and vary the question: Sometimes ask how many units? And sometimes ask how many tens?
Once she's clear on what is a unit and what is a ten, start with subtracting (but pick two items - grapes and raisins, red legos and blue legos, white checkers and black checkers, etc...). Explain that the first item = 1 and the second item = 10.
Then do a problem but also visually.
So, for example - 45 - 33 (we're starting with subtractions that don't involve carrying over).
Lay out four grapes (= 4 x 10 = 40) and 5 raisins (5 x 1 = 5) for the '45'
Lay out 3 grapes and 3 raisins for the '33'.
Now start with the units (in this case raisins). Can you take 3 raisins from 5 raisins (in other words is 3 bigger than 5 - no - so go ahead). 5 - 3 = 2 (set aside for later - we tend to use a fancy bowl for the answers). [by the way you can eat the 3 grapes you're taking away].
Now look at the tens (in this case the grapes). Can you take 3 grapes from 4? Yes - o.k. so what is 4 - 3? Eat three grapes and you should have 1 grape or 10. Move grape to the answer plate and total up using your grape/ raisin codes.
The plate should have 1 grape and 2 raisins
1 grape = 10
2 raisins = 2
10 + 2 makes 12
(if it helps you can have her check the answer - again visually by using grapes and raisins for 33 (3 each). Add the two numbers together and you should get the original number (45) you were subtracting from.
When your DC is working soundly with subtracting two digit numbers from each other without 'borrowing' - then introduce numeric annotation (writing out the problem).
This can be down horizontally or vertically. Us oldies were taught vertically and to work from far right to left - but today in schools problems are presented horizontally. So this is up to you. However, I've found with DD1 she 'got it' faster with the good old fashioned vertical subtraction method.
Regardless, start writing out the problems and then having her work through them with just the numerals.
Once that's secure - introduce 'borrowing'. Return to grapes/ raisins (or whatever you decide upon) and really stress that you are exchanging 1 ten for 10 units (this is the bit they often don't quite get).
So for example give the problem 23 - 19.
Set out 2 grapes and 3 raisins for 23 (grapes = 10 and raisins = 1)
Set out one grape and 9 raisins for 19.
Have two plates for each number and an answer plate. Have extra raisins available for exchanging 1 grape for 10 raisins (1 ten for 10 units).
So 23 - 19 = ?
Start with units. 3 - 9 = ? Can you do this? No - 9 is more than 3 - so we need to borrow some units from our neighbour (the tens column).
exchange one of the grapes from 23 for 10 raisins.
So instead of 23 = 2 grapes and 3 raisins - you should now have 1 grape (=10) and 13 raisins (=13) [10 +13 = 23].
Now go back to the unit problem but this time you have 13 raisins - 9 raisins = ?
The answer is 4 raisins (4 units).
Set the raisins aside to the answer plate.
Now you should have 1 grape left on each plate. 1 grape - 1 grape (10 - 10) will equal 0.
So no grapes move to the answer plate. Now look at the answer plate - you have 4 raisins. So 23 - 19 = 4.
Now teach her how to check the answer. Read the problem in reverse -
4 + 19 = 23. Is that right. Hold the larger number in your head (in this case 19) and count up 4. 19 (in head), 20, 21, 22, 23. Yep 19 + 4 = 23 so 23 - 4 = 19.
Keep practicing with visual clues until you feel they really get it and then move to simply doing the numeric problems.
HTH