If you are talking about a pile of cubes for the ones, some rods for the 10s, and a flat square for the hundreds, then I can help you.

For addition.

I have 32 (pull three rods and 2 unit cubes and put in a small pile)

You have 19 (pull 1 rod and nine unit cube for the second group)

How many do we have all together. Show how when you combine the groups, you can take the 11 cubes and swap out for another rod) So now you have 5 tens and 1 ones, so 51. (At our house I follow up with showing how to carry the extra ten on paper, but you don't need to do that if you are avoiding paper style math)

Similar with subtraction, just sometimes you will need to trade in a ten for some unit cubes (borrowing).

Multiplying/dividing, I stay basic with things like "if there were four groups of kids and each group had 5 kids, how many kids in all" And, then I make the four piles of 5 cubes. We play with the piles. First we count them all, then maybe count by fives, then say it in a sentence "so four groups times 5 kids equals 20 kids". Maybe find other equivalents. . .can we take these 20 kids and put them into 2 equal groups? 3?

Hope this helps.

Amy