counting lots of objects is useful - sooner or later they start to realise that it's faster to count by 2s, for example, or that there are patterns and shortcuts when counting - for example, realising after a while that it's too much trouble to have to say 'a hundred and...' each time in the hundreds, and reaslising that you just say all the same numbers each time, then changing to 'two hundreds and...' and so on. Same thing with thousands. All those sorts of patterns - and especially discovering the patterns themselves - give a better understanding of the whole place value system, and then there is nothing really different about getting into 1000s or other big numbers.
Number lines, tape measures, etc, anything that show the numbers visually are good, as then children start to get a spatial sense of how far apart/close together numbers are, and can make sensible estimates, can visual what half of a number looks like, etc.
Sharing of any sort is great, whether dividing things up, or cutting them into pieces. A lot of children find it hard, for example, to 'cut' a rectangle into four equal pieces by drawing three lines. But as soon as it involves sharing cake between siblings, they are much better at making things equal!
Rearranging objects into patterns - putting things in egg boxes, how many different ways to arrange cubes, just general pattern skills, are great for realising about groups of objects, how 12 can be made up in different ways, etc.