I love division on a numberline - it's the most successful way I've ever taught division! Hard to explain on here without being able to draw a line and jumps, but I'll try. Draw a horizontal line. On the left hand end write 0. Now - the next bit depends on the age and stage of your child, so I'll tell you the longer, more complete way first and then the way with shortcuts.
Draw a jump over the numberline of 3 (using the example you give). If we add 3 to 0, what do we get to? 3. So write 3 under the numberline. Make another jump of 3. If we add 3 to 3, what do we get to? 6. Repeat, repeat, repeat until you get to 21. Can we fit another jump of 3 in? No. Why not? We've only got 2 left. The way we teach this is to draw a jump under the numberline, to show that it's a remainder, and label it 2. Now add up the number of jumps along the top of the numberline you have ie 7, put it with the remainder and you have 23 divided by 3 = 7 remainder 2.
That can get quite tedious, doing all the individual jumps but is worth doing once or twice so the child can see what is happening. Then you can introduce a short cut. Before starting on the division, write down 10x, 5x, 2x and 1x your divisor ie 10 x 3 = 30, 5 x 3 = 15 etc. Very, very few children don't know their 10, 5 and 2 times table! The draw your numberline as before and write the 0 at the left hand end. Can we fit 10 lots of 3 into 21? No. Why not? OK then, can we fit 5 lots in. Yes. So draw a largish jump onto the line and write 5 above it. If I start at 0 and add on 5 lots of 3, what do I get to? 15. Write that under the numberline. Can I fit another 5 lots of 3 in? No. Okay - so can I fit in 2 lots? Draw another jump, write 2 above the jump and then 21 under the numberline (I sometimes write +6 in between the jump and the numberline so we can remember how much we're adding on). Can I fit another 2 lots of 3 in? No. 1 lot then? No. In that case how much do we have left over? 2. Draw a jump under the numberline to show it's the remainder. Add together the numbers you've written on top of the line ie 5 and 2, and you have an answer of 7 remainder 2.
I hope this makes sense - it's an easy thing to draw and very long winded to describe in words! Maybe if you get a bit of paper and draw what I've described, it will all slot into place! The beauty of using the 10x, 5x, 2x and 1x thing is that just about anyone can divide just about anything (OK - for really big numbers I'd add 100x or 1000x, but the principle is the same). If it's still as clear as mud, pm me your email address and I'll send you the calculation policy I wrote for my school.