This year, I anticipate I'll spend very little:
My kids have plenty of shorts and summer clothes, so no real needs there. I will take a look at their shoes to see if those need replacing. End of September / beginning of October, we'll evaluate whether they need jeans. I'd need to clothe them anyway, so I don't really consider that a "school supply".
They both have good backpacks; those don't need replacing every year.
They both have age-appropriate calculators; next year when my youngest starts high school, I'll have to shop for another graphing calculator -- but that's next year.
They'll need notebooks, paper, and so forth, but that's very easy to buy for next to nothing in August. I always pick up enough to last all school year.
I agree MrsPete, new clothes really are back to school costs since they have to have them anyway. Some years I barely buy any back to school clothes until fall when I buy for winter. It just so happened that this year both my girls grew over summer, so I had to buy "back to school" clothes all at once.