What is this tree?

Factual Questions
1

This is our first spring in our small rental house. There is a huge, seemingly very old, tree in our front yard that SHEDS! Can anyone figure out what the tree is by this admittedly feeble description?

It is shedding a couple of different things. One is clumps of green/yellowish blobs, roughly the size and shape of a large caterpillar. It has smallish “buds” on it. When wet, they stick to EVERYthing.

The other thing is small pod-type things, about the size and shape of a shelled pumpkin seed. These nasty things are sticky and are almost impossible to get out of my poor dog’s hair, but more importantly, they stick in between the pads of his feet. They stick to the bottom of shoes and get tracked in no matter how careful we are. Their dropping seems to be slowing down, thankfully.

Any ideas from my sketchy description?

Oh, maybe it doesn’t show, but I am in Madison, WI.

2

I have no idea, but this website will at the minimum allow you to describe the tree in more detail.

3

What color is the bark? What shape are the leaves? You’re not giving us much to work with.

First guess for me would be birch, because you describe caterpillary green things. But it could be any of dozens of trees.

4

No, I know I’m not giving you much to go on, but that is exactly what the caterpillar-y things look like.

My powers of description are not that great. I will hopefully get out with a camera tonight. However, the bark is dark, not white or silver.

5

My first thought was catalpa. Catalpa - Wikipedia (scroll down).
It has a darker bark.

6

Willows have catkins, too, and exist in a huge number of species.

7

OP, don’t you have a camera?

8

With no picture, I’ll add that if it’s droopy looking and has long skinny leaves, some kind of willow is a reasonable guess.