1. Looking out the window, a good idea occurred to me.

2. Running along the road, a giant bear came out from the trees.

3. Walking in the park, a boy was jumping on and on.
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Would you look at the sentences above? Are they okay in everyday conversation? Or do we have to correct the errors?

Actually, no. The idea was looking out the window? The bear was running along the road when it came out from the trees? How can a boy be walking and jumping at the same time?

They all need to be clearer about who was doing the looking, running, etc.

"While I was walking in the park, I saw a boy who was jumping on and on."