～かける： unfinished wor...

One way to say "in the middle of X~ing" and "started to do X (but not finished)" is:

かける/かけの*/かけだ**

This grammar point is relatively easy to grasp. It's definition is listed as:

はじめたが、まだ終わっていない
まだ～している途中だ

例：彼は何かを言いかけたが、急に黙ってしまった。

He was on the verge of saying something, but suddenly held his tongue.

例：途中で小説を止めてしまったから、小説はまだ書きかけだよ。
I stopped in the middle of writing the novel, so it is still half-finished.

例：お爺ちゃんはトイレで新聞を読みかけて、そのままでうとうと寝ちゃった。

Grandpa was reading the paper on the toilet and fell asleep like that!

*かけの is a modifier for nouns (eg. tabekake no ringo)
食べかけのりんご=A half-eaten apple

**かけだ comes at the end of a sentence where だ is derived from です

書きかけだ=it is in the middle of being written