With half an ear
Definition 1 of 1
Pro Tip 1/3Partial Attention
Used when someone isn't completely focused on what they're hearing or doing. 
During the game, he was only listening to the commentary with half an ear.
Pro Tip 2/3Subtle Disinterest
Implies a lack of enthusiasm or a slight disregard toward the speaker or activity. 
She listened to the sales pitch with half an ear, clearly uninterested in the product.
Pro Tip 3/3Multitasking Implication
Often used to suggest someone is doing another task while listening, thus splitting their attention. 
He was cooking and listening to the instructions with half an ear.