The youngster, Rohan, had the Deputy Prime Minister on the ropes with statistics and objections to the meals measures.
At one point during the encounter on his regular LBC radio phone-in Mr Clegg suggested, with a hint of desperation: "You probably need to go back to class."
The pupil, who said he was calling from his school in London, started off by complaining his own school meals were "unhealthy".
"I was wondering why you had decided to introduce free school meals, a very expensive product, when at my school they are quite unhealthy and the evidence shows they don't make children achieve or behave better," he said. Mr Clegg replied: "The evidence shows that it is in fact extremely helpful."
A seemingly disconcerted Mr Clegg, inadvertently referring to the schoolboy as "Ryan", attempted to move the discussion on, asking what kind of lunch he ate.
But Rohan said: "I think a lot of parents could already afford to pay for those meals.
"So I was wondering whether you could just target it to the areas where parents can't afford to pay for the meals better."
Mr Clegg said: "Actually the children who benefit most are the children who are poor, who are not wealthy."
However, Rohan said they would "already be entitled to free school meals."
As Mr Clegg argued that in many areas poorer children were not entitled to free school meals, his inquisitor replied: "Couldn't you just target it to their areas, rather than the whole country?"
A chastened Mr Clegg seized on a sound in the background, saying: "I've just heard your class bell go."
Mr Clegg suggested he might want to go away and read the detailed evidence.
But that only prompted the schoolboy to deploy figures, before adding: "Surely, couldn't you spend some of that money on another project?"
Seemingly eager to wrap things up, Mr Clegg later said: "You probably need to go back to class."