More than 4,500 cryptic boxes were posted to prospective male teachers this week, with the words: "Can you manage an assembly?"
Recipients opened the packs to discover a bag of four dismantled toys which they could assemble to make doctors, policemen and people in other professions.
The Teacher Training Agency commissioned UK-based construction toy-makers Best Lock to produce the figures for men who had called its Teaching Information Line.
TTA spokesman Andrew Bate said the packs were part of its "Men Into Primary" campaign to raise the proportion of men recruited into primary teaching from 17 per cent to at least 20 per cent.
"The packs use the imagery of assembling toys to make the point about teachers building young people intellectually," he said.
"The aim is to get men to apply to become teachers before December 15, the deadline for most applications, because traditionally men have applied later."
The pound;13,000 cost of the packs is unlikely to cause a major dent in the TTA's budget. Its annual report this week revealed that the government grant the agency received in the last financial year was up by almost a third to pound;401 million.
But the agency was left with a pound;15.6m underspend, and the Department for Education and Skills will decide if it should now lose pound;9m.
The toys, sets of which can be bought for around pound;2.99, are the latest in a line of so-called "ambient" advertising from the TTA which has included beer mats, bus tickets and sandwich bags.
The TTA says that the success of past advertising is proven by the increased calls to its telephone line and visits to its website, which saw its visitors double from August to September to 272,326 when TV advertising was running.
The Teaching Information Line is 0845 6000 991 TTA underspend, 11