Mrs May said it meant "more people in work than ever before, wages rising above inflation that's more people with a pay packet, more money in those pay packets".
She added: "What would Labour offer? More taxation and misery for working families."
Mr Corbyn said he was glad to see people in work but attacked the uncertainty in the job markets.
"Of course I welcome anyone who has managed to get a job (to help) keep their families together," Mr Corbyn replied.
"The problem is there is almost a million of them on zero hours contracts who don't know what they're going to be paid from one week to the other."
Jeremy Corbyn accused Theresa May of pursuing an education policy of "segregation" as the pair clashed at Prime Ministers Questions over the Government's aim to introduce new grammar schools.
The Labour leader dedicated a series of questions to the controversial policy, challenging the Prime Minister to name any education experts that back her on introducing more selection into schools.
Mrs May refused to name a significant backer, but accused Mr Corbyn of living in the past, saying: "Can I say to the honorable gentleman that he needs to stop casting his mind back to the 1950s."
Despite opposition from some sections of her own party - including the outgoing former prime minister David Cameron - on selection, she attempted to define the difference between her party and her rival leader.
"He believes in equality of outcome. We believe in equality of opportunity," she said. "He believes in levelling down. We believe in levelling up."
Mr Corbyn replied: "Equality of opportunity is not segregation at the age of 11."
Mrs May said both leaders had benefitted from the system. "He went to a grammar school. I went to a grammar school. It's what got us where we are today."
Mr Corbyn said he wanted the education system to offer "good education for every child".
Jeremy Corbyn used the session to ask the prime minister about the "housing crisis" in Britain.Read the full story ›
The prime minister said Labour was a "laughing stock" as she poked fun the "traingate" story.
Last month, Jeremy Corbyn was filmed sitting on the floor of a train complaining about "completely ram-packed carriages".
But CCTV was later released showing him appearing to walk past empty seats.
Theresa May said everything Mr Corbyn says "tell us all we need to know about modern Labour".
She said: "The train's left the station, the seats are all empty, the leader's on the floor - even on rolling stock they're a laughing stock."
Theresa May mocked Jeremy Corbyn over the responses he got when he asked his Twitter followers to suggest questions for Prime Minister's Questions.
"I thought I would look to see what sort of responses he'd received," she said.
"Lewis writes 'Does she know that in a recent poll on who would make a better Prime Minister, don't know scored higher than Jeremy Corbyn?"
Mrs May added: "What we do know is whoever wins the Labour Party leadership, we're not going to let them near power again."
Jeremy Corbyn challenged Theresa May on house prices at Prime Minister's Questions.
The Labour leader said rising house prices had made owning their own home a "dream" for many people.
He also said the Government was failing to deliver on a "one for one " promise to replace every council house sold under the Right To Buy scheme.
Mrs May said house building was up under the Conservative government and disputed the "one for one" claim, saying the commitment had been met.
A look at some of the most memorable sessions at PMQs.Read the full story ›
The Labour MP accused the prime minister of "putting this House and this country to shame".Read the full story ›
The prime minister is facing the Labour leader in the first post-Panama papers PMQs.
David Cameron may also face questions over the position of the culture secretary after it was revealed he had a relationship with a sex worker.
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Labour leader Jeremy Corbyn has appeared in the House of Commons wearing a 'heart unions' badge.Read the full story ›