The party said 40,000 primary age children were taught in classes of 36 or more in England in 2016, blaming "broken promises" by the government.
But the Tories said Labour's attacks were "a massive own goal".
They said the Labour-led Welsh government had overseen increases in class sizes in Wales.
Mr Corbyn, who insisted on Thursday that he could defy the polls and "change the direction" of the election, has used Labour analysis of Department for Education figures to focus on education.
He said: "The prime minister herself has said that super-sized classes are proof of a school system in a crisis.
"And that's what we've got on the Tories' watch.
"School leaders and teachers have said Tory cuts to school budgets will mean class sizes will be forced to grow even larger. We cannot risk our children's education in this way."
In his speech, Mr Corbyn appeared to confuse some of the statistics released earlier by his party, inadvertently overstating the number of children in large classes.
He told supporters: "500,000 children in England - half a million children - are now being taught in super-sized classes of over 36".
The half a million figure is for class sizes of 31 - 34. A Labour spokesman said Mr Corbyn had mixed the figures up.
A Conservative spokeswoman dismissed Mr Corbyn's comments and pointed out that the number of infants in large classes had risen by 18% in three years in Wales.
"Of course we are not complacent about the situation in England," she added.
"There is more to do and that's why we are spending a record amount on schools - something we can afford to do because of our careful management of the nation's finances."
Elsewhere on the campaign trail on Friday, Mr Farron will challenge Tory MPs who supported staying in the EU to oppose a so-called hard Brexit.
He will add: "If these Tory MPs reject these principles and back a hard Brexit manifesto, then people will know that on the biggest issue of the day they went missing in action."
Chalk and cheese. Black and white. Night and day. Yin and yang.
Theresa May and Jeremy Corbyn are not, repeat not, cut from the same cloth. Their fundamental beliefs differ enormously. Their solutions for society's problems are poles apart.
Politicians in opposing parties are sometimes friends across the boundaries. But it is hard, extremely hard, to imagine the Labour leader and the Tory leader ever quietly enjoying a pootle round the Berkshire countryside of a weekend, or a cappuccino in Islington in a quiet moment.
But right at the start of this election - whisper it - there is something significant they share.
Read Laura's blog in full

The 29-year-old turned down a new deal at beaten League Two play-off finalists Exeter to join the third-tier Pilgrims.
"Not everyone will understand my reasoning but those who do, hopefully they understand," he told BBC Devon.
"The club offered me a deal which we tried to negotiate and it just didn't end probably the way it could've."
Grant joined Exeter on a two-year contract in August 2015 after the club's fans raised £30,000 towards his wages.
He has not played for Jamaica since May 2016 when he scored in a friendly victory over Chile.
"I wouldn't tell any lies, I thoroughly enjoyed my time [at Exeter] and was very close to staying, but it's football," Grant added.
"I made the decision to join Plymouth and now I look forward to the challenge.
"It's [the move] definitely something I had to think about, but I'm delighted to be here now and hopefully I can have a good start."

An Institute of Directors report hailed the business model as a blueprint for success and indicated that the UK could learn from the Manx example.
According to government figures, the estimated value of the Isle of Man space industry for the three years to 2013 will reach Â£1.1bn.
Many investors have been attracted by the 0% rate of corporation tax.
The report, published in London on 18 May, said: "The Isle of Man shows how quickly a powerful niche can be built by a very small player."
It adds: "In the new space economy, you can be small and succeed. You don't need astronauts to be in the space business."
There are currently 30 space companies located in the Isle of Man out of a international total of 54.
Labour says children are being crammed "like sardines" into "super-sized" school classes, as it focuses its general election campaign on education.
[NEXT_CONCEPT]
Jamaica international forward Joel Grant says he came "very close" to staying with Exeter City before joining their Devon rivals Plymouth Argyle.
[NEXT_CONCEPT]
The Isle of Man has been praised for "building a powerful niche" within the global space industry.