Miss Greening praised the modest citizens who make up the “backbone” of Britain.
She also added that working families should not have to “make do” and condemned the struggle to their children into good schools.
New Government analysis shows a majority of selective school places go to students from affluent families.
Education Secretary Justine Greening plans to help working class families get top grammar schools Theresa May's political career in pictures Thu, April 6, 2017
Prime Minister Theresa May has promised to 'build a greater Britain'
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Saudi Arabia's King Salman bin Abdulaziz al-Saud (R) meeting with British Prime Minister Theresa May in the capital Riyadh, Saudi Arabia, 05 April 2017. May is visiting Saudi Arabia as part of her Middle East trip to boost diplomatic ties in the region
Figures also showed that child poverty is most prevalent among children from working families.
The “ordinary” families are usually missed out of poverty measures, but are clearly not wealthy enough to pass as the “privileged few” – which is Ms Greening claims to have made them the focus of her new education reforms.
Speaking at St Mary’s University in Twickenham later today, Miss Greening is expected to say: “Fundamentally, children need more good schools.
"I believe that selection, in new, 21st Century state grammar schools, will add to the options available to young people, to truly help make the most of their talents.
"And grammars should not just be for one better off group in society to attend. We want to see more children from disadvantaged families get into grammars – that's vital."
Theresa May's pledge to reinvigorate grammar schools was a key part of her manifesto
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She will add: “Many young people from an ordinary working class background already attend our existing grammar schools.”
St Mary's University, where Miss Greening is due to speak, recently published research which showed pupils who are eligible for free school meals had become an unreliable measure of poverty.
The researchers said the focus of these pupils missed families who might be working multiple jobs and living in precarious financial circumstances, but above the threshold for free meals.
The study warned that using proportions of free school meal pupils had also become an unreliable way of assessing the fairness of admissions systems.
Shadow education secretary Angela Rayner claimed the Government 'fiddled' grammar school figures
Shadow education secretary Angela Rayner said the Government had “fiddled” the figures regarding grammar schools and needed to invest more in classrooms generally.
She told Radio 4's Today programme: “Grammar schools do not improve social mobility and therefore they are not good for our education system.
“They are trying to bring in a policy where there is a life raft for a very, very tiny minority if you're lucky enough go through the private tuition to get yourself into these grammar schools while the rest of us can rot.“
Pressed on whether she was arguing for policies that a number of senior Labour figures did not believe in in practice because they sent their children to private, or selective, schools, Mrs Rayner said: “Well, I believe in it as practice because I'm looking at the evidence, and my kids are not guinea pigs, let me tell you.
“And all my children go to a comp system because we know what we did is improve school education. We transformed the education system when Labour was in power.”