"About 60 per cent of the children suffer from cerebral palsy," she explains. "They could be premature babies [or the result of] complications, or wrong medical care. Thirty-five per cent have genetic or metabolic disorders and the other group - for me, the saddest one - is the children who were born normally but have suffered some form of abuse or accident.
"We treat them like regular children.They go to the mall, the swimming pool. We invest a lot in social community activities. This is what makes us different."
In a darkened room, an iPad is brought up to a child's face, allowing her to look at herself. Light, sounds, music and smells are also used for teaching and communication.
"Try teaching a child who can't hear, can't see and can't get out of their wheelchair. It's not easy," Ms Grayevsky adds.
Originally from New York, Rachel Fishheimer is the special education school principal at Aleh Jerusalem. "When we raise the bar, they raise the bar," she says of the children. "If we only care for their physical and medical needs, they would be very sad. But if we challenge them intellectually, all of a sudden we get smiles and activity.
"We want to give them the maximum quality of life and that means giving them the maximum independence."
Manchester-raised Rikki Freulich heads the ward run by nurses. "We have a lot of SOS medicine," she says. "We try very hard not to send our children to hospital - doctors don't like our children. They say to me: 'Give me a child I can cure.' Of course this needs to change." To this end, medical students from the Hebrew University now take tours of the centre.
"Our nurses are different," Ms Freulich adds. "They come from a caring, rather than a curing, point of view. But a lot of nurses won't work here because it's hard."
She holds strong views on accident prevention, arguing that "instead of teaching the mother how to put the baby in a nappy, hospitals should teach the parents CPR. I tell all mothers not to have a babysitter who has not had a CPR course."
Police cars are parked outside and officers stand in the entrance. But this is not about security. They are volunteers, talking to the children and using special equipment to walk them around the forecourt. One officer brings out a boombox and sings to a child. Later on, students from a local seminary help put the children to bed.
I also visit Aleh's Moriah centre in Gedera, which cares for over 100 young people who can walk but not talk. Director Naama Sudkewitz says families on the waiting list will benefit from an imminent expansion, raising capacity to 120.
A woman who moved to Israel from New York confides that after making aliyah three years ago, she struggled to find an organisation that would give her 19-year-old autistic son the care he needed - and her an active involvement in his life. At Aleh, "all the staff's attention is on my child. My son is happier. I go home and feel safe that my son is in good hands."
With a carer in close proximity, Chana, who doctors said would never walk, is using a treadmill in the gym for 10 minutes at a time. Physical therapist Esther Zilber says it is "an accomplishment - and fun and healthy. Some people here are almost 30. We are not going to put them in a playpen. It's important to us that handicapped people get exercise. Physical well-being contributes to general health and prolongs life."
I meet Annette, whose daughter Avia, 23, lives at Aleh's Negev base, in a playground equipped by Rafael, the security group behind the Iron Dome anti-missile defence system. The swings are built to take wheelchairs.
Avia has lung and breathing problems and came to live at the centre at 17. "She laughs so much here," Annette says of Avia, who has cerebral palsy and severe intellectual and developmental disabilities. "They care for her 24 hours a day. They have equipment I don't have at home.They stimulate her senses. In the afternoon she plays with animals. I feel there's a deep love and connection here between the staff and people they care for." And confidence in Aleh's care allowed parents to "live our lives more".
Aleh Negev has been recognised globally as a leading centre for special disabilities education. Delegations of British and Americans have viewed its mini-safari, horse-riding centre and specialist equipment .
During the Israel-Gaza conflict last summer, the centre was hit by three rockets, causing some damage to the building. Residents, who can be unnerved by everyday sounds, were taken to a shelter. The war highlighted the need for a hospital in the south specialising in the care of severe disabilities and trauma.
Indeed, it is a military man who is the public face of the charity. Major-General Doron Almog founded the Aleh Negev village in memory of his son Eran, who was severely autistic. Charming and passionate, he is determined to champion Aleh across the world. On a fundraising visit to the UK in 2005, he was caught in a stand-off with counter-terrorism officers, who sought to enforce an arrest warrant for alleged war crimes over the destruction of homes in Gaza. He escaped arrest by remaining on an El Al plane following a tip-off from the Israeli embassy.
"The residents of Aleh Negev in many ways reflect the Jewish people's history," he suggests over coffee. "Being discriminated against, stereotyped, being different. I think a visit to Aleh Negev gives you proportion on what a meaningful life is.
"These are the purest people. They never did wrong to anyone in our society. They are the most ego-less people in our world. We believe the strength of a society is measured by the weakest part of the chain. We need to have mutual responsibility for each other. The spirit of Israel is investing in our relationship with people."
Mossad agents and former prisoners are among the volunteers and he confides that the reaction of the ex-convicts is "amazing. They say: 'I consciously deceived, stole, killed. I come to Aleh Negev and see people who have a greater punishment than me - their body is a jail. They can't do the smallest thing for themselves.'"
He's ready to take Aleh Negev to the next level with the development of the first rehabilitative wing in the south of the country - he notes that it is a "huge burden" for people to regularly travel long distances to visit their loved ones. General Almog also hopes that in five years there will be a special wing for Bar-Ilan student volunteers to stay in.
British ambassador to Israel Matthew Gould is a friend of the Almogs and a staunch Aleh supporter. He has "seen the passion that he and Didi [his wife] put into making Aleh Negev the centre of care they want it to be. I've seen how he and Didi were affected by their own family's story. And Aleh is important because of the message it sends.
"It's important for people to know that there are organisations like Aleh that give reality to the ideology of Israel's founders. Israel should, on the one hand, be a homeland for the Jewish people. And, on the other hand, it should be a country that treats all citizens equally, regardless of whether they're Bedouin, Jewish, Christian or Arab."
And there are lessons for British healthcare providers in the treatment of the profoundly disabled. "I'd be sorry if the only organisations that could learn were the Jewish ones," Mr Gould says. "The issues are universal. Part of the job of my team in Israel is to make sure there is a flow of ideas."
