In one class, Year Six boys at a Newcastle primary school are asked to describe the 'girlish' things they like to do, while the girls say what 'boyish' pursuits they enjoy.
Gendered Intelligence's founder Jay Stewart, who is giving the class, asks the pupils if they think "life will be hard at school if you're a boy at school who likes doing 'girlish things'?"
Mr Stewart then asks the class what they think the word 'transgender' means and he follows this by revealing he is a 'trans man'.
He says: "When I was assigned at birth, I was assigned female when I was born. So I am transgendered. So have you got any questions for me?"
One girl asks if his "friends went off" Mr Stewart after he made the change. He replies: "Most of my friends stayed my friends, which is why they're such good friends. But I've also got lots of friends who are also transgendered and actually there's a whole community of transsexual and transgendered people."
At the second school featured in the film, Westerhope Primary, also in Newcastle, Mr Stewart again tells the pupils that he is transgender - despite teachers asking him beforehand not to do so.
Head teacher Jo Warner says that in a conversation with Mr Stewart and the class's teacher, Katie Salkeld, she said: "We want you to look at gender issues, but at the minute we don't feel absolutely comfortable with you actually saying, 'I'm transgender'."
Yet after the lesson, both Ms Warner and Ms Salkeld said they changed their view and believed Mr Stewart telling the children about his transgender status was right.
Gendered Intelligence describes itself as a not-for-profit "community interest company".
Child psychotherapist Dilys Daws warned: "What can get confused is that children who just happen to be unhappy at the moment actually fixing on this being about their gender, when it might be to do with the relationship with a parent."
Margaret Morrissey, of pressure group Parents Outloud, said four and five-year-olds were "far, far too young" to receive the lessons. She added: "We're in danger of frightening children and making them feel they ought to feel like this."
Mr Stewart said: "It's so important to be teaching children in schools that they can be anything that they want regardless of the gender that they have been given at birth.
"Gendered Intelligence delivers age-appropriate workshops and assemblies by working closely with the senior leadership teams of each of the schools we work with. We are proud of this work and feedback is always incredibly positive."
- Mail On Sunday