The scheme, now in its third summer of operation in eight primary schools in disadvantaged areas of the city, gives all parties the chance to meet in an informal setting before school starts.
The scheme is funded by the community initiative, New Schools , and one long-term aim is that parents will then find it easier to approach their child's teacher with any concerns.
'The whole idea is that the parents attend and take part in activities with the children,' said Jane Prouse, a community education worker for family learning, who runs the project.
'Usually as a parent, you only go into school when you're worried about something or the school is worried. A lot of parents are also worried about how their child will behave in a classroom, and this gives them the chance to see how their child interacts with the teacher.'
This year all 240 children in the social inclusion area due to start Primary One were offered the chance to take part in the project, and there was a 90 per cent attendance rate.
Alongside the more traditional formal introduction to school which parents are given, they are encouraged to take an active role in creative activities with their children.
Puppet-making is just one of a range of activities on offer. Children make a 'writing box' by decorating a shoebox with a pencil case inside, which they can take with them on their first day of school.
They are also given a set of magnetic letters and a board to use at school.
The materials are funded by Edinburgh City Council as part of its commitment to achievement in literacy.
Children and parents also get the chance to meet other key people, such as the nursery nurses attached to the school and a health visitor.
Ms Prouse said the project has been successful in demystifying the first day of school for many pupils. Children already know the name of their teacher and have an idea what to expect. 'Teachers have told us that fewer children are crying at the beginning of term,' said Ms Prouse.
This year the project was also taken into private day nurseries so that children starting at state-run primary schools, whose parents were at work and so not able to get involved at school, could also benefit from the activities.
The sessions take place in the primary school that the child will be attending, and ideally in the actual classroom they will use.
This year the scheme was successful in involving 70% of the children's parents.