The Count Me In 123 project, sponsored by Yorkshire Bank, aims to help children develop numeracy skills before they start school.
Participating children aged from one to five are given bags containing picture books, rhymes, counting activities and interactive games they can do at home.
Dr Christine Merrell, acting primary director at the Centre for Evaluation and Monitoring at Durham University, which tracks the educational progress of children, said that the Count Me In 123 materials 'are just the kind of activities that lead to literacy and numeracy development that is important for the start of school'.
Dr Merrell said, 'Research has shown that if children are encouraged to rhyme, count a few objects and understand simple mathematical concepts such as "longest" and "shortest" before they start school, they are more likely to succeed with reading and mathematics in later years.
'We have monitored the progress of children from the start of pre-school to age seven and we have found that those children who have good vocabulary acquisition for their age, are able to count a small number of objects and solve simple number problems and can hear and repeat words accurately, are likely to make good progress to the age of seven.
'For example, the children are shown a picture of a plate with three biscuits on it and asked how many would be left if one was taken away.'
Leeds is one of the local authorities running the programme.
Lorraine Lee, a Leeds children's development librarian, said that she has found that the project 'brings families together, as it is an activity they can do together'.
She said, 'We lend out the bags to parents, childminders, nurseries and children's centres. They are very popular. There is the anticipation of what will be in the bag and then the fun of reading the story and doing the games.'