I tried mine and it did work !!!
N.B. you may need the cells formatted as 'Date' cells
Your formula looks like it will not work as in the first IF condition there is no 'Value if false' condition
- I would never recommend hardcoding dates into a formula but rather have them in another cell and reference them there
I am guessing that you want to use this year in and year out, hence the dates changing, so pick 2 cells that are going to contain your upper and lower dates to compare against and stick them in the 2 cells (right mouse click on these 2 cells, select format cells and make sure they are shown as 'Date')
Then presumably against each child there is a cell which has a date (which you want to compare against the upper/lower dates) and then next to that there is a empty cell where you want your formula to answer Y or N
In this empty cell use the formula I first posted
=IF(D5<I10,"N",IF(D5>J10,"N","Y"))
To make it easier ....
=IF(Each childs date cell<lower date range cell,"N",IF(Each childs date cell>upper date range cell,"N","Y"))
This is basically an IF condition within an IF condition
All you will ever have to do is for each school term change the 2 cells with the upper and lower date ranges i.e. for the start/end of a school term
If you still cant get it to work then I am guessing you are doing something wrong as it works fine for me