You can use this code for your form

{!! Form::select('numberOfChildren',range(0,10),old('numberOfChildren'),['id'=>'numberOfChildren']) !!}

And Jquery you should change

index = this.selectedIndex;

with

index = $(this).val();

Hi, the form is sent to another page, so when the submit button is pressed the values are stored correctly in the session but the children's ages are set back to default, being 1.

So I need the session values put back into the childrens ages.

I think this code is bestter for you

{!! Form::open(['url'=>'test']) !!}
{!! Form::select('numberOfChildren',range(0,10),null,['id'=>'numberOfChildren'])!!}
<div id="add_select">
    @for($i=0;$i<10;$i++)
        {!! Form::select('age_'.$i,range(1,14),null,['style'=>'display:none;','id'=>'age_'.$i,'class'=>'age_child'])!!}
    @endfor
</div>
{!! Form::submit('Submit')!!}
{!! Form::close()!!}
<script>
    $('#numberOfChildren').change(function(){
        var index = $(this).val();
        for(var u=0; u<index; u++){
            $('#age_'+u).show();
        }
    }).trigger('change');
</script>

I tested. It very ok