Laravel 4 - update data pivot table - database

Question

I have an 'Edit page' with a form, where I want to update some data.
My Models:
Actividad.php:
public function materials()
{
return $this->belongsToMany('Material', 'actividad_material')->withTimestamps();
}
And Material.php:
public function actividads()
{
return $this->belongsToMany('Actividad', 'actividad_material')->withTimestamps();
}
My code (Controller):
public function update($id)
{
$input = array_except(Input::all(), '_method');
$v = Validator::make($input, Actividad::$rules);
// return 'Hala';
if($v->passes())
{
$actividad = Actividad::find($id);
$material_id = Input::get('material_id');
$actividad->materials()->sync($material_id);
Actividad::find($id)->update($input);
// return 'hola';
return Redirect::route('actividads.index');
}
return Redirect::back()->withErrors($v);
}
The application gives me an error:
SQLSTATE[42S22]: Column not found: 1054 Unknown column 'material_id' in 'field list' (SQL: update actividads set updated_at = 2014-07-20 16:20:03, material_id = 1 where id = 16)
I suppose it is because it's looking for a column in my 'actividads' that doesn't already exist! Maybe I have to change $input = array_except(Input::all(), '_method');... I think I'm telling with that, that every inputs in the form are in my 'Actividad', and this is not true. I need to update my pivot table with 'material_id'.
Thank you very much in advance!