It becomes an invalid expression with the usage of interpolation with ng-model expression. You need to provide a property name there. Instead you can use an object and use bracket notation.
i.e in your controller:
$scope.interpretation = {};
and in your view use it as:
ng-model="interpretation[$index + 1]"
Demo
angular.module('app', []).controller('ctrl', function($scope) { $scope.interpretation = {}; $scope.actions = {};});
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.3.8/angular.min.js"></script><div ng-app="app" ng-controller="ctrl"> {{interpretation}} {{actions}} <div class="individualwrapper" ng-repeat="n in [1,2,3,4]"> <div class="iconimage"> </div> <div class="icontext"> <p>Imagine that you are in a health care facility.</p> <p>Exactly what do you think this symbol means?</p> <textarea type="text" ng-attr-name="interpretation{{$index + 1}}" ng-model="interpretation[$index+1]" ng-required="true"></textarea> <p>What action you would take in response to this symbol?</p> <textarea type="text" name="action{{$index + 1}}" ng-model="actions[$index+1]" ng-required="true"></textarea> </div> </div></div>