Two-way binding with range and number input in AngularJS

I'm just starting to play around with AngularJS and trying to understand the binding technique. For starters, I tried to make a simple conversion calculator (dozens to pieces, pieces to dozens). That worked well, but when I tried to bind both a range input and a number input to the same model property the number input does not update when the range value is adjusted. I have a jsfiddle showing the behavior:

common javascript for broken and working fiddles:

var myApp = angular.module('myApp', []);

myApp.controller('CalcCtrl', function ($scope) {
    var num = 0.0;
    $scope.qty = new Quantity(12);
    $scope.num = num;
});

function Quantity(numOfPcs) {
    var qty = numOfPcs;
    var dozens = numOfPcs / 12;

    this.__defineGetter__("qty", function () {
        return qty;
    });

    this.__defineSetter__("qty", function (val) {
        qty = val;
        dozens = val / 12;
    });

    this.__defineGetter__("dozens", function () {
        return dozens;
    });

    this.__defineSetter__("dozens", function (val) {
        dozens = val;
        qty = val * 12;
    });
}

BROKEN FIDDLE

html:

<div ng-controller="CalcCtrl">
    <form>
        <label for="pcs">Pieces:</label>
        <input type="number" min="0" ng-model="qty.qty" size="20" id="pcs"
        />
        <input type="range" min="0" max="100" ng-model="qty.qty" />
        <br/>
        <label for="numOfDozens">Dozens</label>
        <input type="number" min="0" ng-model="qty.dozens" size="20"
        id="numOfDozens" />
    </form>
</div>

However, binding two number inputs to the same model property seems to work fine as shown in this fiddle:

WORKING FIDDLE

html:

<div ng-controller="CalcCtrl">
    <form>
        <label for="pcs">Pieces:</label>
        <input type="number" min="0" ng-model="qty.qty" size="20" id="pcs"
        />
        <input type="number" min="0" max="100" ng-model="qty.qty" />
        <br/>
        <label for="numOfDozens">Dozens</label>
        <input type="number" min="0" ng-model="qty.dozens" size="20"
        id="numOfDozens" />
    </form>
</div>

Any ideas how to get a range and number input bound to a single model property in AngularJS? Thanks.