@Anthony - You are not using the power and the essence of GridLayout in the code written. As you have manually allotted paddings to the views in order to make them appear in the first screen, which is very much possible with any other layout as well. Like below.
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:orientation="vertical"
android:gravity="center" >
<TextView
android:id="@+id/textView1"
android:layout_width="wrap_content"
android:layout_height="0dp"
android:layout_weight="2"
android:text="Some Text Here"
android:textAppearance="?android:attr/textAppearanceLarge" />
<LinearLayout
android:layout_width="match_parent"
android:layout_height="0dp"
android:layout_weight="1" >
<TextView
android:id="@+id/textView1"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_weight="2"
android:text="16"
android:textAppearance="?android:attr/textAppearanceLarge" />
<TextView
android:id="@+id/textView1"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_weight="2"
android:text="17"
android:textAppearance="?android:attr/textAppearanceLarge" />
<TextView
android:id="@+id/textView1"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_weight="2"
android:text="18"
android:textAppearance="?android:attr/textAppearanceLarge" />
</LinearLayout>
<LinearLayout
android:layout_width="match_parent"
android:layout_height="0dp"
android:layout_weight="1" >
<TextView
android:id="@+id/textView1"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_weight="2"
android:text="Text1"
android:textAppearance="?android:attr/textAppearanceLarge" />
<TextView
android:id="@+id/textView1"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_weight="2"
android:text="Text2"
android:textAppearance="?android:attr/textAppearanceLarge" />
<TextView
android:id="@+id/textView1"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_weight="2"
android:text="Text3"
android:textAppearance="?android:attr/textAppearanceLarge" />
</LinearLayout>
And, GridLayout is about rows and columns. So if you want your Views to be placed such that and to use it to fuller, you can supply the row as well as column position where you view should be placed in which order and its other properties will add up to it. Here is a link.
Try this out and I am sure you will understand it much better. Happy coding. :)