How to create a drop down view like Google Calendar using Toolbar?

May you want to take a look to CollapsingToolbarLayout

<android.support.design.widget.CollapsingToolbarLayout
            android:id="@+id/collapsingToolbarLayout"
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            app:layout_scrollFlags="scroll|exitUntilCollapsed"
            app:expandedTitleMarginStart="64dp"
            app:contentScrim="?attr/colorPrimary">
            <CalendarView
                android:layout_width="match_parent"
                android:layout_height="256dp"></CalendarView>

            <android.support.v7.widget.Toolbar
                android:id="@+id/toolbar"
                android:layout_width="match_parent"
                android:layout_height="?attr/actionBarSize"
                android:minHeight="?attr/actionBarSize"
                app:theme="@style/ThemeOverlay.AppCompat.Dark.ActionBar"
                app:popupTheme="@style/ThemeOverlay.AppCompat.Light"
                app:layout_collapseMode="pin"/>

        </android.support.design.widget.CollapsingToolbarLayout>

I recommend you to follow this awesome tutorial to implement this and other interesting things about Design Library. Hope this helps.

I was also trying to create something similar to the Google Calendar app. I've come with this implementation:

I use the CompactCalendarView library for the month widget. And CollapsingToolbarLayout for the drop down.

You can view the source of this implementation at GitHub: https://github.com/GerritHoekstra/CompactCalendarViewToolbar

The main layout can be found here.

I hope this helps you further.