Show how to makee data computed and stored in the main app class available to a screen.

first_screen.kv

@@ -6,6 +6,9 @@
         Button:
             text: 'This button prints a number.'
             on_press: root.print_number()  # In a custom widget's Kv, `root` refers to the custom widget.
+        Button:
+            text: 'This button rolls a new number.'
+            on_press: app.reroll()
         Button:
             text: 'Change…'
             on_press: app.open_second_screen()  # But `app` still refers to the application object.

main.py

+from random import randrange
+
 from kivy.app import App
-from kivy.properties import BooleanProperty, StringProperty
+from kivy.properties import BooleanProperty, NumericProperty, StringProperty
 
 # The following lines ensure that FirstScreen and SecondScreen are available for when the Kv code is loaded.
 
@@ -16,6 +18,8 @@ class TwoScreenApp(App):
     advancing = BooleanProperty(True)
     current_screen_name = StringProperty()  # We must wait to select a screen until the app starts.
 
+    roll = NumericProperty(1)
+
     def open_first_screen(self):
         self.advancing = True
         self.current_screen_name = 'first'
@@ -24,6 +28,12 @@ class TwoScreenApp(App):
         self.advancing = False
         self.current_screen_name = 'second'
 
+    def reroll(self):
+        new_roll = randrange(1, 6)
+        if new_roll >= self.roll:
+            new_roll +=1
+        self.roll = new_roll
+
     def on_start(self):
         self.open_first_screen()  # Once the app starts, we can select the starting screen.
 

second_screen.kv

@@ -5,6 +5,9 @@
             text: 'This is the second screen.'
         Label:
             text: root.message  # In a custom widget's Kv, `root` refers to the custom widget.
+        Button:
+            text: 'This button prints the roll from the first screen.'
+            on_press: root.print_roll()
         Button:
             text: 'Change…'
             on_press: app.open_first_screen()  # But `app` still refers to the application object.

second_screen.py

 from kivy.lang import Builder
 from kivy.uix.screenmanager import Screen
-from kivy.properties import StringProperty
+from kivy.properties import NumericProperty, StringProperty
 
 
 Builder.load_file('second_screen.kv')  # Because this is not the main app, we must load the Kv explicitly.
@@ -8,3 +8,7 @@ Builder.load_file('second_screen.kv')  # Because this is not the main app, we mu
 
 class SecondScreen(Screen):
     message = StringProperty('Hello, World!')  # This property is changed by twoscreen.kv.
+    roll = NumericProperty()
+
+    def print_roll(self):
+        print(f'The latest roll was a {self.roll}.')

twoscreen.kv

@@ -11,3 +11,4 @@ ScreenManager:
     SecondScreen:
         name: 'second'
         message: 'This is a message!'  # The app sends information to the custom widgets by setting their properties.
+        roll: app.roll