diff --git a/activesupport/CHANGELOG.md b/activesupport/CHANGELOG.md
index a384fc3bd2ec5d0f5dd82f497a21bac6947c0ffe..91818c311295f8851ad4686c2a791f04485beffd 100644
--- a/activesupport/CHANGELOG.md
+++ b/activesupport/CHANGELOG.md
@@ -1,3 +1,14 @@
+*   Allow Range#=== and Range#cover? on Range
+
+    `Range#cover?` can now accept a range argument like `Range#include?` and
+    `Range#===`. `Range#===` works correctly on Ruby 2.6. `Range#include?` is moved
+    into a new file, with these two methods.
+
+    *Requiring active_support/core_ext/range/include_range is now deprecated.*
+    *Use `require "active_support/core_ext/range/compare_range"` instead.*
+
+    *utilum*
+
 *   Add `index_with` to Enumerable.
 
     Allows creating a hash from an enumerable with the value from a passed block
diff --git a/activesupport/lib/active_support/core_ext/range.rb b/activesupport/lib/active_support/core_ext/range.rb
index 4074e91d17d7566e41fad564db48b1cc81e36f29..78814fd18961c8e8086ec29325e761787b3f7441 100644
--- a/activesupport/lib/active_support/core_ext/range.rb
+++ b/activesupport/lib/active_support/core_ext/range.rb
@@ -1,7 +1,7 @@
 # frozen_string_literal: true
 
 require "active_support/core_ext/range/conversions"
-require "active_support/core_ext/range/include_range"
+require "active_support/core_ext/range/compare_range"
 require "active_support/core_ext/range/include_time_with_zone"
 require "active_support/core_ext/range/overlaps"
 require "active_support/core_ext/range/each"
diff --git a/activesupport/lib/active_support/core_ext/range/compare_range.rb b/activesupport/lib/active_support/core_ext/range/compare_range.rb
new file mode 100644
index 0000000000000000000000000000000000000000..704041f6de88efa29d21012e381fa82c4fed3b4c
--- /dev/null
+++ b/activesupport/lib/active_support/core_ext/range/compare_range.rb
@@ -0,0 +1,61 @@
+# frozen_string_literal: true
+
+module ActiveSupport
+  module CompareWithRange #:nodoc:
+    # Extends the default Range#=== to support range comparisons.
+    #  (1..5) === (1..5) # => true
+    #  (1..5) === (2..3) # => true
+    #  (1..5) === (2..6) # => false
+    #
+    # The native Range#=== behavior is untouched.
+    #  ('a'..'f') === ('c') # => true
+    #  (5..9) === (11) # => false
+    def ===(value)
+      if value.is_a?(::Range)
+        # 1...10 includes 1..9 but it does not include 1..10.
+        operator = exclude_end? && !value.exclude_end? ? :< : :<=
+        super(value.first) && value.last.send(operator, last)
+      else
+        super
+      end
+    end
+
+    # Extends the default Range#include? to support range comparisons.
+    #  (1..5).include?(1..5) # => true
+    #  (1..5).include?(2..3) # => true
+    #  (1..5).include?(2..6) # => false
+    #
+    # The native Range#include? behavior is untouched.
+    #  ('a'..'f').include?('c') # => true
+    #  (5..9).include?(11) # => false
+    def include?(value)
+      if value.is_a?(::Range)
+        # 1...10 includes 1..9 but it does not include 1..10.
+        operator = exclude_end? && !value.exclude_end? ? :< : :<=
+        super(value.first) && value.last.send(operator, last)
+      else
+        super
+      end
+    end
+
+    # Extends the default Range#cover? to support range comparisons.
+    #  (1..5).cover?(1..5) # => true
+    #  (1..5).cover?(2..3) # => true
+    #  (1..5).cover?(2..6) # => false
+    #
+    # The native Range#cover? behavior is untouched.
+    #  ('a'..'f').cover?('c') # => true
+    #  (5..9).cover?(11) # => false
+    def cover?(value)
+      if value.is_a?(::Range)
+        # 1...10 covers 1..9 but it does not cover 1..10.
+        operator = exclude_end? && !value.exclude_end? ? :< : :<=
+        super(value.first) && value.last.send(operator, last)
+      else
+        super
+      end
+    end
+  end
+end
+
+Range.prepend(ActiveSupport::CompareWithRange)
diff --git a/activesupport/lib/active_support/core_ext/range/include_range.rb b/activesupport/lib/active_support/core_ext/range/include_range.rb
index 7ba1011921ba36e70d60d33e211b9e2f58957b60..2da2c587a31f19fb775b44ebd1b5ab8eb522c6cc 100644
--- a/activesupport/lib/active_support/core_ext/range/include_range.rb
+++ b/activesupport/lib/active_support/core_ext/range/include_range.rb
@@ -1,25 +1,9 @@
 # frozen_string_literal: true
 
-module ActiveSupport
-  module IncludeWithRange #:nodoc:
-    # Extends the default Range#include? to support range comparisons.
-    #  (1..5).include?(1..5) # => true
-    #  (1..5).include?(2..3) # => true
-    #  (1..5).include?(2..6) # => false
-    #
-    # The native Range#include? behavior is untouched.
-    #  ('a'..'f').include?('c') # => true
-    #  (5..9).include?(11) # => false
-    def include?(value)
-      if value.is_a?(::Range)
-        # 1...10 includes 1..9 but it does not include 1..10.
-        operator = exclude_end? && !value.exclude_end? ? :< : :<=
-        super(value.first) && value.last.send(operator, last)
-      else
-        super
-      end
-    end
-  end
-end
+require "active_support/deprecation"
 
-Range.prepend(ActiveSupport::IncludeWithRange)
+ActiveSupport::Deprecation.warn "You have required `active_support/core_ext/range/include_range`. " \
+"This file will be removed in Rails 6.1. You should require `active_support/core_ext/range/compare_range` " \
+  "instead."
+
+require "active_support/core_ext/range/compare_range"
diff --git a/guides/source/active_support_core_extensions.md b/guides/source/active_support_core_extensions.md
index cde217e1e4397cec7d7e50ae7b266c2a65e4afe2..057651e0cf297d1003b7a77b5911e8c4e6e846b3 100644
--- a/guides/source/active_support_core_extensions.md
+++ b/guides/source/active_support_core_extensions.md
@@ -2889,9 +2889,9 @@ As the example depicts, the `:db` format generates a `BETWEEN` SQL clause. That
 
 NOTE: Defined in `active_support/core_ext/range/conversions.rb`.
 
-### `include?`
+### `===`, `include?`, and `cover?`
 
-The methods `Range#include?` and `Range#===` say whether some value falls between the ends of a given instance:
+The methods `Range#===`, `Range#include?`, and `Range#cover?` say whether some value falls between the ends of a given instance:
 
 ```ruby
 (2..3).include?(Math::E) # => true
@@ -2900,18 +2900,23 @@ The methods `Range#include?` and `Range#===` say whether some value falls betwee
 Active Support extends these methods so that the argument may be another range in turn. In that case we test whether the ends of the argument range belong to the receiver themselves:
 
 ```ruby
+(1..10) === (3..7)  # => true
+(1..10) === (0..7)  # => false
+(1..10) === (3..11) # => false
+(1...9) === (3..9)  # => false
+
 (1..10).include?(3..7)  # => true
 (1..10).include?(0..7)  # => false
 (1..10).include?(3..11) # => false
 (1...9).include?(3..9)  # => false
 
-(1..10) === (3..7)  # => true
-(1..10) === (0..7)  # => false
-(1..10) === (3..11) # => false
-(1...9) === (3..9)  # => false
+(1..10).cover?(3..7)  # => true
+(1..10).cover?(0..7)  # => false
+(1..10).cover?(3..11) # => false
+(1...9).cover?(3..9)  # => false
 ```
 
-NOTE: Defined in `active_support/core_ext/range/include_range.rb`.
+NOTE: Defined in `active_support/core_ext/range/compare_range.rb`.
 
 ### `overlaps?`