diff --git a/pandas/core/indexes/frozen.py b/pandas/core/indexes/frozen.py
index 3c6b922178abf..8bb65b0e8a7de 100644
--- a/pandas/core/indexes/frozen.py
+++ b/pandas/core/indexes/frozen.py
@@ -10,6 +10,7 @@
 
 import numpy as np
 from pandas.core.base import PandasObject
+from pandas.util._decorators import deprecate_kwarg
 from pandas.core.dtypes.cast import coerce_indexer_dtype
 from pandas.io.formats.printing import pprint_thing
 
@@ -117,10 +118,9 @@ def __unicode__(self):
                              quote_strings=True)
         return "%s(%s, dtype='%s')" % (type(self).__name__, prepr, self.dtype)
 
-    def searchsorted(self, v, side='left', sorter=None):
+    def searchsorted(self, value, side="left", sorter=None):
         """
-        Find indices where elements of v should be inserted
-        in a to maintain order.
+        Find indices to insert `value` so as to maintain order.
 
         For full documentation, see `numpy.searchsorted`
 
@@ -129,17 +129,20 @@ def searchsorted(self, v, side='left', sorter=None):
         numpy.searchsorted : equivalent function
         """
 
-        # we are much more performant if the searched
-        # indexer is the same type as the array
-        # this doesn't matter for int64, but DOES
+        # We are much more performant if the searched
+        # indexer is the same type as the array.
+        #
+        # This doesn't matter for int64, but DOES
         # matter for smaller int dtypes
-        # https://github.com/numpy/numpy/issues/5370
+        #
+        # xref: https://github.com/numpy/numpy/issues/5370
         try:
-            v = self.dtype.type(v)
+            value = self.dtype.type(value)
         except:
             pass
+
         return super(FrozenNDArray, self).searchsorted(
-            v, side=side, sorter=sorter)
+            value, side=side, sorter=sorter)
 
 
 def _ensure_frozen(array_like, categories, copy=False):
diff --git a/pandas/tests/indexes/test_frozen.py b/pandas/tests/indexes/test_frozen.py
index ca9841112b1d5..1fd16042098ea 100644
--- a/pandas/tests/indexes/test_frozen.py
+++ b/pandas/tests/indexes/test_frozen.py
@@ -69,3 +69,7 @@ def test_values(self):
         assert isinstance(self.container, FrozenNDArray)
         tm.assert_numpy_array_equal(self.container.values(), original)
         assert vals[0] == n
+
+    def test_searchsorted(self):
+        expected = 2
+        assert self.container.searchsorted(7) == expected