diff --git a/narwhals/_arrow/dataframe.py b/narwhals/_arrow/dataframe.py
index 9aab77381..5a03aadcc 100644
--- a/narwhals/_arrow/dataframe.py
+++ b/narwhals/_arrow/dataframe.py
@@ -2,6 +2,7 @@
 
 from typing import TYPE_CHECKING
 from typing import Any
+from typing import Callable
 from typing import Iterable
 from typing import Sequence
 from typing import overload
@@ -195,6 +196,35 @@ def sort(
     def to_pandas(self) -> Any:
         return self._native_dataframe.to_pandas()
 
+    def to_numpy(self) -> Any:
+        import numpy as np
+
+        return np.column_stack([col.to_numpy() for col in self._native_dataframe.columns])
+
+    def to_dict(self, *, as_series: bool) -> Any:
+        df = self._native_dataframe
+
+        names_and_values = zip(df.column_names, df.columns)
+        if as_series:
+            from narwhals._arrow.series import ArrowSeries
+
+            return {
+                name: ArrowSeries(col, name=name, backend_version=self._backend_version)
+                for name, col in names_and_values
+            }
+        else:
+            return {name: col.to_pylist() for name, col in names_and_values}
+
+    def pipe(self, function: Callable[[Any], Self], *args: Any, **kwargs: Any) -> Self:
+        return function(self, *args, **kwargs)
+
+    def with_row_index(self, name: str) -> Self:
+        pa = get_pyarrow()
+        df = self._native_dataframe
+
+        row_indices = pa.array(range(df.num_rows))
+        return self._from_native_dataframe(df.append_column(name, row_indices))
+
     def lazy(self) -> Self:
         return self
 
diff --git a/tests/frame/pipe_test.py b/tests/frame/pipe_test.py
index 6f49966b9..9dd66f10a 100644
--- a/tests/frame/pipe_test.py
+++ b/tests/frame/pipe_test.py
@@ -9,8 +9,8 @@
 }
 
 
-def test_pipe(constructor: Any) -> None:
-    df = nw.from_native(constructor(data))
+def test_pipe(constructor_with_pyarrow: Any) -> None:
+    df = nw.from_native(constructor_with_pyarrow(data))
     columns = df.lazy().collect().columns
     result = df.pipe(lambda _df: _df.select([x for x in columns if len(x) == 2]))
     expected = {"ab": ["foo", "bars"]}
diff --git a/tests/frame/to_dict_test.py b/tests/frame/to_dict_test.py
index b0950c5c9..8fa31c336 100644
--- a/tests/frame/to_dict_test.py
+++ b/tests/frame/to_dict_test.py
@@ -3,16 +3,16 @@
 import narwhals.stable.v1 as nw
 
 
-def test_to_dict(constructor: Any) -> None:
+def test_to_dict(constructor_with_pyarrow: Any) -> None:
     data = {"a": [1, 3, 2], "b": [4, 4, 6], "c": [7.0, 8, 9]}
-    df = nw.from_native(constructor(data), eager_only=True)
+    df = nw.from_native(constructor_with_pyarrow(data), eager_only=True)
     result = df.to_dict(as_series=False)
     assert result == data
 
 
-def test_to_dict_as_series(constructor: Any) -> None:
+def test_to_dict_as_series(constructor_with_pyarrow: Any) -> None:
     data = {"a": [1, 3, 2], "b": [4, 4, 6], "c": [7.0, 8, 9]}
-    df = nw.from_native(constructor(data), eager_only=True)
+    df = nw.from_native(constructor_with_pyarrow(data), eager_only=True)
     result = df.to_dict(as_series=True)
     assert isinstance(result["a"], nw.Series)
     assert isinstance(result["b"], nw.Series)
diff --git a/tests/frame/to_numpy_test.py b/tests/frame/to_numpy_test.py
index 6f516334d..5cfa69bf7 100644
--- a/tests/frame/to_numpy_test.py
+++ b/tests/frame/to_numpy_test.py
@@ -7,9 +7,9 @@
 import narwhals.stable.v1 as nw
 
 
-def test_convert_numpy(constructor: Any) -> None:
+def test_convert_numpy(constructor_with_pyarrow: Any) -> None:
     data = {"a": [1, 3, 2], "b": [4, 4, 6], "z": [7.1, 8, 9]}
-    df_raw = constructor(data)
+    df_raw = constructor_with_pyarrow(data)
     result = nw.from_native(df_raw, eager_only=True).to_numpy()
 
     expected = np.array([[1, 3, 2], [4, 4, 6], [7.1, 8, 9]]).T
diff --git a/tests/frame/with_row_index_test.py b/tests/frame/with_row_index_test.py
index 1b0ad5792..ef54557bd 100644
--- a/tests/frame/with_row_index_test.py
+++ b/tests/frame/with_row_index_test.py
@@ -9,9 +9,9 @@
 }
 
 
-def test_with_row_index(constructor: Any) -> None:
-    result = nw.from_native(constructor(data)).with_row_index()
+def test_with_row_index(constructor_with_pyarrow: Any) -> None:
+    result = nw.from_native(constructor_with_pyarrow(data)).with_row_index()
     expected = {"a": ["foo", "bars"], "ab": ["foo", "bars"], "index": [0, 1]}
     compare_dicts(result, expected)
-    result = nw.from_native(constructor(data)).lazy().with_row_index()
+    result = nw.from_native(constructor_with_pyarrow(data)).lazy().with_row_index()
     compare_dicts(result, expected)
diff --git a/utils/check_backend_completeness.py b/utils/check_backend_completeness.py
index 924115fbb..da8304842 100644
--- a/utils/check_backend_completeness.py
+++ b/utils/check_backend_completeness.py
@@ -22,13 +22,9 @@
     "DataFrame.iter_rows",
     "DataFrame.join",
     "DataFrame.null_count",
-    "DataFrame.pipe",
     "DataFrame.rename",
     "DataFrame.tail",
-    "DataFrame.to_dict",
-    "DataFrame.to_numpy",
     "DataFrame.unique",
-    "DataFrame.with_row_index",
     "DataFrame.write_parquet",
     "Series.drop_nulls",
     "Series.fill_null",