diff --git a/src/dask_awkward/layers/layers.py b/src/dask_awkward/layers/layers.py
index 83e3058f..909dff55 100644
--- a/src/dask_awkward/layers/layers.py
+++ b/src/dask_awkward/layers/layers.py
@@ -261,12 +261,13 @@ def mock(self) -> MaterializedLayer:
             return self
         name = next(iter(mapping))[0]
 
+        npln = len(self.previous_layer_names)
         # one previous layer name
         #
         # this case is used for mocking repartition or slicing where
         # we maybe have multiple partitions that need to be included
         # in a task.
-        if len(self.previous_layer_names) == 1:
+        if npln == 1:
             prev_name: str = self.previous_layer_names[0]
             if (name, 0) in mapping:
                 task = mapping[(name, 0)]
@@ -284,6 +285,12 @@ def mock(self) -> MaterializedLayer:
                 return MaterializedLayer({(name, 0): task})
             return self
 
+        # zero previous layers; this is likely a known scalar.
+        #
+        # we just use the existing mapping
+        elif npln == 0:
+            return MaterializedLayer({(name, 0): mapping[(name, 0)]})
+
         # more than one previous_layer_names
         #
         # this case is needed for dak.concatenate on axis=0; we need
diff --git a/src/dask_awkward/lib/core.py b/src/dask_awkward/lib/core.py
index 51b9e66d..26c5843a 100644
--- a/src/dask_awkward/lib/core.py
+++ b/src/dask_awkward/lib/core.py
@@ -1562,7 +1562,7 @@ def partitionwise_layer(
 
     """
     pairs: list[Any] = []
-    numblocks: dict[Any, int | tuple[int, ...]] = {}
+    numblocks: dict[str, tuple[int, ...]] = {}
     for arg in args:
         if isinstance(arg, Array):
             pairs.extend([arg.name, "i"])
@@ -1575,6 +1575,9 @@ def partitionwise_layer(
         elif is_arraylike(arg) and is_dask_collection(arg) and arg.ndim == 1:
             pairs.extend([arg.name, "i"])
             numblocks[arg.name] = arg.numblocks
+        elif isinstance(arg, Scalar):
+            pairs.extend([arg.name, "i"])
+            numblocks[arg.name] = (1,)
         elif is_dask_collection(arg):
             raise DaskAwkwardNotImplemented(
                 "Use of Array with other Dask collections is currently unsupported."
diff --git a/tests/test_core.py b/tests/test_core.py
index f77cdb78..49a8dd25 100644
--- a/tests/test_core.py
+++ b/tests/test_core.py
@@ -240,6 +240,27 @@ def test_scalar_unary_ops(op: Callable, daa: Array, caa: ak.Array) -> None:
     assert_eq(op(-a1), op(-a2))
 
 
+@pytest.mark.parametrize("op", [operator.add, operator.sub, operator.pow])
+def test_array_broadcast_scalar(op: Callable, daa: Array, caa: Array) -> None:
+    s1 = new_known_scalar(3)
+    s2 = 3
+    r1 = op(daa.points.x, s1)
+    r2 = op(caa.points.x, s2)
+    assert_eq(r1, r2)
+
+    s3 = dak.min(daa.points.x, axis=None)
+    s4 = ak.min(caa.points.x, axis=None)
+    r3 = op(daa.points.y, s3)
+    r4 = op(caa.points.y, s4)
+    assert_eq(r3, r4)
+
+    s5 = dak.max(daa.points.y, axis=None)
+    s6 = ak.max(caa.points.y, axis=None)
+    r5 = op(daa.points.x, s5)
+    r6 = op(caa.points.x, s6)
+    assert_eq(r5, r6)
+
+
 @pytest.mark.parametrize(
     "where",
     [