diff --git a/doc/gallery_src/checkerboard.py b/doc/gallery_src/checkerboard.py
index c17a832..277e0ac 100644
--- a/doc/gallery_src/checkerboard.py
+++ b/doc/gallery_src/checkerboard.py
@@ -9,8 +9,8 @@ Checkerboard function
 =====================
 
 The :class:`verde.synthetic.CheckerBoard` class generates synthetic data in a
-checkerboard pattern. It has the same data generation methods that most
-gridders have: predict, grid, scatter, and profile.
+checkerboard pattern. It has different data generation methods, some of which
+are shared with most other gridders: predict, grid, profile, and scatter.
 """
 import matplotlib.pyplot as plt
 
diff --git a/doc/gallery_src/cubic_gridder.py b/doc/gallery_src/cubic_gridder.py
index cec5d2d..7b388c5 100644
--- a/doc/gallery_src/cubic_gridder.py
+++ b/doc/gallery_src/cubic_gridder.py
@@ -87,5 +87,5 @@ plt.colorbar(pc).set_label("meters")
 ax.plot(*coordinates, ".k", markersize=0.1, transform=crs)
 # Use an utility function to setup the tick labels and the land feature
 vd.datasets.setup_baja_bathymetry_map(ax)
-ax.set_title("Linear gridding of bathymetry")
+ax.set_title("Cubic gridding of bathymetry")
 plt.show()
diff --git a/verde/base/base_classes.py b/verde/base/base_classes.py
index fa74970..30414da 100644
--- a/verde/base/base_classes.py
+++ b/verde/base/base_classes.py
@@ -531,6 +531,12 @@ class BaseGridder(BaseEstimator):
         dimensions and the data field(s) in the output
         :class:`pandas.DataFrame`. Default names are provided.
 
+        .. warning::
+
+            The ``scatter`` method is deprecated and will be removed in Verde
+            2.0.0. Use :func:`verde.scatter_points` and the ``predict`` method
+            instead.
+
         Parameters
         ----------
         region : list = [W, E, S, N]
@@ -570,6 +576,12 @@ class BaseGridder(BaseEstimator):
             The interpolated values on a random set of points.
 
         """
+        warnings.warn(
+            "The 'scatter' method is deprecated and will be removed in Verde "
+            "2.0.0. Use 'verde.scatter_points' and the 'predict' method "
+            "instead.",
+            FutureWarning,
+        )
         dims = self._get_dims(dims)
         region = get_instance_region(self, region)
         coordinates = scatter_points(region, size, random_state=random_state, **kwargs)
diff --git a/verde/scipygridder.py b/verde/scipygridder.py
index 4295e08..88eb3b4 100644
--- a/verde/scipygridder.py
+++ b/verde/scipygridder.py
@@ -124,7 +124,7 @@ class Linear(_BaseScipyGridder):
     rescale : bool
         If ``True``, rescale the data coordinates to [0, 1] range before
         interpolation. Useful when coordinates vary greatly in scale. Default
-        is ``True``.
+        is ``False``.
 
     Attributes
     ----------
@@ -137,7 +137,7 @@ class Linear(_BaseScipyGridder):
 
     """
 
-    def __init__(self, rescale=True):
+    def __init__(self, rescale=False):
         super().__init__()
         self.rescale = rescale
 
@@ -161,7 +161,7 @@ class Cubic(_BaseScipyGridder):
     rescale : bool
         If ``True``, rescale the data coordinates to [0, 1] range before
         interpolation. Useful when coordinates vary greatly in scale. Default
-        is ``True``.
+        is ``False``.
 
     Attributes
     ----------
@@ -174,7 +174,7 @@ class Cubic(_BaseScipyGridder):
 
     """
 
-    def __init__(self, rescale=True):
+    def __init__(self, rescale=False):
         super().__init__()
         self.rescale = rescale
 
diff --git a/verde/synthetic.py b/verde/synthetic.py
index 762e996..3303c06 100644
--- a/verde/synthetic.py
+++ b/verde/synthetic.py
@@ -5,9 +5,12 @@
 # This code is part of the Fatiando a Terra project (https://www.fatiando.org)
 #
 import numpy as np
+import pandas as pd
 
 from .base import BaseGridder
-from .coordinates import check_region
+from .base.base_classes import get_instance_region, project_coordinates
+from .base.utils import check_data
+from .coordinates import check_region, scatter_points
 
 
 class CheckerBoard(BaseGridder):
@@ -113,3 +116,82 @@ class CheckerBoard(BaseGridder):
             * np.cos((2 * np.pi / self.w_north_) * northing)
         )
         return data
+
+    def scatter(
+        self,
+        region=None,
+        size=300,
+        random_state=0,
+        dims=None,
+        data_names=None,
+        projection=None,
+        **kwargs,
+    ):
+        """
+        Generate values on a random scatter of points.
+
+        Point coordinates are generated by :func:`verde.scatter_points`. Other
+        arguments for this function can be passed as extra keyword arguments
+        (``kwargs``) to this method.
+
+        By default, the region specified when creating the class instance will
+        be used if ``region=None``.
+
+        Use the *dims* and *data_names* arguments to set custom names for the
+        dimensions and the data field(s) in the output
+        :class:`pandas.DataFrame`. Default names are provided.
+
+        Parameters
+        ----------
+        region : list = [W, E, S, N]
+            The west, east, south, and north boundaries of a given region.
+        size : int
+            The number of points to generate.
+        random_state : numpy.random.RandomState or an int seed
+            A random number generator used to define the state of the random
+            permutations. Use a fixed seed to make sure computations are
+            reproducible. Use ``None`` to choose a seed automatically
+            (resulting in different numbers with each run).
+        dims : list or None
+            The names of the northing and easting data dimensions,
+            respectively, in the output dataframe. Default is determined from
+            the ``dims`` attribute of the class. Must be defined in the
+            following order: northing dimension, easting dimension.
+            **NOTE: This is an exception to the "easting" then
+            "northing" pattern but is required for compatibility with xarray.**
+        data_names : str, list or None
+            The name(s) of the data variables in the output dataframe. Defaults
+            to ``'scalars'`` for scalar data,
+            ``['east_component', 'north_component']`` for 2D vector data, and
+            ``['east_component', 'north_component', 'vertical_component']`` for
+            3D vector data.
+        projection : callable or None
+            If not None, then should be a callable object
+            ``projection(easting, northing) -> (proj_easting, proj_northing)``
+            that takes in easting and northing coordinate arrays and returns
+            projected northing and easting coordinate arrays. This function
+            will be used to project the generated scatter coordinates before
+            passing them into ``predict``. For example, you can use this to
+            generate a geographic scatter from a Cartesian gridder.
+
+        Returns
+        -------
+        table : pandas.DataFrame
+            The interpolated values on a random set of points.
+
+        """
+        dims = self._get_dims(dims)
+        region = get_instance_region(self, region)
+        coordinates = scatter_points(region, size, random_state=random_state, **kwargs)
+        if projection is None:
+            data = check_data(self.predict(coordinates))
+        else:
+            data = check_data(
+                self.predict(project_coordinates(coordinates, projection))
+            )
+        data_names = self._get_data_names(data, data_names)
+        columns = [(dims[0], coordinates[1]), (dims[1], coordinates[0])]
+        extra_coords_names = self._get_extra_coords_names(coordinates)
+        columns.extend(zip(extra_coords_names, coordinates[2:]))
+        columns.extend(zip(data_names, data))
+        return pd.DataFrame(dict(columns), columns=[c[0] for c in columns])

diff --git a/verde/tests/test_base.py b/verde/tests/test_base.py
index 45fa26e..0f55ca3 100644
--- a/verde/tests/test_base.py
+++ b/verde/tests/test_base.py
@@ -150,7 +150,8 @@ def test_basegridder():
     # Grid on profile
     prof = grd.profile((0, -10), (10, -10), 30)
     # Grid on scatter
-    scat = grd.scatter(region=region, size=1000, random_state=0)
+    with pytest.warns(FutureWarning):
+        scat = grd.scatter(region=region, size=1000, random_state=0)
 
     for grid in grids:
         npt.assert_allclose(grid.scalars.values, data_true)
diff --git a/verde/tests/test_synthetic.py b/verde/tests/test_synthetic.py
new file mode 100644
index 0000000..5f4bd1f
--- /dev/null
+++ b/verde/tests/test_synthetic.py
@@ -0,0 +1,33 @@
+# Copyright (c) 2017 The Verde Developers.
+# Distributed under the terms of the BSD 3-Clause License.
+# SPDX-License-Identifier: BSD-3-Clause
+#
+# This code is part of the Fatiando a Terra project (https://www.fatiando.org)
+#
+"""
+Test the synthetic data generation functions and classes.
+"""
+import numpy.testing as npt
+
+from ..synthetic import CheckerBoard
+
+
+def test_checkerboard_scatter_projection():
+    "Test generating scattered points when passing in a projection"
+
+    # Lets say the projection is doubling the coordinates
+    def proj(lon, lat, inverse=False):
+        "Project from the new coordinates to the original"
+        if inverse:
+            return (lon / 2, lat / 2)
+        return (lon * 2, lat * 2)
+
+    region = (0, 10, -10, -5)
+    region_proj = (0, 5, -5, -2.5)
+    checker = CheckerBoard(region=region)
+    checker_proj = CheckerBoard(region=region_proj)
+    scatter = checker.scatter(region, 1000, random_state=0, projection=proj)
+    scatter_proj = checker_proj.scatter(region, 1000, random_state=0)
+    npt.assert_allclose(scatter.scalars, scatter_proj.scalars)
+    npt.assert_allclose(scatter.easting, scatter_proj.easting)
+    npt.assert_allclose(scatter.northing, scatter_proj.northing)

Deprecate BaseGridder.scatter
**Description of the desired feature**

The `BaseGridder.scatter` enables every Verde gridder class to predict values on a random set of scattered points making use of the `verde.scatter_points()` function. This method doesn't have too many use cases, and even if we want to predict on a set of scattered points, we can do so by combining `verde.scatter_points()` and the `BaseGridder.predict` method, while building the resulting `pandas.DataFrame` can be done manually without too much effort.

Taking this into account, I think it would be better to deprecate it, so we can make maintenance, testing and inheritance much easier. For ensuring backward compatibility, we should deprecate it after Verde v2.0.0 and add a DeprecationWarning meanwhile.



**Are you willing to help implement and maintain this feature?** Yes, but I would leave it to anyone interested in tackling this down.

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verde/tests/test_base.py::test_basegridder
verde/tests/test_base.py::test_check_coordinates verde/tests/test_base.py::test_get_dims verde/tests/test_base.py::test_get_data_names verde/tests/test_base.py::test_get_data_names_fails verde/tests/test_base.py::test_get_instance_region verde/tests/test_base.py::test_basegridder_data_names verde/tests/test_base.py::test_basegridder_projection verde/tests/test_base.py::test_basegridder_extra_coords verde/tests/test_base.py::test_basegridder_projection_multiple_coordinates verde/tests/test_base.py::test_basegridder_grid_invalid_arguments verde/tests/test_base.py::test_check_fit_input verde/tests/test_base.py::test_check_fit_input_fails_coordinates verde/tests/test_base.py::test_check_fit_input_fails_weights verde/tests/test_base.py::test_baseblockedcrossvalidator_n_splits verde/tests/test_base.py::test_baseblockedcrossvalidator_fails_spacing_shape verde/tests/test_base.py::test_baseblockedcrossvalidator_fails_data_shape verde/tests/test_base.py::test_least_squares_copy_jacobian verde/tests/test_synthetic.py::test_checkerboard_scatter_projection