diff --git a/package.json b/package.json
index 73e79caf3ab9..0888e95ddbe3 100644
--- a/package.json
+++ b/package.json
@@ -215,7 +215,7 @@
     "rollup-plugin-commonjs": "^10.1.0",
     "rollup-plugin-node-resolve": "^5.2.0",
     "rollup-plugin-sourcemaps": "^0.6.3",
-    "sass": "^1.34.1",
+    "sass": "^1.38.0",
     "selenium-webdriver": "^3.6.0",
     "semver": "^7.3.4",
     "send": "^0.17.1",
diff --git a/src/material-experimental/mdc-card/card.scss b/src/material-experimental/mdc-card/card.scss
index c82d69bd6ead..a019d020fdd8 100644
--- a/src/material-experimental/mdc-card/card.scss
+++ b/src/material-experimental/mdc-card/card.scss
@@ -1,5 +1,5 @@
+@use 'sass:math';
 @use '@material/card' as mdc-card;
-@use '../../material/core/style/private';
 @use '../mdc-helpers/mdc-helpers';
 
 // TODO(jelbourn): move header and title-group styles to their own files.
@@ -44,7 +44,7 @@ $mat-card-default-padding: 16px !default;
   // When a subtitle is inside of a header, we want to move it up slightly to reduce the space with
   // the title, and add a margin bottom to create space underneath the header.
   .mat-mdc-card-subtitle {
-    margin-top: -(private.private-div($mat-card-default-padding, 2));
+    margin-top: -(math.div($mat-card-default-padding, 2));
     margin-bottom: $mat-card-default-padding;
   }
 }
diff --git a/src/material-experimental/mdc-form-field/_form-field-density.scss b/src/material-experimental/mdc-form-field/_form-field-density.scss
index 6fa708414c1e..6fba9ed1dd50 100644
--- a/src/material-experimental/mdc-form-field/_form-field-density.scss
+++ b/src/material-experimental/mdc-form-field/_form-field-density.scss
@@ -1,8 +1,8 @@
+@use 'sass:map';
+@use 'sass:math';
 @use '@material/density' as mdc-density;
 @use '@material/textfield' as mdc-textfield;
-@use 'sass:map';
 @use '../../material/core/theming/theming';
-@use '../../material/core/style/private';
 @use 'form-field-sizing';
 
 // Mixin that sets the vertical spacing for the infix container of filled form fields.
@@ -55,7 +55,7 @@
   // cannot update the spacing to explicit numbers based on the density scale. Instead, we
   // determine the height reduction and equally subtract it from the default `top` and `bottom`
   // padding that is provided by the Material Design specification.
-  $vertical-deduction: private.private-div(mdc-textfield.$height - $height, 2);
+  $vertical-deduction: math.div(mdc-textfield.$height - $height, 2);
   // Map that describes the padding for form-fields with label.
   $with-label-padding: (
     top: form-field-sizing.$mat-form-field-with-label-input-padding-top - $vertical-deduction,
@@ -78,7 +78,7 @@
   // form-field because we do not know what type of form-field control is set up. Hence
   // we always use a fixed position for the label. This does not have any implications.
   .mat-mdc-form-field .mat-mdc-text-field-wrapper .mdc-floating-label {
-    top: private.private-div($height, 2);
+    top: math.div($height, 2);
   }
 
   // For the outline appearance, we re-create the active floating label transform. This is
diff --git a/src/material-experimental/mdc-form-field/_form-field-native-select.scss b/src/material-experimental/mdc-form-field/_form-field-native-select.scss
index 0cda173843c2..85af7d50791a 100644
--- a/src/material-experimental/mdc-form-field/_form-field-native-select.scss
+++ b/src/material-experimental/mdc-form-field/_form-field-native-select.scss
@@ -1,8 +1,8 @@
 @use 'sass:map';
+@use 'sass:math';
 @use '../mdc-helpers/mdc-helpers';
 @use '../../cdk/a11y';
 @use '../../material/core/theming/palette';
-@use '../../material/core/style/private';
 @use '@material/theme/theme-color' as mdc-theme-color;
 
 // Width of the Material Design form-field select arrow.
@@ -66,8 +66,8 @@ $mat-form-field-select-horizontal-end-padding: $mat-form-field-select-arrow-widt
       content: '';
       width: 0;
       height: 0;
-      border-left: private.private-div($mat-form-field-select-arrow-width, 2) solid transparent;
-      border-right: private.private-div($mat-form-field-select-arrow-width, 2) solid transparent;
+      border-left: math.div($mat-form-field-select-arrow-width, 2) solid transparent;
+      border-right: math.div($mat-form-field-select-arrow-width, 2) solid transparent;
       border-top: $mat-form-field-select-arrow-height solid;
       position: absolute;
       right: 0;
diff --git a/src/material-experimental/mdc-select/select.scss b/src/material-experimental/mdc-select/select.scss
index 30b01a8562e4..c201f400dd2e 100644
--- a/src/material-experimental/mdc-select/select.scss
+++ b/src/material-experimental/mdc-select/select.scss
@@ -1,8 +1,8 @@
+@use 'sass:math';
 @use '@material/menu-surface' as mdc-menu-surface;
 @use '@material/list/evolution-mixins' as mdc-list;
 @use '../../material/core/style/variables';
 @use '../../material/core/style/vendor-prefixes';
-@use '../../material/core/style/private';
 @use '../../cdk/a11y';
 
 $mat-select-arrow-size: 5px !default;
@@ -111,7 +111,7 @@ $scale: 0.75 !default;
   // Delay the transition until the label has animated about a third of the way through, in
   // order to prevent the placeholder from overlapping for a split second.
   transition: color variables.$swift-ease-out-duration
-      private.private-div(variables.$swift-ease-out-duration, 3)
+      math.div(variables.$swift-ease-out-duration, 3)
       variables.$swift-ease-out-timing-function;
 
   ._mat-animation-noopable & {
@@ -143,7 +143,7 @@ $scale: 0.75 !default;
     }
 
     .mdc-floating-label--float-above {
-      $arrow-scale: private.private-div($mat-select-placeholder-arrow-space, $scale);
+      $arrow-scale: math.div($mat-select-placeholder-arrow-space, $scale);
       max-width: calc(100% / #{$scale} - #{$arrow-scale});
     }
   }
diff --git a/src/material-experimental/mdc-slide-toggle/slide-toggle.scss b/src/material-experimental/mdc-slide-toggle/slide-toggle.scss
index 0ae0c919ad3a..b2340c42604b 100644
--- a/src/material-experimental/mdc-slide-toggle/slide-toggle.scss
+++ b/src/material-experimental/mdc-slide-toggle/slide-toggle.scss
@@ -1,11 +1,11 @@
 @use 'sass:map';
+@use 'sass:math';
 @use '@material/switch/switch' as mdc-switch;
 @use '@material/switch/switch-theme' as mdc-switch-theme;
 @use '@material/form-field' as mdc-form-field;
 @use '@material/ripple' as mdc-ripple;
 @use '../mdc-helpers/mdc-helpers';
 @use '../../material/core/style/layout-common';
-@use '../../material/core/style/private';
 @use '../../cdk/a11y';
 
 @include mdc-form-field.core-styles($query: mdc-helpers.$mat-base-styles-query);
@@ -66,6 +66,6 @@
     // Usually 1px would be enough, but MDC reduces the opacity on the
     // element so we need to make this a bit more prominent.
     outline: solid 2px;
-    outline-offset: private.private-div(map.get(mdc-switch-theme.$light-theme, track-height), 2);
+    outline-offset: math.div(map.get(mdc-switch-theme.$light-theme, track-height), 2);
   }
 }
diff --git a/src/material/badge/_badge-theme.scss b/src/material/badge/_badge-theme.scss
index 0e29f537f206..c4d2f099a2ac 100644
--- a/src/material/badge/_badge-theme.scss
+++ b/src/material/badge/_badge-theme.scss
@@ -4,10 +4,10 @@
 @use 'sass:color';
 @use 'sass:map';
 @use 'sass:meta';
+@use 'sass:math';
 @use '../core/theming/theming';
 @use '../core/typography/typography';
 @use '../core/typography/typography-utils';
-@use '../core/style/private';
 @use '../../cdk/a11y';
 
 $font-size: 12px;
@@ -29,13 +29,13 @@ $_badge-structure-emitted: false !default;
 
   &.mat-badge-above {
     .mat-badge-content {
-      top: private.private-div(-$size, 2);
+      top: math.div(-$size, 2);
     }
   }
 
   &.mat-badge-below {
     .mat-badge-content {
-      bottom: private.private-div(-$size, 2);
+      bottom: math.div(-$size, 2);
     }
   }
 
@@ -68,27 +68,27 @@ $_badge-structure-emitted: false !default;
   &.mat-badge-overlap {
     &.mat-badge-before {
       .mat-badge-content {
-        left: private.private-div(-$size, 2);
+        left: math.div(-$size, 2);
       }
     }
 
     [dir='rtl'] &.mat-badge-before {
       .mat-badge-content {
         left: auto;
-        right: private.private-div(-$size, 2);
+        right: math.div(-$size, 2);
       }
     }
 
     &.mat-badge-after {
       .mat-badge-content {
-        right: private.private-div(-$size, 2);
+        right: math.div(-$size, 2);
       }
     }
 
     [dir='rtl'] &.mat-badge-after {
       .mat-badge-content {
         right: auto;
-        left: private.private-div(-$size, 2);
+        left: math.div(-$size, 2);
       }
     }
   }
diff --git a/src/material/card/card.scss b/src/material/card/card.scss
index 9220a1fcc137..e208e4a6d098 100644
--- a/src/material/card/card.scss
+++ b/src/material/card/card.scss
@@ -1,3 +1,4 @@
+@use 'sass:math';
 @use '../core/style/variables';
 @use '../core/style/elevation';
 @use '../core/style/private';
@@ -59,8 +60,8 @@ $header-size: 40px !default;
 
 .mat-card-actions {
   @extend %mat-card-section-base;
-  margin-left: private.private-div(-$padding, 2);
-  margin-right: private.private-div(-$padding, 2);
+  margin-left: math.div(-$padding, 2);
+  margin-right: math.div(-$padding, 2);
   padding: 8px 0;
 }
 
diff --git a/src/material/checkbox/checkbox.scss b/src/material/checkbox/checkbox.scss
index d09c88bd7cab..d5fbe0681db7 100644
--- a/src/material/checkbox/checkbox.scss
+++ b/src/material/checkbox/checkbox.scss
@@ -18,7 +18,7 @@ $_ripple-radius: 20px;
 $_item-spacing: variables.$toggle-padding;
 
 // The width of the line used to draw the checkmark / mixedmark.
-$_mark-stroke-size: private.private-div(2, 15) * checkbox-common.$size !default;
+$_mark-stroke-size: math.div(2, 15) * checkbox-common.$size !default;
 
 
 // Fades in the background of the checkbox when it goes from unchecked -> {checked,indeterminate}.
diff --git a/src/material/core/option/option.scss b/src/material/core/option/option.scss
index 9e3ac2aa67a6..1ba9c5586c34 100644
--- a/src/material/core/option/option.scss
+++ b/src/material/core/option/option.scss
@@ -1,7 +1,7 @@
+@use 'sass:math';
 @use '../style/menu-common';
 @use '../style/vendor-prefixes';
 @use '../style/layout-common';
-@use '../style/private';
 @use '../../../cdk/a11y';
 
 .mat-option {
@@ -78,7 +78,7 @@
 }
 
 .mat-option-pseudo-checkbox {
-  $margin: private.private-div(menu-common.$side-padding, 2);
+  $margin: math.div(menu-common.$side-padding, 2);
   margin-right: $margin;
 
   [dir='rtl'] & {
diff --git a/src/material/core/selection/pseudo-checkbox/pseudo-checkbox.scss b/src/material/core/selection/pseudo-checkbox/pseudo-checkbox.scss
index c505dace5425..b0382bb9b143 100644
--- a/src/material/core/selection/pseudo-checkbox/pseudo-checkbox.scss
+++ b/src/material/core/selection/pseudo-checkbox/pseudo-checkbox.scss
@@ -1,3 +1,4 @@
+@use 'sass:math';
 @use '../../style/checkbox-common';
 @use '../../style/private';
 @use '../../style/variables';
@@ -50,20 +51,20 @@ $_checkmark-size: checkbox-common.$size - (2 * $_padding);
 }
 
 .mat-pseudo-checkbox-indeterminate::after {
-  top: private.private-div(checkbox-common.$size - checkbox-common.$border-width, 2) -
+  top: math.div(checkbox-common.$size - checkbox-common.$border-width, 2) -
       checkbox-common.$border-width;
-  left: private.private-div(checkbox-common.$border-width, 2);
+  left: math.div(checkbox-common.$border-width, 2);
   width: checkbox-common.$size - 6px;
   opacity: 1;
   border-radius: 2px;
 }
 
 .mat-pseudo-checkbox-checked::after {
-  top: private.private-div(checkbox-common.$size, 2) - private.private-div($_checkmark-size, 4) -
-      private.private-div(checkbox-common.$size, 10) - checkbox-common.$border-width;
+  top: math.div(checkbox-common.$size, 2) - math.div($_checkmark-size, 4) -
+       math.div(checkbox-common.$size, 10) - checkbox-common.$border-width;
   left: $_padding - checkbox-common.$border-width * 1.5;
   width: $_checkmark-size;
-  height: private.private-div($_checkmark-size - checkbox-common.$border-width, 2);
+  height: math.div($_checkmark-size - checkbox-common.$border-width, 2);
   border-left: checkbox-common.$border-width solid currentColor;
   transform: rotate(-45deg);
   opacity: 1;
diff --git a/src/material/core/style/_private.scss b/src/material/core/style/_private.scss
index e08f6f2ca8e2..2eecc6c575a3 100644
--- a/src/material/core/style/_private.scss
+++ b/src/material/core/style/_private.scss
@@ -1,7 +1,4 @@
 @use 'sass:map';
-@use 'sass:math';
-@use 'sass:meta';
-@use 'sass:list';
 @use './elevation';
 
 @mixin private-theme-elevation($zValue, $config, $opacity: elevation.$opacity) {
@@ -42,27 +39,3 @@
     @content;
   }
 }
-
-// Private polyfill for the `math.div` function from Sass to be used until we can update the
-// minimum required Sass version to 1.34.0 or above.
-// TODO(crisbeto): replace with `math.div` eventually.
-@function private-div($a, $b) {
-  @if (meta.function-exists('div', 'math')) {
-    @return math.div($a, $b);
-  }
-  @else {
-    @return $a / $b;
-  }
-}
-
-// Private polyfill for the `list.slash` function from Sass to be used until we can update the
-// minimum required Sass version to 1.34.0 or above.
-// TODO(crisbeto): replace with `list.slash` eventually.
-@function private-slash($a, $b) {
-  @if (meta.function-exists('slash', 'list')) {
-    @return list.slash($a, $b);
-  }
-  @else {
-    @return #{$a}#{' / '}#{$b};
-  }
-}
diff --git a/src/material/core/typography/_typography-utils.scss b/src/material/core/typography/_typography-utils.scss
index 9e62a70d76d4..abca4051092c 100644
--- a/src/material/core/typography/_typography-utils.scss
+++ b/src/material/core/typography/_typography-utils.scss
@@ -3,7 +3,6 @@
 @use 'sass:math';
 @use 'sass:meta';
 @use 'sass:string';
-@use '../style/private';
 
 
 // Utility for fetching a nested value from a typography config.
@@ -78,10 +77,8 @@
     font-family: $font-family;
   }
   @else {
-    // Otherwise use the shorthand `font`, because it's the least amount of bytes. Note
-    // that we need to use `list.slash` for `font-size/line-height` in order to prevent
-    // Sass from dividing the two values.
-    font: $font-weight private.private-slash($font-size, $line-height) $font-family;
+    // Otherwise use the shorthand `font`, because it's the least amount of bytes.
+    font: $font-weight list.slash($font-size, $line-height) $font-family;
   }
 }
 
diff --git a/src/material/datepicker/calendar-body.scss b/src/material/datepicker/calendar-body.scss
index f69887ff7ad8..fdc02cecd319 100644
--- a/src/material/datepicker/calendar-body.scss
+++ b/src/material/datepicker/calendar-body.scss
@@ -1,4 +1,4 @@
-@use '../core/style/private';
+@use 'sass:math';
 @use '../../cdk/a11y';
 
 $calendar-body-label-padding-start: 5% !default;
@@ -6,7 +6,7 @@ $calendar-body-label-padding-start: 5% !default;
 // the same amount of padding regardless of the number of columns. We align the header label with
 // the one third mark of the first cell, this was chosen somewhat arbitrarily to make it look
 // roughly like the mock. Half way is too far since the cell text is center aligned.
-$calendar-body-label-side-padding: private.private-div(33%, 7) !default;
+$calendar-body-label-side-padding: math.div(33%, 7) !default;
 $calendar-body-cell-min-size: 32px !default;
 $calendar-body-cell-content-margin: 5% !default;
 $calendar-body-cell-content-border-width: 1px !default;
diff --git a/src/material/datepicker/date-range-input.scss b/src/material/datepicker/date-range-input.scss
index bce7fbbfe418..7db147eb6539 100644
--- a/src/material/datepicker/date-range-input.scss
+++ b/src/material/datepicker/date-range-input.scss
@@ -1,6 +1,6 @@
+@use 'sass:math';
 @use '../core/style/variables';
 @use '../core/style/vendor-prefixes';
-@use '../core/style/private';
 @use '../../cdk/a11y';
 
 $date-range-input-separator-spacing: 4px;
@@ -8,7 +8,7 @@ $date-range-input-part-max-width: calc(50% - #{$date-range-input-separator-spaci
 
 @mixin _placeholder-transition($property) {
   transition: #{$property} variables.$swift-ease-out-duration
-    private.private-div(variables.$swift-ease-out-duration, 3)
+    math.div(variables.$swift-ease-out-duration, 3)
     variables.$swift-ease-out-timing-function;
 }
 
diff --git a/src/material/form-field/_form-field-fill-theme.scss b/src/material/form-field/_form-field-fill-theme.scss
index 0ceec90ae4f8..7d619573e04b 100644
--- a/src/material/form-field/_form-field-fill-theme.scss
+++ b/src/material/form-field/_form-field-fill-theme.scss
@@ -1,8 +1,8 @@
 @use 'sass:map';
+@use 'sass:math';
 @use '../core/theming/theming';
 @use '../core/typography/typography';
 @use '../core/typography/typography-utils';
-@use '../core/style/private';
 
 
 // Theme styles that only apply to the fill appearance of the form-field.
@@ -55,7 +55,7 @@ $fill-dedupe: 0;
 @mixin _label-floating($font-scale, $infix-padding, $infix-margin-top) {
   transform: translateY(-$infix-margin-top - $infix-padding + $fill-dedupe)
              scale($font-scale);
-  width: private.private-div(100%, $font-scale) + $fill-dedupe;
+  width: math.div(100%, $font-scale) + $fill-dedupe;
 
   $fill-dedupe: $fill-dedupe + 0.00001 !global;
 }
diff --git a/src/material/form-field/_form-field-legacy-theme.scss b/src/material/form-field/_form-field-legacy-theme.scss
index 2cec316fd5e7..42e9a6c2e760 100644
--- a/src/material/form-field/_form-field-legacy-theme.scss
+++ b/src/material/form-field/_form-field-legacy-theme.scss
@@ -1,6 +1,6 @@
 @use 'sass:map';
+@use 'sass:math';
 @use '../core/theming/theming';
-@use '../core/style/private';
 @use '../core/style/form-common';
 @use '../core/typography/typography';
 @use '../core/typography/typography-utils';
@@ -55,7 +55,7 @@ $legacy-dedupe: 0;
   -ms-transform: translateY(-$infix-margin-top - $infix-padding + $legacy-dedupe)
                   scale($font-scale);
 
-  width: private.private-div(100%, $font-scale) + $legacy-dedupe;
+  width: math.div(100%, $font-scale) + $legacy-dedupe;
 
   $legacy-dedupe: $legacy-dedupe + 0.00001 !global;
 }
@@ -80,7 +80,7 @@ $legacy-dedupe: 0;
   $subscript-font-scale: 0.75;
   // The amount of space between the top of the line and the top of the actual text
   // (as a fraction of the font-size).
-  $line-spacing: private.private-div($line-height - 1, 2);
+  $line-spacing: math.div($line-height - 1, 2);
   // The padding on the infix. Mocks show half of the text size, but seem to measure from the edge
   // of the text itself, not the edge of the line; therefore we subtract off the line spacing.
   $infix-padding: 0.5em - $line-spacing;
@@ -93,7 +93,7 @@ $legacy-dedupe: 0;
   // text font size, so we need to divide by the scale factor to make it half of the original text
   // size. We again need to subtract off the line spacing since the mocks measure to the edge of the
   // text, not the  edge of the line.
-  $subscript-margin-top: private.private-div(0.5em, $subscript-font-scale) - ($line-spacing * 2);
+  $subscript-margin-top: math.div(0.5em, $subscript-font-scale) - ($line-spacing * 2);
   // The padding applied to the form-field-wrapper to reserve space for the subscript, since it's
   // absolutely positioned. This is a combination of the subscript's margin and line-height, but we
   // need to multiply by the subscript font scale factor since the wrapper has a larger font size.
@@ -146,7 +146,7 @@ $legacy-dedupe: 0;
 
       // We want the subscript to start at the end of the content box, not the padding box,
       // so we move it up by the padding amount (adjusted for the smaller font size);
-      top: calc(100% - #{private.private-div($wrapper-padding-bottom, $subscript-font-scale)});
+      top: calc(100% - #{math.div($wrapper-padding-bottom, $subscript-font-scale)});
     }
   }
 
diff --git a/src/material/form-field/_form-field-outline-theme.scss b/src/material/form-field/_form-field-outline-theme.scss
index b32d9ddffd12..2a53929b0145 100644
--- a/src/material/form-field/_form-field-outline-theme.scss
+++ b/src/material/form-field/_form-field-outline-theme.scss
@@ -1,6 +1,6 @@
 @use 'sass:map';
+@use 'sass:math';
 @use '../core/theming/theming';
-@use '../core/style/private';
 @use '../core/typography/typography';
 @use '../core/typography/typography-utils';
 
@@ -78,7 +78,7 @@ $outline-dedupe: 0;
 @mixin _label-floating($font-scale, $infix-padding, $infix-margin-top) {
   transform: translateY(-$infix-margin-top - $infix-padding + $outline-dedupe)
   scale($font-scale);
-  width: private.private-div(100%, $font-scale) + $outline-dedupe;
+  width: math.div(100%, $font-scale) + $outline-dedupe;
 
   $outline-dedupe: $outline-dedupe + 0.00001 !global;
 }
@@ -99,7 +99,7 @@ $outline-dedupe: 0;
   // Mocks show half of the text size, but this margin is applied to an element with the subscript
   // text font size, so we need to divide by the scale factor to make it half of the original text
   // size.
-  $subscript-margin-top: private.private-div(0.5em, $subscript-font-scale);
+  $subscript-margin-top: math.div(0.5em, $subscript-font-scale);
   // The padding applied to the form-field-wrapper to reserve space for the subscript, since it's
   // absolutely positioned. This is a combination of the subscript's margin and line-height, but we
   // need to multiply by the subscript font scale factor since the wrapper has a larger font size.
diff --git a/src/material/form-field/_form-field-theme.scss b/src/material/form-field/_form-field-theme.scss
index 9f49aaf30a3a..772e7168ff54 100644
--- a/src/material/form-field/_form-field-theme.scss
+++ b/src/material/form-field/_form-field-theme.scss
@@ -1,8 +1,8 @@
 @use 'sass:map';
+@use 'sass:math';
 @use '../core/theming/theming';
 @use '../core/typography/typography';
 @use '../core/typography/typography-utils';
-@use '../core/style/private';
 
 @use './form-field-fill-theme.scss';
 @use './form-field-legacy-theme.scss';
@@ -127,7 +127,7 @@ $dedupe: 0;
 @mixin _label-floating($font-scale, $infix-padding, $infix-margin-top) {
   transform: translateY(-$infix-margin-top - $infix-padding + $dedupe)
              scale($font-scale);
-  width: private.private-div(100%, $font-scale) + $dedupe;
+  width: math.div(100%, $font-scale) + $dedupe;
 
   $dedupe: $dedupe + 0.00001 !global;
 }
@@ -157,7 +157,7 @@ $dedupe: 0;
   // Mocks show half of the text size, but this margin is applied to an element with the subscript
   // text font size, so we need to divide by the scale factor to make it half of the original text
   // size.
-  $subscript-margin-top: private.private-div(0.5em, $subscript-font-scale);
+  $subscript-margin-top: math.div(0.5em, $subscript-font-scale);
   // The padding applied to the form-field-wrapper to reserve space for the subscript, since it's
   // absolutely positioned. This is a combination of the subscript's margin and line-height, but we
   // need to multiply by the subscript font scale factor since the wrapper has a larger font size.
@@ -234,7 +234,7 @@ $dedupe: 0;
 
     // We want the subscript to start at the end of the content box, not the padding box,
     // so we move it up by the padding amount (adjusted for the smaller font size);
-    top: calc(100% - #{private.private-div($wrapper-padding-bottom, $subscript-font-scale)});
+    top: calc(100% - #{math.div($wrapper-padding-bottom, $subscript-font-scale)});
   }
 
   @include form-field-legacy-theme.legacy-typography($config);
diff --git a/src/material/form-field/form-field-fill.scss b/src/material/form-field/form-field-fill.scss
index 2468d5174114..16adea99df38 100644
--- a/src/material/form-field/form-field-fill.scss
+++ b/src/material/form-field/form-field-fill.scss
@@ -1,5 +1,5 @@
+@use 'sass:math';
 @use '../core/style/variables';
-@use '../core/style/private';
 @use '../../cdk/a11y';
 
 // Styles that only apply to the fill appearance of the form-field.
@@ -18,8 +18,7 @@ $fill-line-spacing: 0.75em !default;
 // The scale of the subscript and floating label text w.r.t the value text.
 $fill-subscript-font-scale: 0.75 !default;
 // The horizontal padding between the edge of the subscript box and the start of the subscript text.
-$fill-subscript-padding:
-    private.private-div($fill-side-padding, $fill-subscript-font-scale);
+$fill-subscript-padding: math.div($fill-side-padding, $fill-subscript-font-scale);
 
 
 .mat-form-field-appearance-fill {
diff --git a/src/material/form-field/form-field-input.scss b/src/material/form-field/form-field-input.scss
index 827f4e59caf8..2646d3463e00 100644
--- a/src/material/form-field/form-field-input.scss
+++ b/src/material/form-field/form-field-input.scss
@@ -1,6 +1,6 @@
+@use 'sass:math';
 @use '../core/style/variables';
 @use '../core/style/vendor-prefixes';
-@use '../core/style/private';
 @use '../../cdk/a11y';
 
 // The Input element proper.
@@ -109,8 +109,7 @@
     // Delay the transition until the label has animated about a third of the way through, in
     // order to prevent the placeholder from overlapping for a split second.
     transition: color variables.$swift-ease-out-duration
-      private.private-div(variables.$swift-ease-out-duration, 3)
-      variables.$swift-ease-out-timing-function;
+      math.div(variables.$swift-ease-out-duration, 3) variables.$swift-ease-out-timing-function;
   }
 
   .mat-form-field-hide-placeholder & {
@@ -219,7 +218,7 @@ select.mat-input-element {
     position: absolute;
     top: 50%;
     right: 0;
-    margin-top: private.private-div(-$arrow-size, 2);
+    margin-top: math.div(-$arrow-size, 2);
 
     // Make the arrow non-clickable so the user can click on the form control under it.
     pointer-events: none;
diff --git a/src/material/form-field/form-field-outline.scss b/src/material/form-field/form-field-outline.scss
index 1320a8908654..2d0d42a99f26 100644
--- a/src/material/form-field/form-field-outline.scss
+++ b/src/material/form-field/form-field-outline.scss
@@ -1,5 +1,5 @@
+@use 'sass:math';
 @use '../core/style/variables';
-@use '../core/style/private';
 @use '../../cdk/a11y';
 
 // Styles that only apply to the outline appearance of the form-field.
@@ -17,8 +17,7 @@ $outline-width: 1px;
 // The width of the thick outline (used for focus, hover, and error state).
 $outline-thick-width: 2px;
 // The horizontal padding between the edge of the subscript box and the start of the subscript text.
-$outline-subscript-padding:
-    private.private-div($outline-side-padding, $outline-subscript-font-scale);
+$outline-subscript-padding: math.div($outline-side-padding, $outline-subscript-font-scale);
 
 
 .mat-form-field-appearance-outline {
diff --git a/src/material/input/_input-theme.scss b/src/material/input/_input-theme.scss
index f32ab2a888cd..5ea1e098a3ca 100644
--- a/src/material/input/_input-theme.scss
+++ b/src/material/input/_input-theme.scss
@@ -1,7 +1,7 @@
 @use 'sass:map';
+@use 'sass:math';
 @use '../core/theming/palette';
 @use '../core/theming/theming';
-@use '../core/style/private';
 @use '../core/style/form-common';
 @use '../core/typography/typography';
 @use '../core/typography/typography-utils';
@@ -69,7 +69,7 @@
 
   // The amount of space between the top of the line and the top of the actual text
   // (as a fraction of the font-size).
-  $line-spacing: private.private-div($line-height - 1, 2);
+  $line-spacing: math.div($line-height - 1, 2);
 
   // <input> elements seem to have their height set slightly too large on Safari causing the text to
   // be misaligned w.r.t. the placeholder. Adding this margin corrects it.
diff --git a/src/material/radio/radio.scss b/src/material/radio/radio.scss
index 20485109262c..844ccd72133f 100644
--- a/src/material/radio/radio.scss
+++ b/src/material/radio/radio.scss
@@ -1,7 +1,7 @@
+@use 'sass:math';
 @use '../core/style/variables';
 @use '../core/ripple/ripple';
 @use '../core/style/vendor-prefixes';
-@use '../core/style/private';
 @use '../../cdk/a11y';
 
 
@@ -98,7 +98,7 @@ $ripple-radius: 20px;
     @include a11y.high-contrast(active, off) {
       // Since we use a background color to render the circle, it won't be
       // displayed in high contrast mode. Use a border as a fallback.
-      border: solid private.private-div($size, 2);
+      border: solid math.div($size, 2);
     }
   }
 
diff --git a/src/material/select/select.scss b/src/material/select/select.scss
index ea69d84327a1..82bd3a49f23c 100644
--- a/src/material/select/select.scss
+++ b/src/material/select/select.scss
@@ -1,8 +1,8 @@
+@use 'sass:math';
 @use '../core/style/menu-common';
 @use '../core/style/list-common';
 @use '../core/style/variables';
 @use '../core/style/vendor-prefixes';
-@use '../core/style/private';
 @use '../../cdk/a11y';
 
 $arrow-size: 5px !default;
@@ -129,7 +129,7 @@ $placeholder-arrow-space: 2 * ($arrow-size + $arrow-margin);
   // Delay the transition until the label has animated about a third of the way through, in
   // order to prevent the placeholder from overlapping for a split second.
   transition: color variables.$swift-ease-out-duration
-      private.private-div(variables.$swift-ease-out-duration, 3)
+      math.div(variables.$swift-ease-out-duration, 3)
       variables.$swift-ease-out-timing-function;
 
   ._mat-animation-noopable & {
diff --git a/src/material/slide-toggle/slide-toggle.scss b/src/material/slide-toggle/slide-toggle.scss
index a69c81889f43..5a68bf0df822 100644
--- a/src/material/slide-toggle/slide-toggle.scss
+++ b/src/material/slide-toggle/slide-toggle.scss
@@ -1,8 +1,8 @@
+@use 'sass:math';
 @use '../core/style/vendor-prefixes';
 @use '../core/style/variables';
 @use '../core/ripple/ripple';
 @use '../core/style/list-common';
-@use '../core/style/private';
 @use '../../cdk/a11y';
 
 $thumb-size: 20px !default;
@@ -91,7 +91,7 @@ $bar-track-width: $bar-width - $thumb-size;
 
 // The container includes the visual thumb and the ripple container element.
 .mat-slide-toggle-thumb-container {
-  $thumb-bar-vertical-padding: private.private-div($thumb-size - $bar-height, 2);
+  $thumb-bar-vertical-padding: math.div($thumb-size - $bar-height, 2);
 
   position: absolute;
   z-index: 1;
@@ -143,7 +143,7 @@ $bar-track-width: $bar-width - $thumb-size;
 .mat-slide-toggle-input {
   // Move the input to the bottom and in the middle of the thumb.
   // Visual improvement to properly show browser popups when being required.
-  $horizontal-offset: private.private-div($thumb-size, 2);
+  $horizontal-offset: math.div($thumb-size, 2);
 
   bottom: 0;
   left: $horizontal-offset;
@@ -231,6 +231,6 @@ $bar-track-width: $bar-width - $thumb-size;
   // because otherwise the opaque thumb element will hide the outline.
   .mat-slide-toggle.cdk-keyboard-focused .mat-slide-toggle-bar {
     outline: 2px dotted;
-    outline-offset: private.private-div($height - $bar-height, 2);
+    outline-offset: math.div($height - $bar-height, 2);
   }
 }
diff --git a/src/material/slider/slider.scss b/src/material/slider/slider.scss
index f86bcde25a60..b7882b82aba3 100644
--- a/src/material/slider/slider.scss
+++ b/src/material/slider/slider.scss
@@ -1,6 +1,6 @@
+@use 'sass:math';
 @use '../core/style/variables';
 @use '../core/style/vendor-prefixes';
-@use '../core/style/private';
 @use '../../cdk/a11y';
 
 
@@ -124,8 +124,8 @@ $focus-ring-size: 30px !default;
   @extend %_mat-slider-cursor;
 
   position: absolute;
-  right: private.private-div(-$thumb-size, 2);
-  bottom: private.private-div(-$thumb-size, 2);
+  right: math.div(-$thumb-size, 2);
+  bottom: math.div(-$thumb-size, 2);
   box-sizing: border-box;
   width: $thumb-size;
   height: $thumb-size;
@@ -281,7 +281,7 @@ $focus-ring-size: 30px !default;
 
   .mat-slider-wrapper {
     height: $track-thickness;
-    top: private.private-div($thickness - $track-thickness, 2);
+    top: math.div($thickness - $track-thickness, 2);
     left: $padding;
     right: $padding;
   }
@@ -317,7 +317,7 @@ $focus-ring-size: 30px !default;
     @include a11y.high-contrast(active, off) {
       height: 0;
       outline: solid $track-thickness;
-      top: private.private-div($track-thickness, 2);
+      top: math.div($track-thickness, 2);
     }
   }
 
@@ -333,14 +333,14 @@ $focus-ring-size: 30px !default;
   }
 
   .mat-slider-focus-ring {
-    top: private.private-div(-$focus-ring-size, 2);
-    right: private.private-div(-$focus-ring-size, 2);
+    top: math.div(-$focus-ring-size, 2);
+    right: math.div(-$focus-ring-size, 2);
   }
 
   .mat-slider-thumb-label {
-    right: private.private-div(-$thumb-label-size, 2);
+    right: math.div(-$thumb-label-size, 2);
     top: -($thumb-label-size + $thumb-arrow-gap);
-    transform: translateY(private.private-div($thumb-label-size, 2) + $thumb-arrow-gap)
+    transform: translateY(math.div($thumb-label-size, 2) + $thumb-arrow-gap)
         scale(0.01)
         rotate(45deg);
   }
@@ -373,7 +373,7 @@ $focus-ring-size: 30px !default;
     width: $track-thickness;
     top: $padding;
     bottom: $padding;
-    left: private.private-div($thickness - $track-thickness, 2);
+    left: math.div($thickness - $track-thickness, 2);
   }
 
   .mat-slider-wrapper::after {
@@ -407,13 +407,13 @@ $focus-ring-size: 30px !default;
     @include a11y.high-contrast(active, off) {
       width: 0;
       outline: solid $track-thickness;
-      left: private.private-div($track-thickness, 2);
+      left: math.div($track-thickness, 2);
     }
   }
 
   .mat-slider-focus-ring {
-    bottom: private.private-div(-$focus-ring-size, 2);
-    left: private.private-div(-$focus-ring-size, 2);
+    bottom: math.div(-$focus-ring-size, 2);
+    left: math.div(-$focus-ring-size, 2);
   }
 
   .mat-slider-ticks {
@@ -432,9 +432,9 @@ $focus-ring-size: 30px !default;
   }
 
   .mat-slider-thumb-label {
-    bottom: private.private-div(-$thumb-label-size, 2);
+    bottom: math.div(-$thumb-label-size, 2);
     left: -($thumb-label-size + $thumb-arrow-gap);
-    transform: translateX(private.private-div($thumb-label-size, 2) + $thumb-arrow-gap)
+    transform: translateX(math.div($thumb-label-size, 2) + $thumb-arrow-gap)
         scale(0.01)
         rotate(-45deg);
   }
diff --git a/src/material/snack-bar/BUILD.bazel b/src/material/snack-bar/BUILD.bazel
index 1d77620728b1..9ac99696bfde 100644
--- a/src/material/snack-bar/BUILD.bazel
+++ b/src/material/snack-bar/BUILD.bazel
@@ -51,7 +51,6 @@ sass_binary(
 sass_binary(
     name = "simple_snack_bar_scss",
     src = "simple-snack-bar.scss",
-    deps = ["//src/material/core:core_scss_lib"],
 )
 
 ng_test_library(
diff --git a/src/material/snack-bar/simple-snack-bar.scss b/src/material/snack-bar/simple-snack-bar.scss
index 7012a45bfd09..50188497237a 100644
--- a/src/material/snack-bar/simple-snack-bar.scss
+++ b/src/material/snack-bar/simple-snack-bar.scss
@@ -1,12 +1,11 @@
-@use '../core/style/private';
+@use 'sass:math';
 
 $button-horizontal-margin: 8px !default;
 $button-height: 36px !default;
 $line-height: 20px !default;
 // Button vertical margin is used to ensure that a button height of 36px, when the containing
 // space falls below 36px.
-$button-vertical-margin:
-  -(private.private-div($button-height - $line-height, 2));
+$button-vertical-margin: -(math.div($button-height - $line-height, 2));
 
 .mat-simple-snackbar {
   display: flex;
diff --git a/src/material/stepper/_stepper-theme.scss b/src/material/stepper/_stepper-theme.scss
index 93ffef821fc9..2fef391a9684 100644
--- a/src/material/stepper/_stepper-theme.scss
+++ b/src/material/stepper/_stepper-theme.scss
@@ -1,9 +1,9 @@
 @use 'sass:map';
+@use 'sass:math';
 @use '../core/theming/theming';
 @use '../core/typography/typography';
 @use '../core/typography/typography-utils';
 @use '../core/density/private/compatibility';
-@use '../core/style/private';
 @use './stepper-variables';
 
 @mixin color($config-or-theme) {
@@ -140,7 +140,7 @@
   $density-scale: theming.get-density-config($config-or-theme);
   $height: compatibility.private-density-prop-value(stepper-variables.$density-config,
     $density-scale, height);
-  $vertical-padding: private.private-div($height - stepper-variables.$label-header-height, 2);
+  $vertical-padding: math.div($height - stepper-variables.$label-header-height, 2);
 
   @include compatibility.private-density-legacy-compatibility() {
     .mat-horizontal-stepper-header {
@@ -162,13 +162,13 @@
     // Ensures that the horizontal lines for the step header are centered vertically.
     .mat-stepper-label-position-bottom .mat-horizontal-stepper-header {
       &::after, &::before {
-        top: $vertical-padding + private.private-div(stepper-variables.$label-header-height, 2);
+        top: $vertical-padding + math.div(stepper-variables.$label-header-height, 2);
       }
     }
 
     // Ensures that the horizontal line for the step content is aligned centered vertically.
     .mat-stepper-label-position-bottom .mat-stepper-horizontal-line {
-      top: $vertical-padding + private.private-div(stepper-variables.$label-header-height, 2);
+      top: $vertical-padding + math.div(stepper-variables.$label-header-height, 2);
     }
   }
 }
diff --git a/src/material/stepper/stepper.scss b/src/material/stepper/stepper.scss
index d27d329df52f..6184cf108771 100644
--- a/src/material/stepper/stepper.scss
+++ b/src/material/stepper/stepper.scss
@@ -1,5 +1,5 @@
+@use 'sass:math';
 @use '../core/style/variables';
-@use '../core/style/private';
 @use './stepper-variables';
 
 .mat-stepper-vertical,
@@ -33,7 +33,7 @@
 }
 
 %mat-header-horizontal-line-label-position-bottom {
-  $half-side-gap: private.private-div(stepper-variables.$side-gap, 2);
+  $half-side-gap: math.div(stepper-variables.$side-gap, 2);
   border-top-width: stepper-variables.$line-width;
   border-top-style: solid;
   content: '';
diff --git a/src/material/tooltip/_tooltip-theme.scss b/src/material/tooltip/_tooltip-theme.scss
index c94db3eca0f9..f4abc670b893 100644
--- a/src/material/tooltip/_tooltip-theme.scss
+++ b/src/material/tooltip/_tooltip-theme.scss
@@ -1,17 +1,16 @@
 @use 'sass:map';
+@use 'sass:math';
 @use '../core/theming/theming';
 @use '../core/typography/typography';
 @use '../core/typography/typography-utils';
-@use '../core/style/private';
 
 $target-height: 22px;
 $font-size: 10px;
-$vertical-padding: private.private-div($target-height - $font-size, 2);
+$vertical-padding: math.div($target-height - $font-size, 2);
 
 $handset-target-height: 30px;
 $handset-font-size: 14px;
-$handset-vertical-padding:
-    private.private-div($handset-target-height - $handset-font-size, 2);
+$handset-vertical-padding: math.div($handset-target-height - $handset-font-size, 2);
 
 @mixin color($config-or-theme) {
   $config: theming.get-color-config($config-or-theme);
diff --git a/yarn.lock b/yarn.lock
index c6827b162262..1eaf19ccf2aa 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -12027,10 +12027,10 @@ sass-lookup@^3.0.0:
   dependencies:
     commander "^2.16.0"
 
-sass@^1.26.3, sass@^1.34.1:
-  version "1.37.0"
-  resolved "https://registry.yarnpkg.com/sass/-/sass-1.37.0.tgz#f1b03a9d072ee9053a29d125c8130c78e92827c2"
-  integrity sha512-B+Tu6cSAG8ffs/cqsZl/bgSH2pCmavDaPTYAoW8QA1qNHh/RqndNfVKuABKYkLjUQ5aq/BnCENVpE80cqdSM1w==
+sass@^1.26.3, sass@^1.38.0:
+  version "1.38.0"
+  resolved "https://registry.yarnpkg.com/sass/-/sass-1.38.0.tgz#2f3e60a1efdcdc910586fa79dc89d3399a145b4f"
+  integrity sha512-WBccZeMigAGKoI+NgD7Adh0ab1HUq+6BmyBUEaGxtErbUtWUevEbdgo5EZiJQofLUGcKtlNaO2IdN73AHEua5g==
   dependencies:
     chokidar ">=3.0.0 <4.0.0"