Cover the shower's floor drain cover with masking tape to prevent debris from entering the floor drain and clogging the drainpipe. Put on a set of goggles.
Cut through the grout surrounding the perimeter of the level shower floor, using the grout saw. Slice through the grout surrounding the floor drain, using the utility knife. Removing the grout protects the wall tile and floor drain from damage.
Hold a flat chisel's blade on one of the grout joints in the middle of the level floor. Strike the chisel's handle with a mallet until the chisel digs into the grout and one of the tiles bordering the grout joint breaks free of the shower floor base. Remove the loose tile, exposing the shower floor base.
Set the flat chisel's blade on the shower floor base next to one of the remaining tiles. Hold the flat chisel at a 45-degree angle to the shower floor base and hit the chisel's handle with the mallet, wedging the chisel between the tile and shower floor base. Dislodge the tile with the chisel. Remove the remaining tile on the level shower floor, using the same method used to separate the tile from the shower base.
Clean all of the debris from the shower floor base with a broom and dustpan.
Rub a brick across the shower floor base, working the brick back and forth across each ridge left over from the tile. The brick sands the high spots off the base.
Clean the dust from the shower floor base's pores with a vacuum.
Set one end of a bubble level on the floor drain and position the other end against the shower wall furthest from the floor drain. Lift the end of the bubble level that rests against the shower wall until the level reads about 1/4 inch per foot of slope, using the level's bubble as a guide. Place a pencil mark on the wall tile where the bubble level meets the shower wall.
Hold the bubble level against the shower wall and position the bottom so it rests even with the pencil mark. Adjust the level for plumb, using the bubble as a guide, and trace the bottom of the level on the shower wall with the pencil. Repeat this across each shower wall, creating the new shower floor base's slope layout.
Combine a bag of premixed shower floor mortar mix and latex additive in a wheelbarrow, using the mortar mix manufacturer's mixture ratio. Stir the mixture with a flat shovel until the mixture has the consistency of bread dough. Premixed shower floor mortar mix contains the proper cement-to-sand ratio for a shower floor base.
Dampen the old shower floor base with water. Add just enough water to the shower base to darken the base material. Water helps the new shower base material adhere to the old base.
Cover the shower floor with the mortar mix, using the flat shovel to transfer the mix from the wheelbarrow to the floor.
Compact the mortar mix with the brick or a grout float, using a tamping motion to press the air out of the base material. Continue to add mortar mix until the base material has risen above the slope layout line on the shower wall.
Hold one end of the bubble level on the floor drain and position the other end against a shower wall. Shave the excess base material from the shower floor with the level's edge, working the level back and forth across the base until the top of the base material reaches the slope layout line. If the bubble level shows the shower base contains a valley, add additional mortar mix to the low spots and tamp the base.
Clean the excess base material from the shower floor with the broom and dustpan. Let the base material dry completely before laying the shower floor tile.