Laying a Tile Floor

Laying a ceramic tile floor can be a very difficult process.  Most houses do not have rooms where the walls are close to a perfect 90o, however, most tiles are either square or rectangular and do have corners that are close to a perfect 90o.  However, the side walls should be approximately the same distance apart at the front wall as they are at the back wall, and the front and back walls should be the same distance apart at both of the side walls.  In this investigation, we are going to lay a tile floor with square tiles.  With this investigation we will see that there is mathematics involved in something as simple as laying a tile floor.  In order to lay a tile floor we need to have a working knowledge of algebra and geometry.  We need to understand ratios when working with a scale drawing of our floor, and we need to know algebra to figure out where to start our tiles and how much grout and adhesive we will need to use as well as to be aware of the cost of laying the tile ourselves. 

The room that we are tiling is 12ft x 15ft.  We also know that the tiles are 12in x 12in.  Before laying the tiles we should draw a diagram of our floor that shows approximately where we should place our tiles.  We want a scale model, so we will make our room a 12cm x 15 cm parallelogram to approximate the floor on which we will be laying tile.  Since the corners of our floor are not right angles, we do not want to start with our tiles in a corner, instead we want to begin with a tile placed a few inches from the corner.  We also want the tiles so that the piece of tile that is on the left side of the floor is about the same size as the piece of tile on the right side of the floor.  Similarly, we want the piece of tile at the front of the room to be about the same size as the piece of tile at the back of the room.  When drawing our diagram, we will number the tiles so as to be sure of their placement on the floor.  Here is our diagram:

Now, we have numbered our tiles in order to see approximately how many tiles we will be needing to tile our floor.  So we can see that we will need approximately 208 tiles in order to tile our floor.  One tile will cost $2.39 regardless of the color of the tile, so we will need to spend $497.12 on tiles.  We can also see from our diagram that there are 8 rows that contain 6 black tiles and 8 rows that contain 7 black tiles so we will need 104 black tiles and 104 white tiles.  We will also need adhesive and grout to lay the tile.  The adhesive comes in 3.5 gallon buckets that cost $28.45 each and we will need two buckets, so it will cost $56.90 for adhesive.  The grout comes in one gallon buckets that cost $19.98 each and we will need two buckets, so it will cost $39.96 for grout.  So our total cost for the floor so far is $593.98. 

Now before we lay the adhesive, we need to lay some of the tiles so that we can snap a chalk line to ensure that the tiles will be straight.  We begin by laying tiles #1 through #11 and we try have the same amount of space between tile #1 and the right wall as there is between tile #11 and the left wall.  Next we lay a vertical row of tiles, #12 through #144 and try to make it so that we have the same amount of space between tile #1 and the bottom wall as there is between tile #144 and the top wall.  Now with a felt tip marker outline tile #6 and tile #78.  After removing the tiles, use a chalk line to snap a horizontal line across the top of tile #78 and a vertical line along the left side of tile #6.  Where these two lines intersect is where we will place the upper left hand corner of tile #83.

Now that we have our outline we can begin laying our tile.  We start with laying a small amount of adhesive with the trowel at the center where the vertical chalk line and the horizontal chalk line intersect and begin by laying our tile #83.  We want to lay enough adhesive so that we will be able to lay several tiles before applying more adhesive to the floor.  We lay the tile, alternating between black and white, along the two lines and filling out toward the corners of the room.  Once we have laid all the full sized tiles we are ready to cut the tiles to go along the edges of the room.

To cut tiles, we need to take a full sized tile and lay it upside down, one side flush against the wall, on top of the tile that it will be next to so that it lays over the open space that it will need to fill as illustrated below.

Using a felt tip marker and a ruler we will mark along the bottom of the tile where we need to make our cut using the ceramic tile cutter.  We will do this for each of the tiles along the edge, making two marks on the corner tiles and cutting all using the tile cutter.  Then we lay these tiles as well and prepare our grout.

We mix the grout with water until it is like a thick paste, and use the rubber float to spread the grout across the top of the floor, pressing grout in between the tiles.  For spreading the grout the float should be approximately 45o to the floor.  Turn the float so that it is perpendicular to the floor to wipe away the excess grout.  Finally, after about 30 minutes use a damp sponge to wipe away the remaining excess grout.  You then have the option of applying silicon caulking to finish off your floor after the grout has had time to dry.

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