How Many Tiles?

 The other night while I was reading a passage about people going into the building, the author mentioned the columns were covered with pictures made out of tile.  Columns and tiles.  A perfect real world problem using cylinders.  I have seen columns in the Anchorage airport decorated in tile portraying African animals.

Just think of the math involved in planning it.  One of the first things they had to know was the radius and the height of each column to find surface area, not volume.

The next thing to look at is the type of tile you plan to use.  Most times, they use a small one inch square tile to cover it although I've seen some a bit larger but not larger than 2 inches by 2 inches.  Since the tiles are in square inches, the surface area of the column needs to be in inches and not feet.  This is a good context to help students see why units need to be the same.  I already know a 1 foot by 1 foot rigid tile will not work as well on a cylinder as the small tiles.

If the columns are being covered in one color, then there isn't much left to be done but if a picture is being made out of tiles, one has to calculate the number of tiles needed in each color realizing the pictures are scaled smaller than the actual cylinder.  The easiest way would be to calculate the amount of tile for each color using a percent but that really isn't the easiest.  The easiest way is to draw the picture on graph paper, color it in, and count the number of each color while keeping in mind the scale factor to determine how many of each to order.

This leads to the next step of ordering each color.  The usual rule of thumb is to convert the number of tiles into boxes.  Usually boxes of tiles are labeled as covering so many square feet and your measurements were in square inches so you have to divide the square inches by 144 (12in by 12 in) to determine the square feet.  For projects, its always good to round up to whole numbers because things happen.  Tiles can break and its important to have extra.

One last step is to calculate the cost by multiplying the number of boxes of tile by the cost of each box so you know what you will be spending but its a decent idea to include sales tax for the actual price.  If you want to add one more element, have students include the price of the grout.

 So if say purple is represented by 18 squares and each square is 36 square inches, the total is 648 square inches.  Then 648/144 = 4.5 square feet.  If one box covers 10 square feet, you'd still have to buy one box because that is the minimum.  At $22.00 per box, you'd spend $22.00 x 1 box = $22.00 for the purple alone.

In one activity you've done surface area, conversions, rounding, sales tax, scale factor and total cost.   Let me know what you think, I'd love to hear.  Have a great day.