Google authentication failed. Please try again later!
All Lesson Plans

Border Tiles Puzzle

Puzzle Board

Border Tiles of a Pool – Polypad – Polypad
polypad.org/OEQmCL7HXLIyg

The border tiles is a traditional problem in which you are asked to write an expression to calculate the number of tiles needed to border a given pool. The shape of the pool is usually a square or a rectangle, but any shape can be used as a pool too!

Hints

For younger students, starting with a square pool of 1 by 1 and enlarging the pool one square at a time can help to find the general pattern.

Border Tiles (square) – Polypad – Polypad
polypad.org/DfAAOQFThZxLFg

For the rectangular pool, the following questions may be helpful:

  • What are the dimensions of the pool? What is its area?
  • What are the dimensions of the area enclosed by the border tiles? Its area?
  • What does the difference between areas represent?
  • For an n x m pool, what are the dimensions of the area enclosed by the border tiles?

Solution

Square Pool

,,,,,,,,,,,,,,,,,,,,,,,,,,,,

The beauty of this problem is the endless ways of analyzing the shape. Here are a few different ways to look at a 5 by 5 square pool.

Rectangular Pool

Rectangular Pools are very similar to square pools. The general formula for an n x m rectangle is 2n+2m+42n+ 2m+ 4.

For a 12 x 16 pool, the number of red tiles will be 60.

More on the Border Tiles Puzzle

You may continue to study other shapes to solve the border problems. Here is an L shape pool example;

Border Tiles of an L Shape Poo – Polypad – Polypad
polypad.org/PLZqWIp9IeJgMQ

Visit the Visual Patterns Tasks Page to practice exploring and creating patterns.

Visual Patterns – Polypad
mathigon.org/task/visual-patterns

Next

If you like this puzzle, try this one!

Checkerboard Squares – Polypad – Polypad
polypad.org/O2KD9Dg7qNRnA