1. Power of Patterns: Domino Tiling
 Page ID
 13594
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Power of Patterns: Domino Tiling
Grade 56
OVERVIEW & PURPOSE
Students gain an understanding of visualizing problems and explore the mathematical world of tiling.
OBJECTIVES

Use a systematic approach to discover the pattern of the different tiling (on 2 x n rectangle)

Use knowledge of Fibonacci numbers to help create a proof
MATERIALS NEEDED

Dominoes (6 dominoes per group)

Paper
ACTIVITY

Introduce the concept of tiling to students: focusing on tiling 2 x n rectangles with dominoes. (Provide an explanation of “2 x n” and examples of how dominoes can be moved)

Rules:

There can be no gaps or overlapping on the rectangle

Rotating tiles to create different variations counts as another way of tiling. An example below: these are considered two different tiling


Ask students to create a TTable to keep track of their tiling. Labeled: ‘n’ to indicate how many dominoes they are using and ‘number of tilings’ to indicate the number of possible tiling.

Students will work through the table. Encourage students to come up with a formula for their answer. With prior knowledge: students will discover the sequence is the Fibonacci sequence.
SOLVING

Fibonacci sequence: You add the two previous numbers and continue in the same pattern. (E.g. if your first two numbers are 1 and 2, you add 1+2 = 3, which makes 3 your third number.

Go over the various tiling patterns as a class