Domino Activity

## Teacher Lesson Plan

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This activity is aligned to NCTM Standards - Grades 6-8: Algebra, Problem Solving, Reasoning and Proof, and Communication and to California Mathematics Standards Grade 7: Algebra and Functions #1.1 and Mathematical Reasoning, #1.1, 2.2, 2.3, 2.4, 2.5

Glencoe's Interactive Mathematics text provides an activity (Units 7-12, p. 8) called Pentomino + 1 = Hexomino. During the Math Forum's 1998 Summer Institute I had the opportunity to meet and work with Ron Knott who shared with me a domino activity, Fibonacci Numbers and Brick Wall Patterns. He also loaned me a book titled Polyominoes by Solomon W. Golomb. To make more connections to a variety of mathematics I decided to write a domino activity to replace the hexomino activity presented in the text. The hexomino activity might be appropriate as a follow-up homework assignment.

 Introducing the activity

Materials for each group of 4 students include:
1. 2 grid sheets (one for each pair of students)
2. 30 dominoes (15 for each pair of students) or print and cut out these paper dominoes
3. Scissors (if necessary)
4. Recording sheet for discussion questions

Ask the students to work in pairs within their groups to

show if it is possible to cover the 6X5 grid with their dominoes.

Allow enough time for the pairs to complete the task.

Instruct the 2 pairs in each group to compare answers.

1. Did they have the same answer?
2. If yes, challenge the groups to find more than one answer.
3. If no, challenge the group to find how many possible answers there are.
4. Instruct each pair of students to describe how the dominoes cover the grid.
5. Encourage the use of the terms vertical and horizontal.
Although this may seem a simple exercise the students are becoming familiar with
1. covering a given grid.
2. considering that there may be more than one correct "answer."
3. using the terms vertical and horizontal

 Building a Brick Wall

Materials for each group of 4 students include:
1. 4 sheets of graph paper
2. 30 dominoes or print and cut out these paper dominoes
3. Scissors (if necessary)
Display the following task for your students:

As your group investigates this problem each student records the diagram, process, and solution.

Your Brick-Wall company wants to produce a catalogue of designs to show to customers. If they miss out on a design then a competitor may offer it. So your company had better include all the designs you can. The brick walls are to be two units tall. The bricks are all the same size, 2 units by 1 unit.

How many different ways can you make a wall using
1. one brick?
Hint: There is only 1 possible pattern.
2. two bricks?
Hint: There are 2 possible patterns.
3. three bricks?
Hint: There are 3 possible patterns.
4. four bricks?

5. five bricks?

6. six bricks?

...

7. any number of bricks?

There is a pattern that emerges as you investigate this problem. For an explanation see:

 Project Idea

Instruct the students to use their findings to create their Brick-Wall catalogue including:
1. A title for their company
2. Sketches of the possible wall designs
3. An explanation of how to figure out how many possible designs there are for each certain number of bricks to be used before repeating the design.

 Technology Idea

There is a simple freeware program (Macintosh only) that could be used very easily to model the domino problem.
See sample here.
Download software: Mosaic Patterns by Kurt Kaufman.