Welcome to the Problem Of The Week (P.O.T.W.)!!!

PATTERNS AND GEOMETRY #1

Well, we’re done with pizza (and other circular objects) for a while. As an introduction to tessellations, we are moving on to squares. Specifically, counting squares.

If you draw a picture of 2 X 2 squares arranged in 2 rows of 2 columns, then you really have 5 squares (there will be 4 small squares and one big square).

1	2	5
3	4

Look what happens when we go to 3 X 3…

1	2	3	10		3	1	11		1	2	3	1	2	3	14
4	5	6			6	4			12		6	4	13
7	8	9	7	8	9	7	8	9			9	7

There are 14 squares in 9 squares arranged 3 X 3. (9 small squares, 4 medium squares, 1 big square)

Here are your questions:

· How many squares are in a 4 X 4 arrangement? Draw your answer like the two arrangements pictured above. (4 marks)

· How many squares are in a 5 X 5 arrangement? You are not required to draw your answer. Instead, look for the pattern to help you find the answer. (2 marks)

· Copy and complete the following table. (7 marks)

Arrangement	1x1	2x2	3x3	4x4	5x5	6x6	7x7	8x8	9x9	10x10
Number of Squares	1	5	14

TOTAL MARKS: /13

REMEMBER TO INCLUDE YOUR UNITS AND SHOW ALL YOUR WORK OR YOUR WORK WILL NOT BE CORRECT!!!

Have fun!

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