Day 3 Classwork - a Guide to Understanding "Patterns"
Shape Patterns: Study the pattern below.

 

1. Draw the next three figures in the pattern.
2. Draw the 35^th square in the pattern.
   

 

Solutions:

1. The pattern consists of squares with one corner shaded. The corner that is shaded is rotated in a clockwise direction. The next three figures are drawn below.



You may find a different pattern. For example, the seventh square may be the same as the fifth square, the eighth square may be the same as the fourth square, and the ninth square may be the same as the third square.

2. The pattern repeats after every 4 designs. Since 32 is the greatest number less than 35 that is disible by 4, the 33^rd square will be the same as the first square.
   

     
   
   The 35^th square will have its upper right corner shaded.

 

Numeric Patterns: The numbers 2, 4, 6, 8, 10, and 12 form a pattern called a sequence. A sequence is a set of numbers in a specific order. The numbers in the sequence are called terms.

Find the next three terms in each sequence.

a. 7, 13, 19, 25, …	A study of the pattern in this sequence shows that the numbers increase by 6 units. 7 + 6 = 13, 13 + 6 = 19, 19 + 6 = 25 The next three terms are 31, 37, and 43.
b. 243, 81, 27, 9, …	Each term is 1/3 of the term before it. 243 * 1/3 = 81, 81 * 1/3 = 27, 27 * 1/3 = 9 The next three terms are 3, 1, and 1/3 9 * 1/3 = 3, 3 * 1/3 = 1, 1 * 1/3 = 1/3

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