In the earlier grades you did lots of work with patterns like lining up:
SHAPES (triangle, square, circle, triangle, _____, _____ what comes next??),   COLORS (red, blue, blue, blue, red, blue, blue, blue, red, ____, _____ what comes next?)

But you can also use patterns to understand many math more difficult concepts.  Let's look at the concept of  square numbers.  Get a piece of grid paper and draw an array for the number four.   You could draw it two different ways:  

and write it two different ways:   4 x 1  or draw a 2 x 2 square. Therefore 2² = 4

THE next square number is nine.  On a piece of paper you can draw an array for the number nine two different ways also.

THE next square number is 16.  Without drawing a picture can you  figure out that it would be a picture of a square with a side equal to 4? Therefore 4² = 16

	Can you see a pattern here? Any number that can have an array drawn as a square, is a "square" number.
Some more examples: 25 = a 5 by 5 square = 5²;                    36 = a 6 by 6 square = 6²; 49 = a 7 by 7 square = 7².                      It works for larger numbers also:                                   121 = an 11 by 11 square = 11²

Now let's look at simple numerical patterns and see if an algebraic expression can be written.

The following pattern uses addition, find the next three numbers. 1, 7, 13, 19, 25,...     +6   +6   +6   +6   1 7 13 19 25 Write the number you must add to each number to get the next number. Use the pattern to calculate the next three numbers.     +6   +6   +6      n= 25 31 37 43

The rule would be to add 6, therefore the expression is  n + 6

Remember, if possible, find a pattern to make problem solving easier!

Ready for Practice?