In mathematics, more than any other grade-school subject, kids are asked to recognize and use patterns to solve problems. Exercises are given that contain the patterns the kids are taught to recognize. These exercises sometimes contain not only the "target" pattern but extraneous patterns, too. I wrote this page to highlight some of the patterns I found in my kids' math assignments and to help find and use the patterns to solve problems.
Here's an example similar to ones found in Matthew's 6th grade math book:
The student is supposed to see a pattern, and fill in the blanks, then write an equation for calculating the values in the table. Matthew looked at this and saw the y values were increasing by seven, so he filled in "34" and "41", but that's not the "right" answer. Matthew got it wrong because he recognized an extraneous pattern that wasn't intended by the textbook's author. The pattern Matthew was supposed to see was this: in every row, the y value is obtained by subtracting one from the x value, dividing it three, multiplying it by seven, then subtracting one. Following that procedure, the right answers are "48" and "62".
Here is the procedure for solving this type of problem.
Word Problems, including percents, and the meaning of the words "of", "per", and "what", and much, much more.
The Expansions page gives methods for calculating values, such as Gauss' method for calculating pi.
The webmaster and author of this Math Help site is Graeme McRae.