{"id":130,"date":"2017-07-07T08:45:55","date_gmt":"2017-07-07T08:45:55","guid":{"rendered":"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/?post_type=chapter&p=130"},"modified":"2017-12-26T23:50:35","modified_gmt":"2017-12-26T23:50:35","slug":"the-last-step","status":"publish","type":"chapter","link":"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/chapter\/the-last-step\/","title":{"raw":"The Last Step","rendered":"The Last Step"},"content":{"raw":"

A lot of people \u2014 from Polya to the writers of the Common Core State Standards and a lot of people in between \u2014 talk about problem solving in mathematics. One fact is rarely acknowledged, except by many professional mathematicians: Asking good questions is as valuable (and as difficult) as solving mathematical problems.<\/p>\r\n

After solving a mathematical problem and explaining your solution to someone else, it is a very good mathematical habit to ask yourself: What other questions can I ask?<\/p>\r\n\r\n

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Example:\u00a0Squares on a Chess Board<\/h3>\r\n

Recall Problem 3, \u201cSquares on a Chess Board\u201d:<\/p>\r\n\r\n

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How many squares of any possible size are on a standard 8\u00a0\u00d7 8 chess board? (The answer is not 64! It\u2019s a lot bigger!)<\/p>\r\n<\/blockquote>\r\n

We have already talked about some obvious follow-up questions like \u201cWhat about a 10\u00a0\u00d7 10 chess board? Or 100\u00a0\u00d7\u00a0100? Or [latex]n\\times n[\/latex]?\u201d<\/p>\r\n

But there are a lot of interesting (and less obvious . . . and harder) questions you might ask:<\/p>\r\n\r\n