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: Figure out both where you are and where you need to go before you start working. Look carefully at the problem to be sure you know what the question is. Identify the known and the unknown quantities. Start thinking about the techniques that could beuseful, and the kinds of answers you expect to find.2) Look for familiar patterns: Use your experience to guide you. Have you seen similar problems? Is there anything about the form of an equation or the shape of a graph or the phrasing of a question that seems familiar? If you can compare formulas or terms or shapes to problems you've solved before, it's a good bet that the strategy you used to solve them last timewill help again now.3) Break up the problem: A big complicated problem is often just several small and simple questions stuck together. See if there are pieces you can pull out to work on separately. Maybe you don't know how to find all the variablesall at once, but you might be able to figure them outone at a time. Once you solve the easy parts, those answers can help you get the rest of the way. Divide and conquer!
4) Visualize: A picture is worth a thousand words. Sometimes a verbal description or an equation don't really speak to you. A quick sketch or a careful graph can sometimes make relationships clear in a way that words or numbers don't. A chart, table, or diagram might spark a fresh understanding of the situation. When you create a visual representation of a problem, you give yourself a whole new way to look for answers.5) Try different techniques: If at first you don't succeed, try, try again, isn't just a cliché; it's also a good idea. There will be times when the first approach you try doesn't get anywhere. Don't give up, try another way. Think about why one technique didn't work—did it give you an answer, but not the one you needed? Maybe you broke up the problem without realizing it, and this answer will lead to other answers and eventually to the right answer. Did you get stuck partway through because you didn't have enough information? Perhaps you need to go back and make sure you understand the problem.6) Don’t give up!The truth is out there. If you keep trying, and vary your approach, you will getit. Take a second to step back and look it over with fresh eyes. Try going back over your notes. Eventually, you’ll find what works!Recalling Mathematical PropertiesIf you’ve ever played a video game or packed a suitcase for a long trip, you know that the order and placement of objects makes a difference in the outcome. Some things can be moved around to wherever they are convenient, while others can only go a certain way or they won’t fit.The arrangement of numbers and variables in algebraic expressions works like that too. Some situations allow us to switch values and operations around. Others require that numbers can only be handled one way or the process will go wrong. The ability to play with the parts of an equation (or not) are described by mathematical properties.The same properties that you learned about when you studied arithmetic also work in algebra. If