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How to Solve Math Problems
Edited by Jack Herrick, Ben Rubenstein, Brigitta M., Keegan and 37 others
Although math problems may be solved in different ways, a general method to visualizing, approaching and solving math problems is outlined in the steps found here.
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EditSteps
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1Determine what kind of math you are having difficulty with. Is it multiplying fractions? Solving quadratic equations? Knowing where you need more knowledge is key for focusing your studying.Ad -
2Review. Most math textbooks have a lesson to read, covering new concepts directly before each problem set. If you are having trouble with the newest formula or method, that is where to start.- Seek help if necessary. Asking a teacher, parent or mathematically gifted friend for help is often the best way to receive direct guidance and have your questions quickly answered.
- There are many websites and youtube videos that offer free tutorials or lessons in basic math concepts. Consider visiting one to practice or quickly reference a formula.
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3Begin to solve the problem. Now that you've reviewed, it's time to apply your skills.- Determine what the problem is asking you to solve. There is a big difference between being asked to find the cosine and the sine. Read the directions carefully.
- Guess and check, "Hmm, I guess it is ___, so then it would be ___. I'll see whether that works."
- Use objects, manipulatives, to model the problem
- Use logical reasoning: "If this is ____, then that would give me ____ ..." -- or the negative version, "If not this ____, then it's not that ____" ...
- Look for a pattern -- how series or a sequence changes from one member (element) of a list, back to the previous, and also forward to the next member.
- Do a process -- act it out -- i.e.: experiment as in physical or real world problems.
- Work backward -- reverse the processes of a possible solution to see whether it may connect
- Classify the kind of problem, process, or pattern it fits.
- What do I not know or have (Ask this question: "Can I find an intermediate step toward solving this, for the situation?")
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4Write down your work, step by step. This will allow you to track/double check your thinking and your process for getting the results. Avoid trying to solve the entire problem in your head, getting lost/confused. -
5Make multiple representations (mathematical models/math-models), approaching your problem; here are examples of several forms of representation:
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Verbal. Write your own description of the problem (in your own words).
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Gather data -- using tally marks to keep the count
- x,y chart/table. Often a table can be made of data in columns (x,y) and rows (for example: money made on sales of candy each week).
- Drawing or diagramming. For example: draw the described physical problem situation (possibly involving two dimensional sketch, a geometric figure, or perhaps trigonometry).
- Mapping (if that applies).
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Graphing. Called models, many types of relations and process dynamics may be graphed in mathematical, physical, biological, social and information systems data. Graphs may be of numerous types, but a basic is to graph paired information (pairwise relations), such as growth or decay over a period of time:
- Bar graph;
- Pictograph;
- Cartesian points (x,y) graphed in the Cartesian plane.
- Line graph joining the results of data (such as growth) over time;
- Time-line -- a special graph used for [historical] information over time;
- A circle graph/pie chart = total 1 whole or 100% (a kind of "pizza math")
- Scatter plot, point graph of data (one example is a distribution of data pairs);
- Trend line/simple linear regression (the central tendency compare to the median or average) -- a linear representation of paired data, shows the "average" line, in a data array/distribution;
- Note: A multivariate linear regression has two are more variables (for example, three variables: (1st variable) measure the growth of plant seedlings, (2nd variable) for each of two experimental temperatures, (3rd variable) over the same time period(s));
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Conjecture/structure a function -- another kind of model perhaps, y = f(x) = ______ (using a mathematics, physics or geometric equation or formula) may be constructed to fit the problem parameters (facets);
- Check your data over the domain of x and the range of y (decide parameters); ask: "Is it linear or non-linear?"
- Graph your proposed function.
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Verbal. Write your own description of the problem (in your own words).
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6Double-check your work. Did you drop any decimal places or the decimal point? Accidentally write the numerator as your denominator? Now is the time to find out! -
7Check your answer for reasonableness, accuracy and repeatability.- If your answer doesn't match the correct one, go back and check your work for where you may have made a mistake.
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Categories: Surviving Mathematics
Recent edits by: Ms. Paprika, Maluniu, Jeff
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Español: Cómo resolver problemas de matemáticas, Italiano: Come Risolvere dei Problemi di Matematica, Português: Como Solucionar Problemas Matemáticos, Deutsch: Mathematik Aufgaben lösen, Русский: как решать задачи по математике, Français: Comment résoudre les problèmes de mathématique
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