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.
www.samzyworld.com Determine 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.
Review. 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.
Begin 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?"

Make multiple representations
( mathematical models/math-models),
approaching your problem; here are
examples of several forms of
representation :
Verbal. Write your own description of the
problem (in your own words).
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).
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));
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.
6
Double-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!
7
Check 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.