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Algebra Connections Glossary
Ways of Thinking   
  This course emphasizes five Ways of Thinking about mathematical ideas: justifying (explaining and verifying your ideas), generalizing (predicting behavior for any situation), making connections (connecting your ideas to other ways of seeing or to past or future learning), reversing thinking (solving problems “backward and forward”), and applying and extending (applying your knowledge to new contexts and extending it to help solve new problems).  For example, when confronted with a new type of mathematical problem, you might solve it by reversing your thinking to work backwards or by trying to make connections to problems you have seen before.  Once you have a solution, you might be asked to justify your solution or generalize it to a broader class of problems.  Finally, you might then apply what you have learned on this problem to the next new type of problem that comes along.
web   
  See “representations web.”
x-coordinate   
  See “coordinate.”
x-axis   
  See “axes.”
x-intercept(s)   
  The point(s) where a graph intersects the x-axis.  A graph may have several x-intercepts, no x-intercepts, or just one.  We sometimes report the x-intercepts of a graph with coordinate pairs, but since the y-coordinate is always zero, we often just give the
x-coordinates of x-intercepts.  For example, we might say that the x-intercepts of the graph below are (0, 0) and (2, 0), or we might just say that the x-intercepts are 0 and 2.

x → y table   
 

An x → y table, like the one at right, represents pairs of values of two related quantities.  The input value (x) appears first, and the output value (y) appears second.  For example, the x → y table at right tells us that the input value 10 is paired with the output value 18 for some rule.