Here is a link to an investigation I made that uses the HP prime in a way that allows students to discover and make connections between the many forms of linear equations:  specifically, point-slope, standard, and slope-intercept forms.  I will be trying this next week with my Algebra 2 with Trig students during the long block.  I’ll report back on how it goes.

In this investigation the students use both the Function and Advanced Grapher apps on the HP Prime to discover that a line drawn by connecting two points (with their fingers, what fun!) looks exactly the same as a line drawn from an equation in point-slope form and exactly the same as a line drawn from an equation in standard form and exactly the same as a line drawn from an equation in point-slope form.  How can this be?  They use their algebra skills to realize that all of these different forms can be simplified down to the same equation.  And the pictures on the calculator confirm this!  And they will hopefully understand which pieces of information (points, slope, intercept etc) can be pulled from any given equation to produce a picture of a line.

A summary table at the end pulls this all together.  Why do I like to “teach” linear equations this way?  While I could traditionally teach the students the many forms, this investigative/discovery style is a nice way to use a long block (and to cover two lessons without them realizing it).  It also teaches them to notice patterns, to make deductions, to use their algebra skills as a way to make sense of seemingly contradictory information.  And, simply it’s more fun for me (and hopefully them too!).  I’m sharing this here because this same activity could be duplicated in Algebra 1 and potentially even PreCalculus.  That means all of you (Mathsquad) may be able to use this!