In this age of technology it is sometimes hard to keep students on task and focused with simply pen and paper (white board and marker). Often, to genuinely grab the students interest and really engage them the teacher must someone incorporate some aspect of technology into their lesson. That’s why I recommend interactive websites. These sites allow students to be hands on or engaged as a whole class. They also allow students to see (and create) multiple examples of problems explained as well as allowing them to see how math rules, postulates and theorems always hold true.
One of my favorite websites for such student interaction is call Math Warehouse. Math Warehouse is a website designed for interactive math. It has sections for Algebra, Geometry, and even Trigonometry. It even offers online graphing, scientific and matrix calculators. But I wanted to specifically talk about using this website to help students discover the relation in slopes of parallel lines and perpendicular lines ( Click Here).
The CCSS for knowing Parallel and Perpendicular lines is as follows:
CCSS.Math.Content.HSG-CO.A.1 – Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
The following exploration can be used in a lesson to help students understand the precised definitions of parallel and perpendicular lines, as well as be a review or re-engagement lesson for students who struggle with the definitions and application of parallel and perpendicular lines.
The below screen shot was taken from near the bottom of the page at the above link. It show the interactive applet that Math Warehouse has to help students understand parallel and perpendicular lines. The app can be used in three ways. It be used to manipulate only parallel lines, only perpendicular lines, or as the picture shows, both parallel and perpendicular lines at the same time.
This app helps students to understand the relationship of the slopes of parallel and perpendicular lines by giving both a graphical representation as well as the equation of the lines. This app can also be used as an exploration by having students observe and note what happens to the slope of a line perpendicular and/or parallel to a give line. This app works great as a whole class activity because even though each student will not get the change to move the points and change the lines, some students can be chosen to come up to the computer to move the lines, or even just give points for the teacher to move the lines to. This helps students make the observation that the slopes of parallel lines are always the same and the slopes of perpendicular lines are always opposite reciprocals. Then, they will be able to see that this is always true, not matter what line you have.
I think that this helps students understand more than just drawing examples on the whiteboard becuase they can see many examples. This can also help to gain and keep students interest and involvement throughout the lesson.