MPM1D1 - Day 70 Equations of Parallel and Perpendicular Lines

During yesterday's warm-up, one group was convinced that two of the lines were perpendicular. Based on that comment I thought today's warm-up should be about perpendicular lines.

Once groups found equations for the lines I asked what they knew about how the lines intersected. They responded with the point of intersection and I asked if there was anything else. When they told me that the lines were perpendicular I asked how they knew the lines were perpendicular. Some groups could justify their claim immediately, while others need time to formulate their ideas.  

After the warm-up we moved right into finding equations of parallel and perpendicular lines. We had a conversation to remind them about how to find the equation of a line given two points and what it means for lines to be parallel or perpendicular. They worked on these problems at the board:

None of the groups had any trouble with the first two questions. A couple of groups struggled with the third and all groups needed some reminders about rearranging equations for the last question. When they were finished they went to work on some practice questions.

MPM1D1 - Day 58 Parallel and Perpendicular Lines

Today's problem was one that I was reminded of at a recent professional development session (thanks @chrisleechss ).

This question generated a lot of discussion. Is 1 a big slope? Does it matter if it's negative or positive?  There were lots of good conversations as students continued to solidify their understanding of slopes. For groups that finished early I asked how their answers would differ if they were allowed to use the numbers 0-9.

The consolidation of this problem led us to talk about horizontal and vertical lines. We talked (again) about the slopes of these lines but we also talked (unexpectedly) about the equations of horizontal and vertical lines.

The main lesson for today was investigating parallel and perpendicular lines. I gave this investigation. It was good for students to practice graphing lines but I think I need to rework it for them to get more out of the perpendicular lines portion.

We'll consolidate the investigation tomorrow.