Today we attempted to make the bridge from the concept of slope in the geometry realm
to slope in the algebra world.
Talk about going from concrete to abstract in one big leap.
To begin, students worked through a graphing lab on their graphing calculators
As they tried to make sense of the slope-intercept equation, y=mx+b.
The lab led students through a series of equations to graph and then evaluate what each graph/equation was displaying.
The first series of questions focused on slope...particularly parallel slopes.
The second set of questions focused on the y-intercept.
Students then created equations to fit specific criteria, based on the learning that had just occurred.
We then debriefed our learning as a whole group.
This allowed students to share their findings.
It also allowed students a second chance to find understanding.
As we had our math conversation, we took notes on slope (m).
We then moved the discussion to look at the following equations.
Which equation would create the steeper line? Which equation is less steep?
It was a great way to introduce the concept of x being 1x.
y = 2/3x +3
y = 4x + 1
y = x + 5
(Using one of our free graphing calculator apps on the iPads, each line was a unique color. Before showing the graphs, I had students analyze the equations to decide which one was steeper and keep the answer in their head. I then counted to three and they all had to shout out the color. Everyone was participating and we could have a meaningful discussion afterwards.)
Moving forward is a good thing. If you don't move, you become stagnant. If you become stagnant, you smell. (I'm going with a creek bed analogy here...stay with me). "It Is What It Is" helps us to keep our sanity as we try new things, but at the same time we should never settle for "what it is". We should constantly reflect and learn to move our teaching and our student's learning to higher levels so the classroom doesn't turn stale.
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