I gave the students the equation y=1/2x + 8 and everyone had a white board.
The first task was to write an equation parallel to this equation.
The second task, an equation steeper than this equation.
For those few students that put a fraction for the slope that was less than 1/2,
I simply stated that their equation was not steeper than mine.
They sat there stumped.
I assured them that this mistake was one that would help them down the road.
Which got the attention of other students,
Who now wanted to learn from a mistake!
The third task, the one where I would see how deep their understanding really was,
was to write an equation that was less steep.
I knew that I would see negative numbers pop up as the slope.
And this was one of my goals of our review,
To uncover a misconception and unravel it.
To my surprise, only one student in each class put down a negative number for the slope!
I was expecting so many more.
Also to my surprise, students were showing fractional understanding
As the fractions they were using were mostly less than 1/2.
Wow!
After summarizing what kind of slopes would be less steep.
We dove into the negative slope.
Many students thought that since a negative is less than 1/2 numerically,
As the slope it would have to be less steep.
Another surprise that came out of the lesson
was being able to push their thinking towards what makes perpendicular lines.
When the slope of -2 was given,
We were able to use comparison strategies to figure out what slope makes a line perpendicular to another line.
Score!
We just moved our thinking to the high school level!
Thin slicing.
Whole group discussions.
Mistakes.
When all mixed together, make a great learning experience!
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