Slope in algebra I

Question

What is a good project for teaching y=mx + b and having students discover slopes of lines in classroom or on the classroom buildings?

Answer 1

I used to begin by getting students on a large piece of A3 squared paper (with axes drawn) to plot $(x, y)$ coordinates for those numbers that have a difference of $4$. This would then teach them about the line $y=x+4$ whether they choose both positive or negative numbers is interesting; in nearly all cases most groups chose coords that could be place in the top right quadrant.

Anyway; once this line has been plotted; repeat with (say) differences of $5, -3$ and $0$.

After they know about the lines $y=x+c$ for some $c$ I went onto more creative worded requests like "Plot $20$ coordinates $(x, y)$ such that the $y$-coordinate is twice as much as the $x$". Obviously this teaches about $y=2x$. Repeat similar requests to the above, scaffolding the relationship in their minds, then after a while, they begin to see the role of the coefficient of $x$ and the constant term.

The slope of the line becomes obvious when you begin to choose those different multiples, even choosing fraction say $\frac{1}{2}$ is an interesting conversation. After a little thought though, the relationship becomes obvious in their minds, or that was my experience.

The trick then I found, was to be able to give them the task of "sketch the line $y=2x+1$ for $x \in (-6, 6)$". This took a few lessons; I had a group of 14 year olds who were working at C/D grade GCSE. It worked after a few lessons and they were able to line sketch quite easily by the end of it.

The tough bit was moving onto coordinates of intersecting lines....