So I know the second half of my Algebra 1a class is going to be focusing on the linear part of Algebra 1. I want to look at multiple representations of linear relationships, and I want to tie these relationships to something they can see and measure. Here is what I have done and I will also talk about what I want to do.
Start with solving proportions
I have known that I ultimately want my students to be able to interpret position versus time graphs, so I decided to start with introducing ratios and solving proportions.
I started the worksheet above with this idea from Sarah Hagan (of Math = Love Blog fame). I wanted to stay away from even mentioning cross multiplying when solving proportions because I see students try and use it everywhere… regardless if it applies or not. So I really emphasized solving an equation techniques. I also wanted students to get used to working with units. These numbers have meaning. Please state the meaning.
We spent a lot of time writing and solving proportions. Some were doing really well with it. I then wanted to begin a graphical representation of ratios and all the proportion solutions.
Students were expected to come up with their own scale for the graphs. Also, I have been emphasizing all year long that a graph always needs three things, the quantity for both axes, the units for both axes, and the scale for both axes.
So now I wanted students to find other solutions from looking at the graph. Also notice that I am asking students to write the ratio of distance over time. Again, that is to preface our slope discussion, and to show that this distance over time has meaning!
There is more to come… part 2 will be up soon.