High School: Algebra
Creating Equations HSA-CED.A.2
2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
This standard has two significant components. The first is translating word problems into equations with two or more variables. The more the merrier. Well, maybe not in this case. Translating word problems to create simple equations with two or more variables is not that different conceptually from creating equations with one variable.
The main difference is that more complicated mathematical relationships such as systems of equations, functions, and proportions may develop (along with nausea, headaches, and spontaneous yodeling). In any case, this aspect of this standard should be taught with the previous one.
The second component is creating graphs of equations on coordinate axes, which incorporates multiple skills such as visual perception, interpreting data, and synthesizing information. Such graphs relate to equations with multiple equations by relating one variable to another.
Take lines, for example. In the form y = mx + b, we can look at either x or y and any defined value for x will give us a defined value for y, and vice versa. Graphs can help visualize these relationships between variables and facilitate the connection of equations to the graphs that represent them. Yearnin' for more graphin'? Don't worry. There'll be more down the line.