# Exploring relationships between two quantitative variables – progression part 1

I have been thinking about a progression for scatter graphs for a few months now.  The big question for me has been what is the progression of ideas before we get to level 6.  Through talking with others and reading extensively the following progression is mooted.

Curriculum level 4- introducing the idea of graphing paired quantitative variables, mostly through examples where we are looking at equivalence e.g. height = arm span. Leonardo da Vinci’s Vitruvian man is full of ideas about equivalent proportions of the human body and can provide a starting point for this sort of exploration.   See  My Modern Met website, click here  for a fuller list of these.

These types of exploration allow students to start to explore using scatter graphs and thinking about where the pairs of data are equal, where one variable is larger than the other and vice versa. Looking at the difference between the two variables can be interesting as well and a useful additional analysis to do.

This video shows how to do this using CODAP.

Further ideas for level 4: this equivalence idea can be used for situations where students start to explore before and after data.  For example looking at whether practice and instruction improves throwing and catching ability.  Data about students throwing and catching ability is captured at the start of the unit of work.  They engage in the unit of work designed to improve their throwing and catching ability.  At the end data about their throwing and catching ability is captured.  The paired data is shown in a scatter graph, differences are calculated and the difference is graphed.  The two graphs provide a richer picture for description that either one by itself.