'Use the power of these virtual manipulatives to play with the ideas behind scattergraphs, correlation and lines of best fit.'
The study of statistics at school is a great opportunity to show mathematics in a practical context, but this activity is really about playing with the more abstract mathematics behind the statistics. In doing so an extra depth of understanding is added to the study of the concepts in context.
This activity makes use of two excellent and freely available virtual manipulatives that really allow and encourage playing. By entering and moving points on a scattergraph, the aim is to explore the features of different types of correlation, the positioning of a line of best fit and the idea of measuring the degree of correlation.
A paragraph to explain what the aims of the activity are. This is useful for student and teacher and can be phrased equally. Stuff for teachers only is on the teacher notes page.
Scatterplot and Correlation
Least Squares Regression Concept
Scattergraphs, regression lines and correlation coefficient.
New Applications and interpretation - SL4.4 and SL4.10 Studies - Section 4.2 and 4.3
Here follows an outline if what the task is. If students are not reading this page then the teacher will need to show and give this overview.
- Using any internet enabled device(computer/phone/tablet), students use the above virtual manipulatives.
- Investigate 'Types of correlation' by adding and moving points so that they show different types of correlation.
- Investigate lines of best fit by exploring where they 'look like' they should go and then checking.
- Try and add/move points so that the line of best fit is a given equation.
- Try and add/move points so that the correlation coefficient is a given value.
- Take screenshots of the results to keep as a record.
- Fun, two-player game to develop a good conceptual understanding of the least squares regression method. To get good at winning the game motivates, and requires, students to gain a deeper understanding of the sort of data that makes it difficult to estimate a line of best fit without using the least squares method.
I did it my way!
As a practising maths teacher I know that most of us like to give activities our own little twist and do them 'our way'. It would be great to add a little collection of 'twists' from users. You can either add your twist to the comments section below or e-mail them directly to me at firstname.lastname@example.org In time some of these twists may appear here....