By the end of this lesson, students can:
Use information technologies to investigate bivariate-numerical-data sets; where appropriate, students use a straight line to describe the relationship, allowing for variation (ACMSP279)
Introduction: Class discussion - Pause, think and predict (LIT) [15 minutes]
The teacher presents various scatter-plots that illustrate a strong positive correlation, a weak correlation or no correlation, including cases of positive and negative correlation. These graphs should have no labels on the axes. The teacher asks students to think-pair-share and propose labels for the axes that would be reasonable for the different graphs displayed. The teacher should not mention any statistic-related vocabulary proactively using student discourse to describe the associations in the scatter-plots.
The teacher defines the term ‘correlation’ by connecting it to previous discourse. (The teacher can support students' literacy by continually substituting correlated to describe associations between two variables.) (LIT)
Working in pairs, students create a claim using two variables that they believe will have a strong correlation (linear relationship), for example: Is there a relationship between height and torso length? The students vote. Hand up: agree; hand down: disagree, and discuss the validity of the claims.
Body: Graphing activity (ICT) [30 minutes]
Students use given data collected either from real life, or a reputable source, and plot a scatterplot.
With teacher guidance as necessary, students plot their scatterplots using the following resource: http://www.shodor.org/interactivate/activities/Regression/
This resource allows students to plot a scatterplot and fit their own line of best fit and compare it to the actual line of best fit. The resource also gives students an "r value" which the teacher can mention as a number that indicates the strength of the correlation. The teacher can scaffold their thinking and fitting of their line of best fit through prompting questions - What line best fits the pattern of the data? Do we include the points that don't fit the trend? Should we draw the line through the end points? Why/Why not?
After considering their scatterplots, students describe the strength of the correlation. Here, they use language such as ‘linear relationship’, ‘positive’ and ‘strong’, with the teacher writing these words on a whiteboard as they arise for future lessons on trends.
The teacher can create more claims, such as ‘My leg length is double my waist measurement’. The students attempt to justify this claim by measuring class members’ legs and waists and plotting the data on a scatterplot.
Extension: DESMOS Graphing lines of best fit [20 minutes]
Students explore how lines of best fit allow them to predict data points without having real data.
Questions to ask students:
Conclusion:
Ask students to complete the following worksheet that asks them to plot points and draw a line of best fit.