# Linear modelling of the life expectancy of Canadians ## Overview

In this lesson, students will gain a better understanding of the parameters of the slope-intercept form (y = mx + b) of a linear equation. They will extract data from E-STAT on the life expectancy of Canadians, both overall and separately for males and females, and import them into spreadsheet software or dynamic statistical software. Within the software, students will approximate a line of best fit and then will compare their approximation to the software-generated line of best fit. By comparing the equations of the line of best fit for males and females, students will estimate, using graphical techniques, the point of intersection. Students will also practise converting linear equations to standard form (Ax + By + C = 0) and performing slope calculations.

Contributors: Jennifer Hall and Joel Yan, Statistics Canada

## Objectives

• Through investigation, determine the relationships between the graphs and the equations of linear functions
• Through investigation, determine the basic properties of linear functions
• Explain the role of slope and y-intercept in the slope-intercept form (y = mx + b) of a linear equation
• Interpret the meanings of points on scatter plots that represent linear relations
• Collect data that may be represented by linear functions from secondary sources
• Fit the equation of a linear function to a scatter plot using an informal process, and compare the results with the equation of a line of best fit produced by using graphing software
• Determine the point of intersection of two linear functions using graphical methods

• Mathematics

## Duration

• Two to three 75 minute periods

## Prior knowledge

• Linear equation in slope-intercept (y = mx + b) and standard (Ax + By + C = 0) forms
• Slope equation • Basic knowledge of E-STAT and spreadsheet or dynamic statistical software

## Classroom instructions

1. Discuss important properties of the slope-intercept form of the linear equation as a review.
2. Using the computer projector, demonstrate to the students the important features of E-STAT.
3. Hold a brief class discussion on the topic of life expectancy to assess students' prior knowledge and share information on the topic. Discuss what factors would lead to an increase or decrease in life expectancy.
4. Have students complete (independently or in pairs) Worksheet 1: Overall life expectancy: Student version (also available in .PDF printer-friendly format) and Worksheet 2: Life expectancy by sex: Student version (also available in .PDF printer-friendly format), using the E-STAT instructions and statistical software instructions provided.

## Enrichment

• Discuss factors leading to sex differences in life expectancy.
• To compare with more recent data, complete the activity using CANSIM table 102-0511.
• To compare with older data for each of the provinces, please see the Canadian Human Mortality Database on the Université de Montréal website. For life expectancy data on 38 countries, in some cases going back to the 18th century in some cases, please see international Human Mortality Data base.
• Investigate life expectancies around the world. What factors lead to Canadians having such high life expectancies compared to people in African countries, for instance? What factors lead to Canadians having higher life expectancies than people in some other developed nations?

## Evaluation

Students can be informally assessed on their work habits and computer skills throughout this activity. They can be formally assessed via the worksheets, which can be handed in to be marked using a marking scheme of the teacher's choice.