# Lesson Overview

Solar energy systems work by placing solar energy cells on the roof of a building and using these to capture energy from the sun. This energy is then converted into electricity.

Through the use of technology, the electricity generation data provided by solarschools.net enables students to obtain electricity generation data from schools in several geographical locations in Australia. By using this and data obtained from the Bureau of Meteorology, students can compare electricity generation between schools in the same region.

This activity has been designed to show real life applications of Mathematics. It can be used as a stand-alone activity or as a basis for an assessment task. The activity relates to the curriculum links suggested below but is not intended as a comprehensive coverage of all aspects of the listed outcomes.

# Key Focus

• Students should be encouraged to develop a working knowledge of some elementary concepts in exploring and interpreting data and encouraged to develop skills in recognising different types of data situations.
• In developing this knowledge, students will become aware of some fundamental concepts used in models for data.
• Calculators (or computers) should be used routinely for calculations and graphical displays. The emphasis is on exploration and inference and should also aim to help students develop confidence through a range of life-related scenarios.
• Students' learning will be enhanced by the use and/or formation of models as required and the use of electronic technology.

# Queensland Curriculum Mapping

## QCAA Mathematics A Senior Syllabus (2008)

#### Exploring and Understanding Data

Subject matter:

• Use of summary statistics to draw and analyse conclusions, represent data and make inferences (SLEs 1–5)
• Interpretation and use of sample statistics (including sample means and medians) as estimates of parameters to predict underlying population values or of values in a model (SLEs 1–5)
• Interpret relationships between variables and make predictions by identifying and using trend lines (both linear and non-linear) (SLEs 6, 12, 13).
• Sample standard deviations and interquartile range as descriptors of spread (SLEs 7–12)

## QCAA Senior Mathematics – General (v1.1 2019)

### Unit 3: Bivariate Data, Sequences and Change, and Earth Geometry

#### Topic 1: Bivariate Data Analysis

##### Identifying and describing associations between two categorical variables

In this sub-topic, students will:

• Define bivariate data.
• Construct two-way frequency tables and determine the associated row and column sums and percentages.
• Use an appropriately percentaged two-way frequency table to identify patterns that suggest the presence of an association.
• Describe an association in terms of differences observed in percentages across categories in a systematic and concise manner and interpret this in the context of the data.
##### Identifying and describing associations between two numerical variables

In this sub-topic, students will:

• Construct a scatterplot to identify patterns in the data suggesting the presence of an association.
• Describe an association between two numerical variables in terms of direction (positive/negative), form (linear) and strength (strong/moderate/weak).
• Calculate and interpret the correlation coefficient (????) to quantify the strength of a linear association using Pearson’s correlation coefficient, where covariance and standard deviation are determined, using appropriate technology.
##### Fitting a linear model to numerical data

In this sub-topic, students will:

• Identify the response variable and the explanatory variable
• Use a scatterplot to identify the nature of the relationship between variables
• Model a linear relationship by fitting a least-squares line to the data
• Use a residual plot to assess the appropriateness of fitting a linear model to the data
• Interpret the intercept and slope of the fitted line
• Use, not calculate, the coefficient of determination (R2) to assess the strength of a linear association in terms of the explained variation
• Use the equation of a fitted line to make predictions
• Distinguish between interpolation and extrapolation when using the fitted line to make predictions, recognising the potential dangers of extrapolation.
##### Association and causation

In this sub-topic, students will:

• Recognise that an observed association between two variables does not necessarily mean that there is a causal relationship between them
• Identify and communicate possible non-causal explanations for an association, including coincidence and confounding due to a common response to another variable
• Solve practical problems by identifying, analysing and describing associations between two categorical variables or between two numerical variables.

# ACS Codes

ACMGM048 ACMGM049 ACMGM050 ACMGM051 ACMGM052 ACMGM053 ACMGM054 ACMGM055 ACMGM056 ACMGM057 ACMGM058 ACMGM059 ACMGM060 ACMGM061 ACMGM062 ACMGM063 ACMGM064 ACMGM065

##### Curriculum Subjects
• General Mathematics