Lesson

Year 11 - General mathematics - Solar energy across regions

Lesson Overview

Year 11 - General mathematics - Solar energy across regions

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 the practicalities and concepts involved in collecting, handling, preparing, describing, presenting and summarising data, and of some elementary concepts in data quality and exploring data to describe key features.
  • Students should be encouraged to develop skills in recognising data quality and practical problems, and in commenting on data in context.
  • It is expected that calculators (or computers) will be used routinely for calculations and graphical displays.
  • The emphasis should be on the practicalities, concepts and interpretation of data, and also on students developing confidence through a range of scenarios.

Queensland Curriculum Mapping

QCAA Mathematics A Senior Syllabus (2008)

Statistics and Probability: Data Collection and Presentation

Subject matter relating to Data collection and presentation:

  • Practical aspects of collecting and handling data for observation, experimentation or survey, including possible data problems (SLEs 1–6, 9, 12)
  • Descriptions of key features of data with reference to suitable selections of graphical and tabular displays (SLEs 3, 10, 11, 12)
  • Data displays including scatterplots, simple and compound stem-and-leaf plots, and box-and- whisker plots (SLEs 4, 12)
  • Sample means and medians as measures of central tendency (SLEs 7–12)
  • Sample standard deviations and interquartile range as descriptors of spread (SLEs 7–12)

QCAA Senior Mathematics – General (v1.1 2019)

Unit 2: Applied trigonometry, Algebra, Matrices and Univariate Data

Topic 3: Univariate Data Analysis

Making sense of data relating to a single statistical variable

In this sub-topic, students will:

  • Define univariate data.
  • Classify statistical variables as categorical or numerical.
  • Classify a categorical variable as ordinal or nominal and use tables and pie, bar and column charts to organise and display the data, e.g. ordinal: income level (high, medium, low); or nominal: place of birth (Australia, overseas).
  • Classify a numerical variable as discrete or continuous, e.g. discrete: the number of rooms in a house; or continuous: the temperature in degrees Celsius.
  • Select and justify an appropriate graphical display to describe the distribution of a numerical dataset, including dot plot, stem-and-leaf plot, column chart or histogram.
  • Describe the graphical displays in terms of the number of modes, shape (symmetric versus positively or negatively skewed), measures of centre and spread, and outliers and interpret this information in the context of the data.
  • Determine the mean and standard deviation (using technology) of a dataset and use statistics as measures of location and spread of a data distribution, being aware of the significance of the size of the standard deviation.
Comparing data for a numerical variable across two or more groups

In this sub-topic, students will:

  • Construct and use parallel box plots (including the use of the Q1 - 1.5 × IQR = ???? = Q3 + 1.5 × IQR criteria for identifying possible outliers) to compare datasets in terms of median, spread (IQR and range) and outliers to interpret and communicate the differences observed in the context of the data.
  • Compare datasets using medians, means, IQRs, ranges or standard deviations for a single numerical variable, interpret the differences observed in the context of the data and report the findings in a systematic and concise manner.

ACS Codes

ACMGM026 ACMGM027 ACMGM028 ACMGM029 ACMGM030 ACMGM031 ACMGM032 ACMGM033