Introduction
Hi, I’m Jack and welcome to Solar sums. I need your help addressing a common financial problem, high electricity bills. You’ll investigate solar panels as a possible solution. Your end task is to produce a presentation based on your findings.
Yesterday, my dad received our electricity bill. It was really high! He was so mad he called a family discussion. I’m just about to call my friend Asmina and tell her about it.
Check out Jack's phone call. View Transcript of Jack’s phone call.
Measuring electricity use
Before looking at solar panels, the first thing is to understand our power bill. That means understanding how household power use is measured. Have you ever wondered about that?
Measuring electricity is not as simple to imagine as measuring something like water—it’s not like we can fill up a bucket with electricity!
Electricity use over time is measured in kilowatt hours (kWh).
Learn more about kilowatt hours.
Compare the energy use and runnings costs of 9 appliances in Watts to compare.
Conduct your own electricity use audit.
For more about energy use, read Understand your energy bill.
The family power bill
It’s time to review the electricity bill my dad received. This will tell us what the power company charges for electricity per kWh and other costs we pay for.
Review the power bill.
Alternative: power bill (.pdf 203kB) and power bill info (.pdf 259kB)
Find out more about the power bill household statistics.
Take the Power bill quiz. Alternative: Power bill quiz (.pdf 90kB)
You may also want to take another look at the Australian government’s web page, Understand your energy bill.
Solar panel basics
We understand how electricity use is measured. We know what the power bill is telling us. Now, on to investigating whether solar panels are the way to go.
In order to undertake this investigation, you need some information about solar panels. Here is what you need to cover.

Read the Newton home facts because these will help with the research.

Learn a bit about solar panels, including if they are all the same.

Collect the following information on 4 different systems:
Explore these suggested web links to get started. You will use the information you collect on the 4 solar panel systems in the investigation in the next tab.
Investigation: Are solar panels profitable?
Your task is to investigate whether solar panels are profitable and to prepare a presentation based on your findings. Complete the following steps.

Find out how much the Newtons are charged for electricity per kWh by examining their power bill (.pdf 203kB).

Enter your findings about solar panel systems and the amount per kWh the Newtons pay for electricity in the Solar power savings spreadsheet (.xls 75kB).

Interpret the calculated data, draw your conclusions and make a recommendation.

Prepare your findings and recommendations as a presentation.
Reflection
In working through this resource, you have:

developed an understanding about how energy usage is measured

read and interpreted an electricity bill

learnt a bit about solar panels using online resources

entered relevant findings into a solar panel savings spreadsheet

drawn a conclusion based on facts and investigation

organised your information and conclusion into a logical and clear presentation.
In summary, you have investigated power and the way it can have an effect on our lives financially and our world as a whole. You have made a wellresearched and informed decision about a real life problem that many people face.
However, your decision may not be right for every situation.
Discuss the following with your classmates, friends or family:

What factors may influence people making the decision to install solar panels?

What are other ways that you might reduce your power bills to save money?

How do your individual decisions affect others in your family, community and the world?
Teaching notes
The information below supports the implementation of Solar sums, a resource for Mathematics Year 9.
Overview
Solar sums is a problembased investigation that challenges students to apply mathematical concepts to solve a common household issue. Using a hypothetical scenario, students investigate how consumers can reduce electricity consumption to improve cost efficiency.
Students will compare the overall value of a range of goods and services using IT tools and comparison websites to make informed and effective consumer and financial decisions. The culminating activity asks students to investigate the efficiency of solar panels and produce a multimedia presentation based on their findings.
The resource can be completed as a whole class, in small groups or individually with teacher direction, and as an independent homework task. It can be tailored to suit individual class needs and abilities with some students requiring more teacher support.
While the resource presents a scenario, this could be adapted for realworld situations where a school or other community organisation might be considering the installation of solar panels.
Display the Outcomes tab to read how this resource links to the National Consumer and Financial Literacy Framework and to the Australian Curriculum.
Display the Activities tab to read a description of each section in the resource, along with suggestions for class or group discussions and important points to bring to students’ attention in order to support their learning and make the context more authentic and relevant.
Outcomes
Note: the student learnings in the National Consumer and Financial Literacy Framework (.pdf 6.9MB) are divided into, and are applicable over, bands covering two chronological years. The Year 10 band covers both Years 9 and 10.
Year 10
Knowledge and Understanding:

Identify and explain strategies to manage personal finances

Analyse and explain the range of factors affecting consumer choices
Competence:

Use a range of methods and tools to keep financial records in ‘reallife’ contexts

Investigate the financial decisions required at significant lifestage events

Analyse relevant information to make informed choices when purchasing goods and services and/or resolve consumer choices

Compare overall ‘value’ of a range of goods and services using IT tools and comparison websites as appropriate
Responsibility and Enterprise:

Apply informed and assertive consumer decisionmaking in a range of ‘reallife’ contexts

Apply consumer and financial knowledge and skills in relevant class and/or school activities such as student investigations

Appreciate that there is often no one right answer in making financial decisions because these depend on individual circumstances, preferences and values

Demonstrate awareness that family, community and sociocultural values can influence consumer behaviour and financial decisionmaking
Number and Algebra: Real numbers

ACMNA 208 – Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems

Using electricity charge as a rate students engage with directly proportional rate of electricity usage versus cost. Students also investigate Solar Panel savings as a rate and savings over a period of time.

Statistics and Probability: Chance

ACMSP227 – Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians

Students investigate the average electricity use of different sized households. They go to the source of the data and research how this information was collected and what factors affect the figures.

Statistics and Probability: Data representation and interpretation

ACMSP228 – Identify everyday questions and issues involving at least one numerical and at least one categorical variable and collect directly from secondary sources

Students conduct an audit of their own electricity use related to certain appliances. They are then asked to find secondary sources about how these are being used on average in Australian households and compare their usage to the average.

This unit of work contributes to the bolded sections in the following aspects of the Achievement Standard in Mathematics for Year 9.
By the end of Year 9, students solve problems involving simple interest. They interpret ratio and scale factors in similar figures. Students explain similarity of triangles. They recognise the connections between similarity and the trigonometric ratios. Students compare techniques for collecting data in primary and secondary sources. They make sense of the position of the mean and median in skewed, symmetric and bimodal displays to describe and interpret data.
Students apply the index laws to numbers and express numbers in scientific notation. They expand binomial expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment. They sketch linear and nonlinear relations. Students calculate areas of shapes and the volume and surface area of right prisms and cylinders. They use Pythagoras’ Theorem and trigonometry to find unknown sides of rightangled triangles. Students calculate relative frequencies to estimate probabilities, list outcomes for twostep experiments and assign probabilities for those outcomes. They construct histograms and backtoback stemandleaf plots.
Literacy – Students learn vocabulary to do with financial literacy. They explore and understand financial texts, engage with financial data to extract meaning and use literacy to explain and discuss this meaning.
Numeracy – As students learn to become financially literate they are developing their numeracy skills and deepening their understanding of the numeracy as it applies to finance.
ICT – Students learn to use ICT to investigate and inform decisionmaking in a financial context. They engage with multimodal technology to collect and analyse information. They engage with spreadsheets as a tool to calculate and promote understanding of key concepts.
Critical and creative thinking – Students are challenged to question choices and engage in investigations to clarify concepts and ideas, seek possibilities and consider alternatives in a financial and sustainable context. They are encouraged to look at alternative ways to be smart consumers and financially responsible citizens.
Personal and social capability – By developing financial literacy skills, students are adding to their personal and social capability. They engage with realworld learning activities that will assist them to make informed consumer decisions and to understand the consequences of these decisions for them, their families and for the environment.
Ethical understanding – As students investigate financial concepts, they are continually being asked to analyse materials in an ethical way by finding appropriate comparisons, evaluating general statements and interrogating financial claims and sources.
Intercultural understanding – As students investigate their own financial decisions they are encouraged to understand how differences in cultural and socioeconomic backgrounds can affect the financial decisions of others, broadening their awareness and understanding of issues related to social diversity.
Sustainability – Sustainability provides a rich, engaging and authentic context in which students can explore the concepts involved with financial literacy. They are opened to the idea that sustainability and financial responsibility are often very closely related both for individuals and society in general.
Activities
The headings below relate to the sections within this resource. Expand each one to read a description of the section content, along with suggestions for class or group discussions and important points to bring to students’ attention in order to support their learning and make the context more authentic and relevant.
Students are introduced to the scenario at the centre of this resource and the related learning content. A high cost electricity bill has been received by the Newton family. The son, Jack, relates the family discussion over the electricity bill to his friend Asmina. His parents want Jack to reduce his electricity consumption but Jack believes his usage is essential to his lifestyle. He suggests solar panels as an alternative but his dad thinks the cost outweighs the benefits.
Students could:

discuss electricity consumption, how essential some of their electricity usage is, and how they could reduce their consumption

brainstorm energy saving ideas and different lifestyle priorities. This could be done using collaborative online tools such as Linoit or Google Docs

evaluate and critique the opinion ‘that the cost of solar panels outweighs the benefits’. After their solar panel investigation students can reflect on this initial opinion and discuss whether their thinking has changed, giving reasons.
Students are introduced to the kilowatt hour, the unit of measurement in which electricity use is charged, and asked to calculate kWh usage of three household items. Students compare the wattage and running costs of some common household appliances and conduct an electricity use audit in their own homes. An understanding of the concept of the kilowatt hour is essential to understanding the usage and cost of electricity. Electricity, unlike water, is not a resource that can be easily seen and measured.
Students could:

discuss the concept of the kWh, and further practice working out the amount of electricity appliances of different wattage use. This is a good connection to rates and can be tied into solving equations

discuss lowering energy consumption, reducing use, using more efficient appliances, and sustainable choices

view the Australian government’s web page Understand your energy bill to get more details about energy bills.
Home electricity audit
The home electricity audit could be conducted by students before they engage with the learning object in class. This will enhance the context and relevance of this learning object, making for a more authentic learning experience.
Students could:

consider how electricity is used in their own homes. Television and air conditioner usage for example, can be taken for granted and inaccurately estimated

use collaborative tools to build a combined class audit based on their individual data. Students might contribute to a common spreadsheet or table. Google Docs or other collaborative tools may be useful for this activity. The larger sample would make the data more reliable and students could examine the whole group results and also compare their individual results, considering reasons for any differences.
Students build on their financial literacy as they examine the electricity bill that Jack’s family received. Students with little experience with bills and the information they present can select ‘Bill info’ to learn about aspects of the bill including total amount owing, due date, overdue charges, household statistics and the electricity rate being charged. Finally, they complete a short quiz about key information on the bill.
Students could:

use a printout of the PDF version of the bill to read the information on the bill, make notes and write questions

use the ‘Bill info’ section to familiarise themselves with different aspects of an electricity bill and evaluate the importance of the information

look at their own household electricity bills and compare information given by different providers.
Answers to the power bill quiz are found in Power bill quiz—Responses and feedback (.pdf 97kB). This PDF also includes some feedback on each question.
Household statistics
Students learn about electricity usage data that appears on the bill. All electricity bills have a section that compares individual usage with average household usage, based on the information from www.energymadeeasy.gov.au.
Students could:

engage with the statistics and question how the data is gathered and the factors influencing it

view How is average electricity usage calculated?, consider the following questions and post their answers and thoughts on a common wiki or other collaborative tool such as Linoit.

How does location affect energy use?

Is the usage versus people in the house a linear variation? Would a oneperson household use half the electricity of a twoperson one? Why or why not?

What variance would seasons create?

What other factors in the house might impact on electricity consumption? This might include swimming pools, ducted cooling or using other energy sources such as gas.

Is supplying this information to consumers on their electricity bill helpful?

This section could lead into other statistics topics. Further investigation could explore the populations in suburbs and regions, time spent on various activities and the energy expenditure of these activities, and a discussion about averages and statistics in general and the dangers of misinterpretations and misleading conclusions.
Students prepare to undertake their investigation by gathering some general information about solar panels and then choosing four different solar panel systems and finding out how much each one costs and the amount of electricity it generates.

Before gathering any information, students should be familiar with each step of the task. Discuss the content in the three links with students:

The ‘Newton home facts’ provides information relevant to choosing an appropriate system, as well as factors impacting on cost and electricity output.

What does the system cost? explains that cost varies depending on the type of system. It lists some of the factors influencing cost. Relate these to the Newtons’ situation (‘Newton home facts’).

How much electricity is generated? explains that output varies from one system to the next but also many factors are governed by where you live. Relate these to the Newtons’ situation (‘Newton home facts’).


Students could hold a discussion to pool their knowledge of solar panel systems either before or after learning about them on the internet. Students only need to explore the basics of solar panels so a time limit could be set for this task. Some classes may not need to undertake further inquiry if students have sufficient prior knowledge.

Students should use the information of the ‘Newton home facts’ when selecting the four solar panel systems. If further information is required to determine the system (and therefore cost and energy output), the teacher will need to make an educated decision.

Some suggested web links are provided to help students start their research. These include links to general sites about solar panels as well as to two major suppliers. It may be useful to find further websites relevant to your local area prior to starting this task.
Students undertake their investigation about solar panels. They find information about the different types of systems, the cost of installing these systems and the amount of energy they can generate. Students need to be aware that:

they should critically evaluate the websites where they find information

the website should be based in Australia. It is no use finding information about solar panels in another country

prices found on the internet may be subject to change and are not always reliable

the amount of energy generated by solar panels is usually presented at optimum conditions, and as maximums or averages, and understand the implications of this.
Solar panel savings spreadsheet
The Solar panel savings spreadsheet can be used as a tool to calculate the savings, or lack of savings, of installing solar panels. There is room in the spreadsheet to compare four different systems with different costs and capacities. The worksheets are protected to prevent changes to the formulas. Unprotect them to view the formulas. This does not require a password. Note, when viewing the resource on a tablet or mobile device, open the spreadsheet in an app that allows you to edit it.
Students will:

in the first worksheet, input the cost of installation, the number of kWh generated in a year by each system and the cost of electricity per kWh. The spreadsheet will then calculate the gross savings over 10 years, the gross cost, and the net savings or loss over 10 years

in the Graphs’ worksheet (display via the Graph tab), engage with four line graphs comparing the savings and the cost. Using these graphs, students will easily see at what point the solar panels become profitable and how much profit is made at the end of a 10year period

include the graphs as part of the presentation they create

in the third worksheet, view the breakdown of the savings yearbyyear.
The Presentation
Students design a multimedia persuasive argument for or against solar panels based on their research findings. They may present this to the whole class, to a small group of classmates or submit it to the teacher. Students should be encouraged to use a range of mediums to present their findings and convince their intended audience of their point of view based on the facts they have discovered. The presentation could be a:
More support can be found in the DER NSW collections UCreate and Tools4U.
This presentation could be a rich and engaging assessment task for students.
Assessment
The suggested marking rubric (.pdf 123kB) addresses student assessment relating to the Australian Curriculum Content Descriptions—Year 9.
It is important that students reflect on their learning. Three discussion questions are included to facilitate this reflection. Other questions may be relevant to individual classroom settings.