* Here are some examples of mathematical problems for classroom and beyond using data/information about sustainability themes.

* Some examples are suitable for Stage 1 and Stage 2, others for Stage 3.

*Problems can be made simpler or more demanding to suit different student ability and experience levels. Figures in brackets are suggestions of how they might be made more difficult.

*All of them will be more effective with teacher support, structuring and guidance - and learning will be deeper and more powerful!

*The problems are based on information gathered from 'real world'- home/family life, from inside and outside the classroom as well as from books and websites.

*Some of the information gathered could also be turned into different types of graphs, tables, databases or spreadsheets.

*Engagement of other classes, parents and community are important.

### EV maths

***Counting the number of EVs on the road**:

* This is a very simple but powerful activity. Boys and girls as young as 5/6 years of age can do this successfully, individually or in pairs.

* EVs are very easy to spot! They have no exhaust pipe(s) and there is nothing coming out the back of them!

* Also in NSW all EVs have a** BLUE triangle** affixed to their front and back number plates. Students could research why the BLUE triangle is a requirement and who they might help? In what circumstances?

* **There are two counts you have to make. This why it is good to work in pairs!**

The first is the number of EVs spotted. But this has to be as part of 100 cars [not trucks/double B’s/semi-trailers] going by. So one person counts the number of EVs. The other person counts up to 100 vehicles, including the EVs passing -AND makes sure the person counting the EVs knows when 100 vehicles have gone by. WHY?

** *Because it is the percentage of EVs [%]that is important - how many in the 100 vehicles are EVs.**

Developing recording sheets can also be part of the students’ work prior to the count The counting can be done on a road(s) at home or a road outside the school fence. The time over which the counting is done doesn’t matter! But several counts at different times and from different locations would be useful.

**NOTE: TIP!! One of the best places to count is at cross streets with traffic lights - because cars have to usually slow down - and it's easier to see the BLUE triangles on the registration plates!!**

[FOR THE TEACHERS:

* For more advanced students, simple research on comparisons between what they have found and NSW [currently 4% EVs], other Australian states, and other countries adoption of EVs can be used for oral and written reports.

* Stage 3 students might be asked to discuss/write about reasons/explanations for why some countries have more or less EVs.

* Maybe a class debate – ‘That Australia should build their own EV cars’- a very current issue!.

* Tables/graphs/charts/timelines can also be easily prepared and from this projections/ predictions calculated for different time periods. When will Australia reach 100% EVs?

**IMPORTANT NOTE:**

Don’t get too dispirited by the low count of electric vehicles you are likely to find: 1-2% is quite usual. Australia is a long way behind countries in Scandinavia and Europe.

While the current figures for ownership of electric cars in NSW is 4% and for Australia 3.8%, we have started from a very low base – but in 2023 Tesla sold more electric cars in the world than any other car company, beating Toyota that had previously held that record.

And in Australia – between January and May 2023 Tesla EVs sold more than 8000 new cars with 3000 in May alone. And this was only one of three Tesla electric models! And there are many more EVs becoming available in Australia. For example, BYD [Build Your Dream] EV company already in Australia is having a strong impact.

So, we are catching up to countries that started before us and have larger populations. EXAMPLE: This task was written in August, 2023 and in every count I had done the result was only 1-2% of EVs. BUT- by beginning December, 2023 - many of my counts has doubled that to 4% - and some 5%! - So we are catching up!!

What could make the catch-up faster?

### Electrical Maths

***Solar Panels/Home Batteries**: The same sorts of maths activities can be carried out counting the number of houses around students’ homes that have solar panels, and/or the number of students’ homes who have home storage batteries or EV Chargers.

*Differences between results for those students who live in different postcode areas/suburbs and those living in houses and those in apartments and possible explanations for the differences could be explored. Equity is an important issue in installation of renewable energy because of costs and available funds and resources.

**IMPORTANT NOTE TO THE TEACHERS**:

**Australia with 30% of our homes with solar panels, leads the world on number of solar roof panels!**

Currently, NSW leads with nearly 900,000 homes having solar roof panels.

Students might like to explore why? - we have in Australia 10,000 times the amount of energy we use every year just from the Sun! Much more than most other countries.

**Australia also leads the world in battery storage** – and in the production of large storage batteries! The **number of home storage batteries has increased 55% from 2022.** In 2022 one in every 12 solar roof systems installed also had a battery installed. In 2023 it is now one in every 7! About 180,000 homes now have a storage battery.

Students might like to discuss why home battery storage is so important/useful.

There is a very useful resource ‘Security Not Cost is the Energy Issue’ by Angus Robinson on the ‘electrifyingbradfield.org’ website.

* Students might also research why the installation of roof solar panels and battery storage is so important in the transition to renewable energy. What important role will solar roof energy and home batteries play in the transition? Could this reduce demand on the national electricity transmission grid? Why is this important? What are VPPs [VIRTUAL POWER PLANTS]? Are they useful? Why?

* You can extend this activity for Stage 3 and more able Stage 2 students by doing some simple demonstrations/experiments with batteries and electrical circuits. You can get some simple kits to do this from toy and model shops. Tell them you want them for school and you might get them for less!

**Once students have some ideas about electric circuits and flows of energy they could research some of the latest developments in battery technology**. For example batteries made from **salt/saltwater** [see Na-ion website] or **compressed air storage batteries** [installed to power a new mine in Broken Hill in NSW] that also can produce thousands of litres of water for drought affected regions: both energy and water! The **use of electric car batteries for both domestic and electricity grid power. **

Students could also research batteries that are used in Electric Vehicles, particularly lithium-ion. The positives and negatives of lithium-ion batteries- and what is replacing lithium.

Also research the **prototypes of cars with inbuilt roof solar panels **and why this is very important technology for a future sustainable world using renewable energy. What roles will electric car generated electricity and batteries play in the transition to renewable energy.

**SOME SIMPLE MATHS PROBLEMS**: [Probably for Stage 2 and particularly Stage 3 students.]

- I have 8 solar panels [PVs] on my roof. Each panel can produce 44 watts of electricity every hour during a sunny day. How many watts in total can the 8 solar panels produce every hour? [8 lots of 44: 8X44]
- If the sun shines on my panels for 5 [5.5 etc] hours a day, how many watts could my panels generate in a day? [Multiplication: 5 lots of ]
- If 1000 watts make a Kilowatt (KW) of energy, how many Kilowatts can my panels produce on a sunny day? [Division].
- But my house has a large tree near it. Only 4 panels are in the sun all day and four are in the shade for half of the day. How many watts could my panels produce? [Subtraction, division, addition] How many KWs would they produce?
- If my 8 solar panels can produce 3 Kilowatts (KWs)[for more advanced students 2.5 KWs or 2.7 KWs] in one hour of sunshine. How many KWs will they produce with 6 hours of sunshine [for more advanced 5.5: if half my panels are in shade for ½ a day, ¼ day etc]
- A house with two parents and two children uses 20 KWs [more advanced 17 or16.5 KWs etc] of electricity per day. How many sunny days with no shade will I need to be able to generate enough electricity for 5 days [7, one month of 30 days etc] days? How many days if half my panels are in shade for half a day?
- An average family uses 20KWs a day. Does your family? Check your electricity bill!
- My electricity bill for 3 months [90 days] is $360 [or $400.00; $410]? How much am I paying per day for my electricity? [Division] A 10% increase in electricity prices has just been announced. How much will my 3 monthly bill be now if each month is 30 [31] days?
- How much more will I have to pay because of the increase? [Subtraction]
- I am generating 15 [18 or 14.5] KWs of solar energy per day. I am selling it to an electricity company at 10 cents [6 or 7 or 12 or 7.5 cents] per KW. How much am I earning from my solar generation each month [30 or 31 days]? How much am I earning per year?
Given:

a) the amount I am paying for my electricity bill;

b) the amount my provider is paying me for every KW of electricity I generate, and;

c) how much electricity I use each day

is it better for me to sell the electricity I am generating or to use it in my home? Why? Why not?

- The installation of my solar panels cost $2,000.00 [or $2500 or $2200 etc]. Given your answer in Question 10, how many years will it take me to recoup the cost of the installation of my panels?
- If I am going to use the electricity I generate in my house I will need to buy a home battery to store the electricity I’m generating. A battery will cost $3500.00 [$3900.00; $3891.00].
**Having a battery means I am not paying for any electricity [$360; $400;$410].** - If I am saving that money, how many months or years will it take me to pay for my battery?
- I can install another 8 panels for $1800.00. 16 panels will produce 30 [28, 28.5 etc] KWs/day. This means that I am producing much more electricity than what I need. I can send what I don’t need to my electricity company and get paid for it like before. Do your answers to Questions 10,11,12 and 13 change? Why? What will your answers to those questions be if I install the extra 8 panels?

### ELECTRIC CARS

- I have just bought an electric car. I had to pay $40,000.00 [$40,800.00; $44,640.00]. But the government paid me $3,000.00 [$3500.00; $3425.00] for buying an electric car instead of a petrol-combustion one. They also refunded $1000.00 [$1630.00; $1575.60] for the Sales Tax I paid. With these refunds from the government how much did the car finally cost me?
- My car has a range of 250 kilometres [in other words when my battery is fully charged I can travel 250 [243; 226;] kilometres before I need to recharge my battery]. One charge costs me $10.00 [$15.00; $12.30] for electricity and
**I need one charge every week**.

With my old petrol car I used to buy 40 [45; 42]litres of petrol every week. Each litre of petrol cost me $2.00 [$2.25; $1.87].

How much am I saving each week [month, year] by having my electric car and not having to buy petrol?

- I travel 20,000 kilometres each year. My old petrol car used to use 8 [7.5; 6.7] litres for every 100 kilometres I travelled. If petrol cost $1.50 [1.85, 2.27] for me to travel 20,000 kilometres?
- How much will it cost me for charging my battery to travel 20,000 kilometres in my electric ca if each charge costs $10.00 [$12.00. $12.25]?
- How much am I saving each year by driving my electric car rather than my old petrol one?
- Considering how much I am saving each year, and the final cost of my electric car, how many years will it take me to save the cost of my electric car.
- Do you think that buying my electric car was a good investment? Why? Why not?

**PLOTTING AN EV JOURNEY**: A very realistic extension EV activity!

One challenge of driving an electric car is that you have to do a little more planning - you have to find out where electric car fast-charging stations are located in the towns and cities along the way! – you can’t just hang out for the next petrol station!

There are many electric car [EVs] charging stations – some people in electric cars have driven right round Australia in their electric car! Do an online search and see where the charging stations are - you might be surprised!!

* Look at a road map and choose a journey you would like to make in NSW.

* Assume the EV you are driving has a range [how far you can travel before you need to recharge your battery] of 450 kilometres.

*Looking at the scale of the map and the towns you are going to be driving through identify the towns that are about 400 kilometres apart [better to be a bit cautious and still have some juice in your battery!] If you have trouble with this you can always cheat and Google how far places are apart from each other!

*Go online and Google to find out which of these towns have an EV fast charger.

****Just remember, some of the towns you have identified won’t have a fast charger but maybe other ones nearby will.**

**The NRMA website** is useful and has maps of all the places that have fast chargers. Also if you just ask Google or another search engine if there is an EV fast charger in that location you should get an answer. Sometimes hotels/motels/resorts in towns also have fast chargers – check them too!

From all the information you have found plot your journey.

*Identify all the places you will stop to recharge your battery.

*Allow 1 hour for each recharge.

* Now work out how many hours/days/weeks your journey will take assuming you are only able to be driving between 9.00 am and 4.00pm each day and you will have to stop an hour for each recharge and an hour for lunch. Will you have to stop overnight? How many nights?

- Given the number of recharges you will require and that half the recharges don’t cost anything and half cost $15.00 each how much will your trip cost?
- If you stay overnight assume it costs $95.00 for each night for each person for accommodation and you spend $50.00 for each person each day for meals and refreshments. What is the total cost for your trip?
- Work out the difference the trip would cost if you were driving a petrol car that required 7 litres of petrol for every 100 kms travelled and petrol cost you $2.00 [$2.22; $2.26] a litre.

Hope you enjoyed your trip!

### Water Maths

**VOLUME**: In their mail brochure‘Sydney Water’ claims that by turning off the tap when you brush your teeth ‘you will save **30 litres of water**!. See if they’re right?

Put a plug in the basin but leave the tap running and collect the water while you brush your teeth.

**NOTE: Most basins will not be large enough to collect 30 litres! Mine only holds about 6 litres! So, you may have to interrupt cleaning your teeth to collect the water more than once as the basin fills.**

Another way is to use a bucket. It usually holds 12 litres. Empty the bucket when it is full. If Sydney water is correct you would have to empty the bucket twice as you were brushing – and have 6 litres left at the end of the experiment!

Don’t be surprised if you collect less! 30 litres is a lot of water!

What do you think might be a problem with what Sydney Water claims? What other things might influence how much water you save?

Think of people cleaning their teeth and how long it takes? Why might some people take longer than others? What else might affect how much water someone uses? Are 30 litres saved in one brushing? Or over time?

Get everyone in class to do it. Graph the results. Maybe write a class letter to ‘Sydney Water’ and let them know what you found.

Do your results make you want to change how you brush your teeth? If you want to save even more water, use a cup of water to brush your teeth!

**BUT REMEMBER! No matter how much water you save it is still much better to turn off the tap while you are brushing! Every drop of water saved is important for sustainability!**

[compiled by David Smith [Electrifying Bradfield] October 2023.