Teaching Notes. Contextualised task 27 Gas and Electricity

Transcription

1 Contextualised task 27 Gas and Electricity Teaching Notes This task is concerned with understanding gas and electricity bills, including an opportunity to read meters. It is made up of a series of 5 questions, where learners are asked to calculate what their bills would be with given usage, what factors may contribute to high or low energy usage, and how to convert between the gas meter reading that shows cubic feet (Ft 3 ), and the estimated energy (in kwh) using the energy company s own published formula. Learners are also introduced to the TCR (Tariff Comparison Rate) initiated by OFGEM in 2014 to help customers compare their costs with that of other suppliers. The task centres on a young person (Dan) moving into his own house for the first time (in May), and the bills he receives during the summer. He sets up a direct debit, using the energy company s estimate that he should pay 121 per month. The resources provided for this task are: Gas and Electricity Learner resource sheets: 5 questions; Solutions and mark scheme; PowerPoint and script for teachers. Learners will also need: Calculators; Pencils/pens, paper; Mini- whiteboards (or equivalent, to display answers in class, when reading the meters). Additionally: You may also bring in your own, or ask learners to bring in examples of old gas and electricity bills, for use in the classroom. The resource sheets use calculations and wording from different energy suppliers. The wording is authentic, and has not been diluted it is what any customer will face when presented with their bills and therefore provides teachers with the opportunity to support their learners with addressing the difficulties they are likely to have in understanding how their bills are calculated. The questions are: 1) Calculating the electricity bill from the energy company s estimate of usage. 2) Calculating the gas bill from the estimate. 3) Why is Dan in credit? Exploring reasons for low- or high- energy usage. 4) Actual usage, actual bill: recalculating the bill given the actual rather estimated usage. 5) Using the TCR (Tariff Comparison Rate) to compare suppliers. 1

2 Teachers may wish to use these resources in a variety of ways: As one task, in sequence. However, learners will have to show some resilience in reading quite a lot of information, so the task may be best distributed over a number of lessons, as in the following examples. As starters or plenary questions over a sequence of lessons, that may be focused on written calculation work. As occasional challenges, making sure that learners are provided with all the relevant information included on the PowerPoint. Tier of entry/support Understanding a gas and electricity bill must be within the remit of a candidate working at Foundation tier. There may be a lot of reading to do: but making sense of the information in front of them is a critical life skill for any young person. The calculations are not likely to present problems, but working out what to do from the text might be more difficult. So the support has to be focused on enabling learners to read the text, explain what they think they have to do, and sharing ideas across the classroom. Questions such as the following may be useful: What information is useful to this problem? What information don t you need to solve this problem? What calculation do you think you need to do? Can you do this mentally, in writing, or is it best to use a calculator? If using a calculator, how will you key in the calculation? What units are involved in your calculation? How will you check that your answer is correct? Does your answer make sense? Support Further resources are available online to support learners with understanding the energy bills: s/your_bill_explained_pdf.pdf electricity/guides/energy- bills/ service/pay- your- bill/your- bill- explained/your- gas- bill- explained gas/bill/ 2

3 Gas and Electricity: Teachers script for PowerPoint presentation This script works through the whole set of 5 questions. Teachers may wish to break the presentation at any point, returning at a later stage. The text in the right- hand boxes provides a possible script to be read to students. However, it is probably preferable to use your own words and elaboration. When questions are asked, time for discussion in pairs/groups should be provided. Ensure that students are given opportunity to explain their reasoning in response to these questions. Teacher guidance is written in italics. Suggested dialogue is in plain text, along with questions for the class, which are bulleted. Expected student responses are in bold. Question 1: The Electricity Bill Slide 1 Slide 2 Keep this slide on the screen until you are ready to start the presentation. At this point, if you are using mini- whiteboards and pens (or any other form of individual response display), ensure these are ready for use. Energy bills have changed in recent years. They now show the important information more clearly than before. Usually, these bills arrive every quarter. How often is every quarter? Every 3 months. The amount you have to pay is here ( ). If you are in credit it is also shown here. How could you be in credit to an energy supplier? Some people make regular monthly payments, so that they don t have to pay hundreds of pounds all at once. If your bill arrives once every 3 months, it could be 300 or 400 sometimes more, if you have a large house. This (10 th October) shows the latest date when you have to pay. These numbers are the meter readings. Where are the meters in your house? Unfortunately, many people do not really understand the energy bills, and many people do not know how to read their meters. We are going to look at some meters, and try to read them. 3

4 Slide 3 Slide 4 Slide 5 Slide 6 Read the text on the slide, and invite learners to read the two meters, perhaps presenting answers on a whiteboard. Point to the red numbering on the meter on the right. This number is usually ignored when reading for the bill. An important question might be: What units are being used here? The solutions are: Kilowatt hours Left meter: kwh The initial zero is important, similar to reading bearings! Why is the initial zero important? Right meter: kwh Some questions to help learners read this meter may be: Which dials should be read clockwise? What are the numbers by the dials? What units are being used here? Point out again that the red dial is not usually used in reading for bills. Emphasise the words on the slide: take the lower value when the dial is between two numbers. Write down your reading (on your whiteboards). Solution: kwh Sometimes, the dial may be between two numbers, but very close to one of them. What makes this difficult to read? Write down your reading (on your whiteboards). Solution: kwh Hand out Learning Resource sheet 1: Electricity, ready for use over the next two slides. This is the story of one young man going to live on his own in a new home. He could be a student at university, or going to work in a new town and renting a place. As you see, he will be joined by some housemates later in the year, in September, but he has moved at the end of May. It could be that his friends are all students, but he has a job in the town, which is why he has moved in earlier. It could be any of you in about 3 or 4 years time. Why has he set up a direct debit for the energy bills? 4

5 Slide 7 Let s make sure we can interpret everything on this bill. Who do you think made the first meter reading of 89597? (Dan) Did anyone read the meter on the 14 th of June for this bill? (No, it is estimated by the energy company). How has the 144 kilowatt hours been calculated? By taking the initial reading from the estimated reading. How has the rest of the bill been calculated? What is a standing charge? Let s check the figures on the bill are correct. Give time for learners to replicate the calculations on the bill, addressing any problems that arise. Do you notice that the 5% VAT has been truncated, or rounded down, rather than to the nearest penny? Dan s reading is What lines of this bill would definitely change if this reading were used instead of the estimate? Lines 2, 3, 4, 6, 8 and 9. We don t know for sure if the dual fuel discount will change, so for now we will leave that as it is. Have a go at question 1 over the page. Fill in the blank lines of the bill. Show your working at the bottom of the page or on another sheet. Set a suitable period of time for this. You may want the students to hand in their work now, swap their answers for peer marking, or simply ask the class for their answers and methods. It may be necessary to explain the note about the Standing Charge and the VAT calculations. These are truncated to the penny below, and not rounded to the nearest penny. However, the gas and electricity calculations are rounded normally. Errors in rounding / truncating will be common, and should be dicussed here. Question 2: The Gas Bill 5

6 Slide 8 Slide 9 Slide 10 Keep this slide on screen as you hand out Question 2: The gas bill. We should go back to reading the gas meter. Here are two. What units are used here? What does a metre cubed look like? What does a foot cubed look like? How might this explain why you might take a full reading for the meter on the right? A fraction of a metre cubed say 0.5 metre cubed is more than a foot cubed. If we estimated how many cubic feet divide into a cubic metre, it might be =27. That s a lot of gas! So the companies might ignore the fractions of a cubic foot in the readings for bills, but not necessarily fractions of a cubic metre. Solutions: Left meter: 5148 ft 3 Right meter: m 3 The units on the meter are not kilowatt hours. The energy company has to convert the units to kilowatt hours to calculate the energy used in the bill. On your sheet is the explanation why they do this. (Read and discuss the explanation in class as necessary). They show how they calculate this on the next slide. Dan s meter is an old, cubic feet one. The energy company shows how it converts between cubic feet and kilowatt hours. We are going to use this formula for Dan s gas bill. To answer part a) what is the first thing we have to do? Do we get the answer for part a) just by going through the formula with the amount of gas Dan used? If not, what else do we have to do? Have a go at the whole question. Give a suitable time for the class to complete this. Question 3: Why is Dan in credit? Slide 11 Hand out the sheet: The Total Bill, Question 3: Why is Dan in credit? Before answering the question, it may be useful to address some of these questions with the class: Why was the balance zero on the 28 th of May? How was the calculated? 6

7 Slide 12 Remember the front page of the bill looks like this. Where it says here, instead for Dan it will show in credit Slide 13 Now try to think of as many reasons as you can why Dan is in credit on his first bill. This slide should remind you of his situation. Give a suitable time to complete the question. A mark scheme is available for this question: it can be used for self, peer or teacher assessment. However, ideas may be shared around the class before using it. 7

8 Question 4: Actual usage, actual costs Slide 14 Keep this slide on the screen until you are ready to start. Hand out the sheet: Energy usage and monthly payments, which includes Question 4: Actual usage, actual costs. You should be able to work out Dan s energy bill from the readings on the screen or in your sheet. What is the first thing to do? What do you do with that information? What are all the stages of calculating an electricity bill? What are all the stages of completing a gas bill? Have a go! Give a suitable time for completing this task. A mark scheme is available. Remind learners about rounding accurately, and truncating if calculating VAT and Standing Charges. If Dan s actual bill is 66 for two months, should he ask to change his direct debit? Question 5: Estimating bills, using the TCR Slide 15 Keep this slide on the screen until you are ready to start. Hand out the sheet: Switching supplier, which includes Question 5: Estimating bills, using the TCR. On your bills, the energy companies have to put a figure that enables you to compare your bills with other suppliers. It is called a Tariff Comparison Rate or TCR. Some companies show a TCR for three types of user low, medium or high. Most companies only show a TCR for the medium user. Slide 16 To estimate your bill, simply multiply the usage in kwh by the TCR. Slide 17 Let s check that this working is correct. Do this on your calculators. Now have a go at the questions on your sheet. Note the usage is in the textbox. Give a suitable time for completing this task. Again, a mark scheme is available for self, peer or teacher marking. 8

9 Solutions and mark schemes Question 1: The electricity bill A completed bill should look like this (entries in bold): 28 May you gave us your first meter reading June Dan s meter reading kwh used over 18 days 104 kwh p = Cost of electricity used this period Standing charge 18 days at p per day Total electricity used Dual fuel discount VAT at 5.00% Total electricity including VAT The electricity used is 104 kwh. The cost is 11.7p 104 kwh = p This rounds to VAT at 5% on becomes This will round down to 79p. Mark scheme Full credit A completed bill with all figures correct. Accept rounding of VAT to 80p, therefore a final bill of Accept also if the student has omitted to enter 104 in line 4. Partial credit Calculates kwh to give 104 kwh, and multiplies this by Up to two errors in the final bill. No credit Any other response 9

10 Question 2: The gas bill a) 12 cubic feet converts to kwh kwh 4.080p per kwh = p The gas charge is b) = is 1.01on this. The total is c) The sequence of calculations can be simplified to multiplying by Mark scheme Full credit a) Gives the answer showing appropriate calculations. b) Gives the total 21.24, breaking down the calculation to show VAT. c) The sequence of calculations simplified to multiply by Partial credit Accept one error for each part of the question. Errors may include: Omits rounding; omits final answer. VAT calculated at incorrect rate (e.g. 20%) or calculated before adding the standing charge. Rounding to a number of decimal places that are fewer than the published multiplier for the volume correction: (despite the last two digits being zero). No credit Any other response 10

11 Question 3: Why is Dan in credit? Any of the following reasons could explain why Dan s energy bill for June is much less than the monthly direct debit the energy company estimated he should pay. It is summer, and energy usage is less in summer than in winter. Dan is living on his own until September, and the usage for one person is much less than for 4 people. The bill was calculated only after 18 days and not a full month. Dan could have been on holiday for part of the time as it is in summer, and therefore there would be no usage at all. Having just moved in, it may be that the house is not fully furnished with electrical items, or it may be that the gas central heating system is not yet working. It may be that Dan does not use the electric oven to cook for one. Mark scheme Full credit Suggests two (or more) acceptable reasons Partial credit Suggests one acceptable reason No credit Any other response 11

12 Question 4: Actual usage, actual costs a) Electricity and gas costs For electricity: 247 kwh are used. 247 kwh p = p This rounds to For gas: 3 Ft = 96.71kWh 96.71kWh 4.080p = p This rounds to 3.95 b) There are two months of standing charges one month of 30 days and one of days p = pence. This rounds to for each fuel: Gas standing charge Electricity standing charge Total c) Electricity Gas Standing charges = % VAT on = 3.15 Total bill Mark scheme Full credit Electricity: Calculates correctly 247 kwh from , and multiplies this result by p. Rounds the answer p to Gas: Uses the simplified calculation, or otherwise, for kwh. Multiplies this by 4.080p to give p. Rounds this to Standing charge: calculates for both fuels a standing charge of 15.11, giving in total. Total bill: Correctly calculates 63.07, then adds 5% VAT to give a total of Partial credit a) By this time in the question, we should no longer be accepting rounding errors or giving the final answers in and pence. Therefore, only accept one calculation error for partial credit. b) Misses that the standing charge is for each fuel gives a correct answer for only one fuel. c) May use the wrong VAT rate e.g. 20%. No credit Any other response 12

13 Question 5: Estimating bills, using the TCR Mark scheme Full credit All calculations for parts a) and b) are correct, including showing a difference between the actual bill for gas and the TCR estimation. a) (i) kwh 4.93p per kwh = p. This rounds to (ii) The actual bill was (answer to question 2b). There is 2.17 difference. Teachers may wish to discuss with the class why there is a difference, which may be explained by the low usage of gas, and the relatively high proportion of the bill given to the standing charge. b) Gas: kwh 3.85p per kwh = p. This rounds to Electricity: 144kWh 11.62p per kwh = p. This rounds to Partial credit There are 4 calculations. Allow partial credit for 2 or 3 of the four being fully correct. No credit Any other response 13

14 GCSE Content GCSE Mathematics Numeracy and GCSE Mathematics Understanding number and place value Rounding decimals to the nearest whole number or a given number of decimal places. GCSE Mathematics only Understanding number relationships and methods of calculation Using the facilities of a calculator to plan a calculation and evaluate expressions. Knowing how a calculator orders its operations. Using calculators effectively and efficiently. Reading a calculator display correct to a specified number of decimal places or significant figures. Addition, subtraction, multiplication and division of whole numbers, decimals, fractions and negative numbers. Finding a fraction or percentage of a quantity. Solving numerical problems Interpretation and use of mathematical information presented in written or visual form when solving problems. Money: The basic principles of personal and household finance, including fuel bills and VAT. Giving solutions in the context of a problem, interpreting the display on a calculator. Knowing whether to round up or down as appropriate. Understanding and using equations and formulae Substitution of positive and negative whole numbers, fractions and decimals into simple formulae expressed in words or in symbols. Understanding and using properties of shape Simple solid figures: cube Understanding and using measures Reading and interpreting scales, including decimal scales. Calculating the volume of cubes. Key Foundation tier content is in standard text. Intermediate tier content that is in addition to foundation tier content is in underlined text. Higher tier content that is in addition to intermediate tier content is in bold text. 14

15 Progression in reasoning Identify processes and connections Identify, measure or obtain required information to complete the task Finds the kwh used for electricity and for gas Finds the kwh used for electricity and for gas, and then multiplies this by the unit charge to find the cost of the energy used Adds standing charge, subtracts dual fuel discount and adds VAT to previous calculations to find the final bill Represent and communicate Refine methods of recording calculations Sets out calculations clearly, showing all working Uses an efficient method e.g. uses a decimal multiplier to find VAT Simplifies the energy company s conversion of volume of gas used (cubic feet) to the kwh Review Interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible Checks that individual bills for gas and electricity are reasonable e.g. within the tens rather than hundreds or thousands Uses more complex indicators that the bills are reasonable e.g. uses TCR and compares with original working Identifies factors that contribute to bills (as in question 3) 15