Insulation and Energy Saving, Grade 7: Efficiency, and the Formula That Is Wrong
You will see energy efficiency given as a formula in a box: energy efficiency = energy input − energy output.
That is not the efficiency. That is the energy lost.
And the remarkable thing is that the same topic states it correctly three more times further on, as a ratio, every time. The formula in the box is the odd one out, and it is the one a learner will copy into a test.
What efficiency actually is
Efficiency is a ratio, not a difference.
Efficiency = useful energy out ÷ total energy in, written as a percentage.
Three reasons the subtraction version cannot be right, and a Grade 7 can follow all three.
| Why it fails | What it means |
|---|---|
| The units are wrong | A difference between two energies is itself an energy, so it comes out in joules. An efficiency is dimensionless: it has no units at all, because you are dividing joules by joules |
| It cannot compare two different-sized things | A mansion and a shack that each lose 100 J are not equally efficient. The shack started with far less. Only a ratio can tell you that |
| It gets the direction backwards | You will read that something is "more efficient if the difference has a lower value". A low difference can also just mean a small appliance. A torch loses less energy than a power station and is not more efficient than one |
The quick test: if your answer to an efficiency question has joules after it, you have calculated the loss, not the efficiency.
Where this fits in the curriculum
| Subject | Natural Sciences |
|---|---|
| Grade | 7 |
| Term | 3 |
| Strand | Energy and Change |
| Topic | Insulation, energy saving, and energy transfer to the surroundings |
| Status | Carries the Term 3 project, which is formally assessed |
| Marks | The project is 40. The topic revision is 20. Our worksheet is 40 |
Three energy budgets in this topic do not balance
In a topic whose whole point is that energy cannot be created or destroyed, three of the figures add up wrong. They are worth checking in front of a class, because finding them is the lesson.
1. A television that makes energy out of nothing
| Appliance | Energy in | Energy out, as printed | Adds up? |
|---|---|---|---|
| Hairdryer | 350 J | 150 + 150 + 50 = 350 J | Yes |
| Electric drill | 400 J | 300 + 30 + 70 = 400 J | Yes |
| Television | 500 J | 150 + 400 + 50 = 600 J | NO |
A hundred joules appear out of nothing, in the one topic that exists to teach that this cannot happen. Two of the three rows are correct, which makes the third easy to spot and genuinely satisfying to catch.
2. A double-glazing diagram with three separate errors in it
| What it says | The problem |
|---|---|
| Of 100 % of the sunlight: 60 % reflected, 36 % absorbed, 5 % transmitted | 60 + 36 + 5 = 101. One per cent too much light |
| Of the 36 % absorbed: 20 % re-radiated outwards, 15 % inwards | 20 + 15 = 35, not 36. One per cent has gone missing again |
| Total reaching the inside: 22 % | 5 transmitted + 15 re-radiated = 20, not 22 |
Ask a class to add up a figure before they copy it. That is a better exercise than anything the diagram was meant to teach, and it takes two minutes.
3. And two that do balance, which is how you know the method works
The power station to light bulb chain is correct and it is excellent: 100 units of coal in, 62 lost in the station, 38 into the lines, 2 lost on the way, 36 reaching the bulb, 34 turning into heat, 2 units of light.
That is an overall efficiency of about 2 per cent, and notice it is stated as a ratio. It is also the single best argument for insulation anyone has ever drawn: to get two units of light into a room, fifty times as much energy had to leave a coal seam.
The car diagram balances too: 65 lost as engine heat, 17 lost idling, 5 to wheel friction, 13 to actually moving forwards. 65 + 17 + 5 + 13 = 100.
Useful and wasted energy
A 100 W bulb draws 100 J every second and gives out about 5 J of light and 95 J of heat.
So an old filament bulb is a heater that happens to glow. That is 5 per cent efficient, and it is the clearest number in the topic.
One caption worth correcting on the board. You will see a photograph labelled "LED light tubes" that shows fluorescent tubes, which is exactly the thing the sentence beside it is contrasting LEDs against. The two look similar at a glance and behave very differently.
Three fair tests that break their own rules
The newspaper on one container only
The comparison of metal, glass, polystyrene and plastic containers is a good experiment, and then step one wraps only the metal container in newspaper.
That changes two things at once for a single sample, so the metal result cannot be compared with the other three. Either wrap all four or wrap none.
And then the questions ask whether the experiment was a fair test and to explain the answer. The honest answer is no, and the reason is the newspaper. It is an accidental masterpiece: a question whose correct answer exposes the design of the experiment it belongs to. Set it deliberately and give marks for spotting the newspaper.
The solar heater run on different days
The black-pipe solar water heater is a genuinely good, genuinely cheap practical. Then the method says to repeat it three times, each time with a different pipe arrangement.
Run on different days, the sunshine changes, and sunshine is the one variable that matters most. You would be measuring the weather.
Run all four arrangements side by side at the same time. The topic's own fair-testing pages demand exactly that a few units earlier.
The reading that can never be reached
One method has a steel container of boiling water standing inside a polystyrene container of cold water, and says to keep taking readings until the two temperatures are the same.
The polystyrene is there precisely to stop that happening. A class will still be sitting there at the bell.
Read for a fixed 15 or 20 minutes and compare the two curves. That is all the questions actually need.
U-values, with the units put back
A U-value measures how fast heat leaks through a square metre of something. Lower is better.
| Element | Uninsulated | Insulated |
|---|---|---|
| Brick wall | 1,7 | 0,6 |
| Tiled roof | 2,2 | 0,5 |
| Window | 5,6 single glazed | 2,9 double glazed |
The figures are sound but you will usually see them printed with no units at all. A U-value is measured in watts per square metre per kelvin, W/m²·K. A number in a physics table without a unit is half a fact.
Read the table for the real lesson: the roof is the worst offender and the cheapest to fix. That is why ceiling insulation is the first thing anyone recommends, and it is the single most useful thing in this topic for a learner to take home.
The Term 3 project, and the only thing you have to buy
This is formally assessed, it is worth 40 marks, and every Grade 7 class in the country has to do it.
| Part | What the learner does | Marks |
|---|---|---|
| 1 | Research eco-friendly homes | 6 |
| 2 | Research indigenous and traditional homes | 9 |
| 3 | Read the interviews and pick out the materials | 5 |
| 4 to 5 | Build a cardboard model house, and make one conducting roof and two insulating roofs | 10 |
| 6 | Test each roof with hot water and a thermometer, then evaluate the variables | 10 |
The printed total is 40 and it is correct. We recounted it: 6 + 9 + 5 + 10 + 10.
The whole apparatus list is a thermometer, two identical containers and hot water. Everything else is cardboard, newspaper, foil and whatever the class brings from home. That is the entire Grade 7 Term 3 kit.
The one thing that decides whether the test is fair: the volume of hot water.
Each container has to start with the same volume at the same starting temperature, and you cannot pour equal volumes by eye. A measuring cylinder is what turns this from a demonstration into an experiment, and it is the instrument the method forgets to ask for.
The indigenous homes section is the best content in the grade
This is properly researched and genuinely local, and it is worth more lesson time than it usually gets.
| Home | Where | How it handles heat |
|---|---|---|
| Traditional Xhosa home | Transkei | Thick earth walls, thatch, small openings |
| Fisherman's cottage | Arniston, Western Cape | Thick lime-washed walls against sun and wind |
| Zulu beehive | Zululand | Woven frame and thatch, shaped to shed rain and hold still air |
| Matjieshuis | Steinkopf, Namaqualand | Reed mats that swell shut in the wet and open to breathe in the heat |
| Stone house | Lalibela, Ethiopia | Stone mass that holds the night's cool into the day |
The interviews that follow are just as good: mealie-stalk walls in Zimbabwe, hay bales, the Cape Town Sandbag Housing Project, retractable windows, and a polystyrene-on-steel-frame house.
One place name to fix before you hand it out. One of the interviews places a matjieshuis in "Nababib, Namaqualand". There is no such town. The intended name is almost certainly Nababeep, which is in Namaqualand, and the earlier section uses Steinkopf, which is also real.
And a modern one worth knowing: Greensulate, an insulation grown from mushroom mycelium, patented in 2009 by Gavin McIntyre and Eben Bayer. That part is accurate and it lands well with a class, because it is insulation you could grow.
Safety: the box this topic never had
One method has learners screwing bulbs in and out of a mains lamp on an extension cord, repeatedly, with a towel spread underneath to catch drips. There is no safety note anywhere near it.
An incandescent bulb runs at 200 to 250 °C. That is hot enough to blister a finger instantly and hot enough to scorch fabric.
Three rules, and they are not optional:
- Unplug at the wall before touching a bulb. Every time, not just the first time
- Let it cool completely before unscrewing it. Minutes, not seconds
- Take the towel away. Use a tray or a tile. Never put fabric under a hot lamp
Better still, make it a teacher demonstration. The learners can read the thermometer and keep the table without anyone handling a live fitting.
If it does not work
| Problem | Cause | Fix |
|---|---|---|
| The two temperatures never become equal | Nothing. The polystyrene is doing its job | Stop at a fixed 15 or 20 minutes and compare the curves instead |
| The metal container looks like the best insulator | It is the one wrapped in newspaper | Wrap all four or none. That is the answer to the fair-test question |
| The roofs give nearly identical results | Different volumes of water, or different starting temperatures | Measure the water with a cylinder and start all of them within a degree |
| The solar heater results contradict each other | The arrangements were run on different days | Run all four at the same time |
| The model house collapses | Hot water in a cardboard box | Keep the water in a container inside the house, never against the cardboard |
| An efficiency answer comes out in joules | The subtraction formula was used | Divide, do not subtract. An efficiency is a percentage |
| The class cannot agree on the hottest roof | One thermometer passed between containers | One thermometer per container, read at the same moment |
One more wording slip worth catching
You will read that "heat moves from a body of higher heat to a body of lower heat". It is temperature, not heat, and the topic has it right earlier on.
Heat is the energy that moves. Temperature is what tells you which way it will go. A bath at 40 °C holds far more heat than a cup of tea at 80 °C, and the heat still flows from the tea to the room.
How the 40 marks are made up
| Part | Marks |
|---|---|
| Energy efficiency, and the formula that is wrong | 10 |
| The energy budgets that do not balance | 8 |
| Useful and wasted energy | 6 |
| Fair testing the insulation experiment | 8 |
| U-values and choosing a material | 8 |
The project is the assessed piece at 40 marks, and the topic revision is 20. Our worksheet is a separate 40 and the split above is ours. It is written to be set before the project, so that a learner meets the fair-test trap on paper rather than in an assessment.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 40 marks, including the efficiency calculation, the television budget to audit and the fair-test question
- Marking memorandum, with what to accept and the five answers that look right and score nothing
Related practicals
- Properties of Materials, Grade 7. The insulation fair test itself, run earlier in the same year, and the rehearsal for this project
- The Cost of Running Household Appliances, Grade 9. What all that wasted energy actually costs a household
- The Atmosphere and the Greenhouse Effect, Grade 9. The same heat-trapping idea at the scale of a planet
- Heating and Cooling Curves of Water, Grade 10. Where careful thermometer work goes next
What you need to run it
| Item | Price | What it is for |
|---|---|---|
| Thermometer, red spirit, −10 to 110 °C | R35 | The one thing this topic cannot be done without. Buy a class set |
| Measuring cylinder, glass | R55 | The instrument that makes the test fair. Equal volumes cannot be poured by eye |
| Beaker, borosilicate | R7 | The containers for the roof test. Two per group |
| Beaker, borosilicate, low form | R19 | The heavier-walled option if these live in a school cupboard |
| Safety goggles | R30 | Boiling water, and the bulb demonstration |
Why the thermometer argument is stronger here than anywhere else in Grade 7. This one topic uses a thermometer in four separate activities, and the assessed project is a fifth. One of those activities needs four thermometers running at the same time, because four containers have to be read together, which makes it a class-set requirement rather than a one-per-lab one.
At R35 each, a set of ten is R350, and across the Grade 7 year it comes back in the properties topic, in heat transfer, and in a formal assessment. It is the most re-used instrument in the grade and the cheapest thing on this list to get wrong.
One honest note on the range. We stock the same thermometer reading to 150 °C, but it is out of stock at the moment. The −10 to 110 °C version is the right one for this topic anyway, since nothing here goes above boiling water, and it reads to half a degree instead of a whole one.
We do not sell cardboard, newspaper, foil or polystyrene cups, and this project does not need us to. The thermometers and the cylinder are the purchase; the house is a shoebox.
Thermometers are in thermometers and the glassware is in laboratory glassware.