Stage 3 · about 12–15
Structure and Evidence
The inner structure of each subject; argue from evidence.
Interactive labs, discussion groups, open problems.
All subjects at this stage
C
Chinese
How do you prove your reading?
- How a word's meaning moves through time Meanings drift: in classical Chinese 走 meant 'run' and 去 meant 'leave', so read an old text with the old meaning, and let the context prove it. Try it
- Map an argument: claim, reasons, evidence An argument is a claim held up by reasons, and each reason needs evidence; a reason with nothing under it does not hold the claim up. Try it
- Explain a thing: numbers, comparison or analogy Listing numbers makes a fact exact, comparing with something known makes the size graspable, and an analogy makes it vivid but only roughly right; a writer picks the method by what the reader needs. Try it
E
English
Why is this structure used here?
- The skeleton of a long sentence Strip away the clauses and phrases and a long sentence still stands on its subject and main verb (and object); find the main verb first. Try it
- REcord or reCORD? In English one syllable of a word is stressed — longer, louder, higher — and moving it can change the word: in many two-syllable pairs the noun is stressed first (a REcord) and the verb second (to reCORD). Try it
P
Physics
How are force and motion related?
- Do heavy things fall faster? Without air, everything falls with the same acceleration g; differences come from air resistance, which matters more for light, wide objects. Try it
- How far would a cart roll with no friction? The smoother the floor, the farther the cart rolls; with no friction at all it would never stop. Try it
- Is current used up in a bulb? The current is the same all the way round a series loop: a bulb turns energy into light and heat, it does not use up charge. In parallel each branch gets the full battery voltage and the branch currents add up. Try it
- Where does a lens put the picture? Rays from one point of the object meet again at one point of the image; move the object closer (but still beyond f) and the image moves away and grows; inside f there is only an upright, magnified virtual image, as in a magnifier. Try it
- Why doesn't a bed of nails hurt? What presses in is pressure, force divided by area: the same weight spread over a thousand nails or a wide snowshoe presses a thousand times more gently than on one nail. Try it
- How hard does water push up? The upward push equals the weight of the water the object shoves aside; once it is fully under, going deeper does not change it. Try it
- Where is the person in the mirror? A plane mirror's image sits behind the glass, as far behind as you are in front, so to see your whole body you need a mirror half your height, wherever you stand. Try it
C
Chemistry
How does one substance turn into another?
- Atoms are rearranged, never lost In a reaction atoms regroup into new molecules; the count of each kind of atom, and so the mass, stays the same. Try it
- Snap atoms into molecules Each atom makes a fixed number of bonds, so only certain molecules can be built. Try it
- Same atoms, different stuff Properties come from how atoms are arranged, not from the atoms themselves: graphite and diamond are both pure carbon. Try it
- pH: every step is ten times Each step down the pH scale means ten times more hydrogen ions. Try it
- New stuff, or the same stuff changed? A change is chemical only when a new substance forms; melting, boiling and dissolving keep the same molecules, burning makes new ones. Try it
- What does a nail need to rust? Iron rusts only when water and oxygen are both present; take away either one and the nail stays almost bright. Try it
- A mole is a number, like a dozen A mole is a fixed count of particles, 6.02 × 10²³; a mole of magnesium weighs twice a mole of carbon because each magnesium atom is twice as heavy. Try it
B
Biology
How is life organised?
- Zoom into a leaf, a hand, a pond Zoom in far enough on any living thing and you find cells. Try it
- Why are cells so small? When a cell doubles in width, its volume grows eight times but its surface only four, so big cells cannot feed themselves. Try it
- Where does a tree's mass come from? Most of a plant's dry mass is carbon taken from carbon dioxide in the air by photosynthesis, not from the soil. Try it
- Where does fat go when you lose weight? Most of the mass of burned fat leaves the body as carbon dioxide you breathe out; the rest leaves as water. Try it
- Mendel's peas: why the 3 : 1? Each parent passes on one of its two copies of a gene at random, so a hidden trait comes back in about a quarter of the grandchildren. Try it
- Why does a potato shrink in salt water? Particles never stop moving; water crosses a cell membrane both ways, and the net flow is towards the side where water is scarcer, the saltier side. Try it
- The heart is two pumps Blood goes through the heart twice per lap: the right side pumps it to the lungs, the left side pumps it to the body; it is always red, bright when full of oxygen and dark when not. Try it
- Breathing is not respiration Breathing only moves air in and out of the lungs; respiration, releasing energy from glucose (almost always with oxygen), happens inside every living cell, day and night, in plants too. Try it
G
Geography
Why do people here live the way they do?
- Read a place from its climate graph Twelve bars of rain and a line of temperature tell you the climate type, and the climate tells you what grows there. Try it
- What a population pyramid tells you The shape of the pyramid shows today's births and deaths and predicts the population of the next 30 years. Try it
- How a river bends itself In a bend the water runs fastest on the outside, which wears the bank away, and slowest on the inside, which drops sand — so bends grow and wander. Try it
- Is Greenland as big as Africa? A round Earth cannot be flattened without stretching; the Mercator map keeps directions true but blows up areas near the poles, so Greenland looks like Africa although Africa is about 14 times larger. Try it
H
History
Why should we believe this happened?
- How old is it? Tree rings and radiocarbon Carbon-14 in once-living things halves about every 5,730 years, so what is left works like a clock; tree rings, counted year by year, check and calibrate that clock. Try it
- Which source would you trust? Every source was made by someone, at some time, for some purpose; asking who, when and why tells you what the source can and cannot show. Try it
- What travelled the Silk Roads? The Silk Roads were a web of routes; goods, ideas, religions and inventions passed hand to hand through chains of traders, and few people travelled the whole way. Try it
- Where did your dinner come from? Many ‘traditional’ foods depend on crops that crossed the oceans between the Americas and the rest of the world only after 1492: chilli, potato, tomato, maize and sweet potato came from the Americas, while wheat, rice, sugar cane, cattle and horses went the other way. Try it
- Two people saw it — and told it differently Each eyewitness saw from one place, at one moment, with their own concerns, so honest witnesses can disagree; the parts that independent accounts share are the firmest evidence. Try it
C
Computing
How do we make a program smarter?
- Counting with only 0 and 1 In binary each place is worth twice the place to its right, so any whole number is a sum of 1, 2, 4, 8, …. Try it
- The sorting race Different step-by-step methods give the same sorted list but need very different numbers of comparisons. Try it
- Variables are labelled boxes A variable is a named box that holds one value at a time; putting a new value in throws the old one away, so swapping two boxes needs a third. Try it