Numbers Every Science Teacher Should Have on Tap: Deep Time, Molecules, and the Air in Your Lungs

Some numbers don't teach content on their own — they teach scale. A student can memorize that atoms are mostly empty space, that life has existed on Earth for billions of years, that a single breath holds an almost unspeakable number of molecules, and still not feel any of it, the way Everybody's Science's Ch. 3, “The Edge of the World,” argues a person has to in order for deep time to mean anything at all. The three numbers below are the ones worth keeping in your pocket, ready to produce cold, the next time a student asks a question that's really asking how big, how old, or how much. Each one is small enough to say out loud in fifteen seconds and large enough to change how a room is thinking when you say it. After the three deep dives below, this page also grows into a standards-aligned bank of shorter numbers — and a way of actually using any of them in a real lesson, not just knowing them.

How long have we been standing up?

In 1978, at a site called Laetoli in Tanzania, a trail of footprints was found pressed into a layer of volcanic ash and hardened by a later rainfall — a literal snapshot of a walk taken one ordinary afternoon, 3.66 million years ago. The trackway belongs to Australopithecus afarensis, the same species as the famous “Lucy” skeleton, and detailed biomechanical analysis of the prints (weight transfer, stride, foot proportions) shows a gait already remarkably close to a modern human's — not a transitional shuffle, but functionally upright walking, preserved directly rather than inferred from bone shape alone. It remains the oldest unequivocal physical evidence of obligate bipedalism in the human lineage.

That single number reframes the whole timeline. Life has existed on Earth for roughly 3.8 billion years. Bipedal walking — the thing that freed the hands that eventually held tools, and pens, and phones — has existed for about 0.1% of that span. If life on Earth were a 224-year-old person the age of the United States, upright walking would have started roughly two weeks ago. The evidence gets murkier before Laetoli: candidate bipeds like Sahelanthropus (roughly 7 million years old) and Orrorin (roughly 6 million years old) show skeletal hints of upright posture, but the evidence is skeletal inference, not a footprint you can put your own foot next to. And a fully modern, efficient long-distance walking gait — the kind built for endurance, not just balance — doesn't clearly show up until Homo erectus, around 1.9 million years ago.

There's a chemistry story hiding inside the biology one, too: that Laetoli ash layer wasn't dated by guesswork. Volcanic rock layers like it are dated using potassium-argon decay — potassium-40 decays to argon-40 with a half-life of about 1.25 billion years, the same radiometric-dating principle behind the Carbon-14 one-pager on this site, just with a much slower clock suited to a much older rock. The footprints are a biology story that only exists because someone could answer a chemistry question first.

Biology BIO.7 Chemistry CH.2

How many molecules are in the ice cube in your drink?

Measure an ordinary ice cube from a tray — about 3 cm on each edge — and the math from there is exactly the mole concept a Chemistry student is already building toward, just run on something they can hold in their hand instead of a beaker:

• Volume: 3 cm × 3 cm × 3 cm = 27 cm³
• Mass: 27 cm³ × 0.9167 g/cm³ (density of ice) ≈ 24.75 g
• Moles: 24.75 g ÷ 18.015 g/mol (molar mass of water) ≈ 1.37 mol
• Molecules: 1.37 mol × 6.022 × 10²³/mol ≈ 8.3 × 10²³ molecules

That ordinary ice cube contains more than a full mole of water — which means, using a widely cited (if necessarily rough) planetary estimate of about 7.5 × 10¹⁸ grains of sand across every beach and desert on Earth, the ice cube in one glass of tea holds roughly 110,000 times more water molecules than there are grains of sand on the entire planet. And it's the same story every cell in your body is quietly running: water is the medium almost every biochemical reaction in a living thing happens inside.

Chemistry CH.4

How many moles of air are you holding right now?

An adult's total lung capacity is roughly 6 liters. At body temperature (37°C, or 310 K) and normal atmospheric pressure, the ideal gas law turns that volume directly into a mole count:

• n = PV ÷ RT
• n = (1 atm × 6 L) ÷ (0.0821 L·atm/mol·K × 310 K)
• n ≈ 0.24 mol of air, held in a full pair of lungs

A single ordinary breath (about 0.5 L of the full 6 L capacity) is closer to 0.02 mol — still roughly 1.2 × 10²² molecules moving in and out with one unremarkable inhale. Air itself is a mixture, so that 0.24 mol splits out further: about 0.18 mol is nitrogen and about 0.05 mol is oxygen, sitting side by side in the same breath at their own partial pressures — Dalton's law made physically real, in your own chest, right now. And the reason any of that oxygen matters biologically is the same gas-law chemistry running in reverse across the walls of every alveolus, trading oxygen for carbon dioxide with each of those roughly 0.24 mol breaths.

Chemistry CH.6

Turning numbers into holds, pivots, and checkpoints

Having a number on tap isn't the same as using it. The three deep dives above, and the bank below, only earn their keep if they show up inside a real lesson at one of three specific moments.

Three ways to put this into a real week, none of which need more than a few minutes of setup:

• A wall chart. Print the table at the bottom of this page and post it. A number a student can glance at from across the room gets asked about, unprompted, far more often than one buried in a notebook.
• A rotating bell-ringer. Pull one number from the bank below as the first question of class, unannounced, disconnected from whatever unit you're currently teaching. The disconnect is the point — it tests whether the number survived past its original lesson.
• Thumbs up, or write it down. Say the number, ask for a silent thumbs up if the room remembers what it means, and call on someone with a thumb down before moving on. Or skip the show of hands entirely and have every student write the number and one line about it in their notes — the retrieval-practice habit this site's AI-literacy protocol and peer-review article both build on elsewhere.

A standards-aligned number bank to grow all year

Use these the same three ways — as holds, pivots, or checkpoints — not as a list to cover in one sitting. Add to it as your own year turns up numbers worth keeping.

Print this as a wall chart

Every number on this page, in one table — the flagship three above, plus the full bank, in the order they appear.

Laetoli footprint age, species attribution, and gait analysis: Masao F.T. et al., “New footprints from Laetoli (Tanzania) provide evidence for marked body size variation in early hominins,” eLife, 2016; Hatala K.G. et al., “Laetoli Footprints Preserve Earliest Direct Evidence of Human-Like Bipedal Biomechanics,” PLOS ONE, 2010; Liutkus-Pierce et al. and related Nature Communications/Nature coverage of Laetoli Site S, 2021. Sahelanthropus, Orrorin, and Homo erectus dates: standard paleoanthropology references. Potassium-argon dating half-life and volcanic-ash dating method: standard geochronology references, and this site's own Carbon-14 one-pager. Ice density (0.9167 g/cm³ at 0°C), water's molar mass (18.015 g/mol), and Avogadro's number (6.02214076 × 10²³/mol, CODATA exact value): standard physical-chemistry references. Grains-of-sand planetary estimate (≈ 7.5 × 10¹⁸): widely cited University of Hawaii estimate, presented here as an order-of-magnitude comparison, not a precise count. Adult total lung capacity (≈ 6 L) and body-temperature ideal gas law calculation: standard human-physiology and chemistry references. Age of Earth (4.54 ± 0.05 billion years) and age of the universe (≈ 13.8 billion years): current scientific consensus, cross-checked July 2026 — the 4.54 billion figure is from radiometric dating of meteorites, not Earth rock directly, since Earth's oldest surface rock has been recycled by plate tectonics. The “ten percent law” of trophic energy transfer: standard ecology curriculum content (Lindeman's trophic-dynamic concept, 1942, is the classic source; modern estimates vary roughly 5–20% depending on ecosystem, with 10% used as the standard teaching approximation). Chromosome counts (46 somatic / 23 gamete), meiosis/mitosis daughter-cell counts, codon length (3 nucleotides), and standard amino acid count (20): standard genetics curriculum content. Molar volume of an ideal gas at STP (22.4 L): traditional STP convention (0°C, 1 atm) most Virginia courses and this course use — note IUPAC's current formal STP definition (0°C, 100 kPa) gives 22.7 L instead, worth confirming which convention your own assessments use. Standard atmospheric pressure (1 atm = 101.3 kPa = 760 mmHg), 0 K/273 K conversion, and water's freezing/boiling points: standard physical-chemistry references. Octet rule (8 valence electrons): standard chemical-bonding curriculum content. pH scale (0–14 range, 7 neutral): standard acid-base chemistry references. Virginia SOL codes (BIO.3, BIO.5, BIO.6, BIO.7, BIO.8, CH.2, CH.3, CH.4, CH.5, CH.6) verified against the 2018 Virginia Science Standards of Learning Curriculum Framework (doe.virginia.gov), current as of July 2026 — recheck before publishing, and before adding new numbers to the bank above.