Lesson 4 — Critiquing the Numbers in Public Claims

Summary

Learners put orders of magnitude to work on real public claims about populations, energy, and carbon: they estimate what the number should be, compare it to the claim, and write a verdict of plausible or not. They learn the back-of-the-envelope check as an everyday honesty tool, and distinguish evidence (what the numbers say) from values (what we should do about them).

Objectives

• Reason quantitatively about large systems and critique the numbers used in public claims. (D05.S1.12.02)

Connection

A headline says a country will “use one hundred times more energy by 2050,” or that a new project will “power a million homes.” Before you repeat it, you can check it: does a million homes match the order of magnitude of the country’s population? Is “one hundred times” even possible in one generation? A quick estimate turns you from someone who receives numbers into someone who checks them — a skill that matters wherever public decisions are made, from a village meeting to a national energy plan.

Materials

• Claim-critique sheet
• Math journal
• Low-tech: a headline with a number, scratch paper

Preparation

• Gather two or three real, recent claims with large numbers (energy, population, carbon).
• Retrieval: from Lesson 3, the powers-of-ten ladder and Fermi estimation. Today we aim them at a claim.
• Prepare the four-step critique as a worked example to model first (S-011).

Facilitator note

This lesson is written to the learner (“you”). The idea to land: a four-step check — read the claim, estimate what the number should be, compare, and write a verdict — turns orders of magnitude into a working honesty tool. Teach the worked example explicitly, then let learners run the loop on fresh claims (S-011). Keep two things distinct: the factual question (is the number even plausible?) and the value question (what should be done?), because conflating them is exactly what misleading claims exploit.

The ethics lens: checking a number before repeating it is a small act of honesty that compounds in public life. The egalitarianism lens: the skill is free and universal — it puts a citizen and a headline on the same footing, and it protects the people a false number would harm (a mis-stated risk, an inflated benefit). The global lens: the same check applies in every place; a per-capita reading (“per person,” not just “total”) keeps big countries from dwarfing small ones by raw size (S-006). The technology lens: the numbers we check increasingly arrive through feeds and dashboards, so the skill scales to screens as much as to print. The environment lens: energy and carbon claims are where this matters most — gigatonnes, terawatt-hours, and “homes powered” are checkable against authoritative climate data (S-005, S-006). Preview: Lesson 5 begins modeling systems with equations.

Procedure

1. Recall (5 min). From Lesson 3, name the rungs of the ladder and one Fermi problem you solved. Today the ladder becomes a lie-detector.
2. Read the claim (6 min). “A new power plant will supply electricity to 10 million homes.” Read it aloud and underline the number and the thing it counts.
3. Worked example — the four-step check (15 min). (1) Estimate: how many homes does one power plant roughly serve? A big plant is on the order of 1 GW; a home draws on the order of a few kW, so roughly 10^5 to 10^6 homes — a million at most. (2) Compare: the claim says 10 million, ten times more. (3) Verdict: implausible — off by about an order of magnitude. (4) Say — or write, sign, gesture, or use AAC to show — what you’d need to believe it: a plant ten times bigger than any built. Write all four steps.
4. Per capita (6 min). A raw total can hide the per-person story: 1 million tonnes of carbon sounds enormous, but across 100 million people it is 10 kg each. Compute per capita to compare fairly.
5. Critique a fresh claim (15 min). With a partner, run the four-step check on a different claim (energy, population, or carbon). Estimate, compare, and write a verdict with the reasoning visible. Be ready to say — or write, sign, gesture, or use AAC to show — whether the number is wrong or whether you simply disagree with the values behind it — those are different.
6. Share and check (6 min). Pairs exchange verdicts and check each other’s estimate — does the order of magnitude hold up? Give one specific improvement.
7. Close (2 min). Say — or write, sign, gesture, or use AAC to express — what a “plausibility check” is and why “I don’t know the exact number” is not an excuse to skip it.

Differentiation

• Support: Check only whether the claim is “bigger than a city or bigger than a country,” using the ladder, before computing anything.
• Extension: Write a corrected, honest version of the claim, and state the per-capita figure with the comparison to an authoritative source.
• Number access (dyscalculia): Use the step-3 claim-critique sheet as a pre-printed organizer — boxes for “estimate,” “compare,” and “verdict” already labeled — so the learner fills phrases rather than computations; offload the per-capita division (1 million tonnes ÷ 100 million people) to a partner or calculator; and take the verbal route — ask only “is this number bigger than a city or bigger than a country?” and answer in words, reaching the plausibility verdict without any arithmetic.
• Communication access: Every spoken step — saying, naming, reading aloud, discussing, or closing — can be done in writing, sign, gesture, or AAC instead. Learners who are non-speaking, d/Deaf, hard-of-hearing, or who use AAC complete every task in their preferred mode; no step requires producing or hearing sound.

Assessment

• Formative (peer + self): Can the learner estimate an order of magnitude for a claimed quantity, compare it to the claim, and write a reasoned verdict separating fact from value?
• Portfolio artifact (unit): One completed claim critique with all four steps, added to the math journal.

Home connection

Find one number in a news story or ad at home, estimate what it should be, and write one sentence verdict: plausible or not, and why. Bring the claim and your check to share.

Resources

• On worked examples and guided practice: Kirschner, Sweller & Clark (2006) (S-011).
• On global energy, carbon, and per-capita figures to check against: IPCC (S-005); Our World in Data (S-006).