Five warm-ups for grades 9–12. Each takes three to five minutes. Answers and teacher notes are in the collapsed box under each prompt.
ELA
Each sentence is in the passive voice. Rewrite each one in the active voice. If a sentence doesn’t say who did the action, decide who it probably was. Then answer: for which sentence might the passive voice actually be the better choice, and why?
- The window was broken by a soccer ball.
- Mistakes were made in the group project.
- The water temperature was recorded every five minutes.
Answer and teacher notes
1. A soccer ball broke the window.
2. Sample: We made mistakes in the group project. (Students must name an actor; any reasonable one works.)
3. Sample: We recorded the water temperature every five minutes.
Passive voice moves the receiver of the action to the front and makes the doer optional (“was broken by…”). Sentence 3 is the strongest case for passive: in a lab report, the measurement matters more than who took it, so scientific writing often uses passive. Sentence 2 is a classic example of passive used to dodge responsibility, since it hides who made the mistakes. Discussion: when you read a passive sentence with no actor, ask, “Who did this, and why isn’t the writer saying?”
Math
On Monday, October 19, 1987, known as Black Monday, the Dow Jones Industrial Average closed at 1,738.74. It had closed the previous trading day at 2,246.74. (a) Find the drop in points and as a percent. (b) What percent gain would the Dow need to climb from 1,738.74 back to 2,246.74? (c) Within two trading sessions, the Dow regained 288 points. What percent of the Black Monday loss was that? (d) Explain why a 22.6% loss takes more than a 22.6% gain to undo.
Answer and teacher notes
(a) 2,246.74 − 1,738.74 = 508 points. 508 ÷ 2,246.74 ≈ 0.2261 = 22.6%, still the largest one-day percentage drop in the Dow’s history.
(b) 508 ÷ 1,738.74 ≈ 0.2922 = about 29.2%. Check: 1,738.74 × 1.2922 ≈ 2,246.8.
(c) 288 ÷ 508 ≈ 0.567 = about 57% of the loss.
(d) A percent change is measured from the starting value. The loss is a percent of the larger number (2,246.74), but the recovery is a percent of the smaller number (1,738.74), so the same 508 points is a bigger percent of the smaller base. Extreme example: a 50% loss needs a 100% gain to recover. Context: after the crash, regulators created “circuit breakers” that pause trading during very large declines, and U.S. markets passed their pre-crash highs in less than two years.
Sources: Federal Reserve History: Stock Market Crash of 1987; Wikipedia: Black Monday (1987) (closing values)
Science
The Orionid meteor shower peaks on the night of October 21 into the morning of October 22. The meteors are bits of debris left behind by Halley’s Comet, which orbits the Sun about once every 76 years. Kepler’s third law says that for objects orbiting the Sun, T² = a³, where T is the period in years and a is the semi-major axis (half the long axis of the orbit) in astronomical units (AU). (a) Find a for Halley’s orbit. (b) At its closest, Halley is 0.5871 AU from the Sun. The closest and farthest distances add up to 2a. How far from the Sun does it get at its farthest? (c) Halley last passed closest to the Sun in 1986. 1986 + 76 = 2062, yet astronomers expect it back in 2061. Suggest a reason.
Answer and teacher notes
(a) a³ = 76² = 5,776, so a = ∛5,776 ≈ 17.9 AU. Check: 17.9³ ≈ 5,735, and 18³ = 5,832, so a is between 17.9 and 18.
(b) Farthest distance = 2a − 0.5871 ≈ 2(17.94) − 0.59 ≈ 35.3 AU, beyond Neptune’s orbit. NASA lists Halley’s farthest distance as 35.25 AU, so the estimate is very close.
(c) “76 years” is an average. The gravity of the planets, especially Jupiter and Saturn, tugs on the comet and changes each orbit slightly. Halley’s period has ranged from about 74.4 years (1835–1910) to about 79.3 years (451–530).
Viewing tip: a bright waxing gibbous Moon will wash out fainter meteors this year, so the best chance is the few hours before dawn, after the Moon sets. Halley’s debris also causes the Eta Aquariid shower each May.
Sources: NASA: Comet 1P/Halley; NASA: What’s Up, October 2026 Skywatching Tips
Social Studies
On October 19, 1781, British General Charles Cornwallis surrendered about 8,000 soldiers at Yorktown, Virginia, nearly assuring American independence. Consider this evidence: Washington’s 2,500 American troops in New York were joined by 4,000 French troops under the comte de Rochambeau for the march south. A French fleet of 24 ships under Admiral de Grasse blockaded Cornwallis by sea and turned back a British fleet at the Battle of the Virginia Capes on September 5. By early October, about 14,000 French and American troops surrounded Yorktown. Write a one-sentence claim answering: Was Yorktown mainly an American victory or a joint Franco-American victory? Support it with two pieces of evidence.
Answer and teacher notes
Answers will vary; grade the claim-evidence link. A strong “joint victory” answer: the French made up a large share of the land force (4,000 French next to 2,500 Americans from New York), and only the French navy could cut off Cornwallis’s escape and resupply by sea. A strong “American victory” answer: Washington commanded the combined army, American troops already in the region (about 4,500) had pinned Cornwallis down, and the war was fought for American goals.
Push for nuance: an army can be led by one side while depending on another for success. Extension: France had its own reasons to fight Britain. What might they have been? (Rivalry with Britain and the chance to weaken it after losing territory in the Seven Years’ War are common answers.) Quick math: 2026 − 1781 = 245 years ago today.
Source: Britannica: Siege of Yorktown
Current Events
A Max Planck Institute for Radio Astronomy team reported this weekend in Monthly Notices of the Royal Astronomical Society what they call “compelling evidence” that the galaxy Markarian 501 holds two supermassive black holes orbiting each other, possibly close enough to merge in as little as 100 years. The two are too close together to be seen separately. Instead, the team used radio observations taken over about 23 years, tracked a second jet of material, and found repeating brightness patterns that suggest one orbit takes about 121 days. (a) About how many orbits would have happened during 23 years of observations? (b) Why does seeing a pattern repeat many times make the case stronger than seeing it once? (c) Why do the scientists say “evidence” instead of claiming they have proved the pair exists?
Answer and teacher notes
(a) 23 years × 365.25 days ≈ 8,401 days. 8,401 ÷ 121 ≈ 69 orbits.
(b) A single change in brightness could be random. A pattern that repeats on a steady schedule dozens of times is much harder to explain by chance and points to a regular cause, such as an orbit. (c) They are inferring the pair from indirect clues, not imaging two separate black holes, and even the Event Horizon Telescope cannot resolve them. Other explanations are still possible. The article says confirmation could come from pulsar timing arrays detecting low-frequency gravitational waves from the pair. Discussion: what is the difference between “we observed it” and “the evidence strongly suggests it”?
Source: ScienceDaily: Two Monster Black Holes Could Collide in Just 100 Years (Max Planck Institute for Radio Astronomy; Monthly Notices of the Royal Astronomical Society, 2026)
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