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 has a dangling or misplaced modifier, so it accidentally says something odd. Explain what the sentence literally says, then rewrite it.
- Walking into the gym, the smell of popcorn hit us.
- After finishing the essay, the printer jammed.
- She almost drove her little brother to practice every day.
Answer and teacher notes
1. Literally, the smell was walking into the gym. Fix: Walking into the gym, we smelled popcorn.
2. Literally, the printer finished the essay. Fix: After I finished the essay, the printer jammed.
3. Literally, she nearly drove him but never did. Fix: She drove her little brother to practice almost every day.
Rule of thumb: an opening -ing or “after” phrase describes whatever noun comes right after the comma, so make that noun the one doing the action. Limiting words like almost, only, just, and nearly modify the word right after them; move them next to what they really limit.
Math
Satellite records show global sea level has risen an average of 3.64 mm per year since 1999. (a) Using that average, about how much did sea level rise from 1999 to 2026, in millimeters and centimeters? (b) At the same rate, how many years would it take to rise one foot (304.8 mm)? (c) What assumption does your model make, and why might it be wrong?
Answer and teacher notes
(a) 2026 − 1999 = 27 years. 27 × 3.64 = 98.28 mm ≈ 9.8 cm, close to 10 cm (about 4 inches).
(b) 304.8 ÷ 3.64 ≈ 83.7 years. Check: 83.7 × 3.64 ≈ 304.7 mm.
(c) It is a linear model: it assumes the rate stays constant. An average over many years can hide a rate that is speeding up or slowing down, so the model could be off in either direction. Good follow-up: what kind of graph would you need to see to know whether the rate is changing? This figure comes from Europe’s new Sentinel-3C satellite announcement; its radar altimeter measures the height of the ocean surface.
Source: ScienceDaily: Europe’s New Sentinel-3C Satellite Just Sent Back Spectacular Images of Earth (European Space Agency)
Science
On October 15, 1783, Jean-François Pilâtre de Rozier rose about 250 feet over France in a tethered hot-air balloon, one of the earliest times a person went up in one. Air at 20 °C (293 K) has a density of about 1.20 kg/m³. At constant pressure, gas density is inversely proportional to absolute temperature. (a) What is the density of air heated to 100 °C (373 K)? (b) How much lift does each cubic meter of hot air provide? (c) About how large must the balloon be to lift a total of 250 kg (envelope, basket, and passenger)?
Answer and teacher notes
(a) ρ = 1.20 × (293 ÷ 373) ≈ 0.943 kg/m³, about 21 percent less dense.
(b) 1.20 − 0.943 ≈ 0.257 kg of lift per cubic meter.
(c) 250 ÷ 0.257 ≈ 970 m³ (about 960 m³ if you round the lift to 0.26 first).
The balloon floats for the same reason a cork does: it pushes aside outside air that weighs more than the balloon’s hot air plus its load. Discussion: why do hot-air balloons fly best on cool mornings? (A bigger temperature difference means more lift per cubic meter.) A month later, Pilâtre de Rozier and the Marquis d’Arlandes made an untethered flight of about five and a half miles.
Source: PBS NOVA: History of Ballooning
Social Studies
You have a free Saturday afternoon. You could (A) work a 4-hour shift at $12 an hour, (B) spend $30 on a ticket to a game with friends, or (C) study for a big test on Monday. Choose one. Then identify your opportunity cost, and explain why it is not simply “everything else.”
Answer and teacher notes
Opportunity cost is the value of the next-best option you give up, not the sum of every option. You can only do one thing with that afternoon, so you only lose your second choice.
Example: a student who picks the game and ranks working second gives up the $48 they would have earned (4 × $12) and spends $30, so the afternoon really “costs” $78 in money terms. A student who picks studying may say the cost is the $48 in wages, or the fun of the game, depending on their ranking. Accept any choice; grade whether students name one specific next-best option and explain it. Extension: how is a nation choosing between two uses of the same budget like this?
Current Events
The Moon’s near side, the one always facing Earth, has wide plains of dark volcanic rock. The far side is mostly old, heavily cratered highlands with a much thicker crust. A Nanjing University team reported this week in National Science Review that, after the Moon became tidally locked to Earth, tides heated the near side of its molten interior more, driving currents that carried crust-forming material toward the far side. Their evidence includes the first rocks ever returned from the far side, collected by China’s Chang’e-6 mission in 2024. (a) Why does the Moon always show Earth the same face? (b) Why were far-side samples so important for testing this idea?
Answer and teacher notes
(a) The Moon is tidally locked: it rotates once on its axis in the same time it takes to orbit Earth once, so the same side always faces us. Earth’s gravity slowed the Moon’s spin until the two periods matched.
(b) Earlier sample missions brought back rock only from the near side, so scientists could not directly compare the chemistry of the two halves. A hypothesis about why the sides differ needs evidence from both sides. The team found the deep mantle material looks chemically similar on both sides while the crust differs, which fits their idea that the difference formed as the magma ocean cooled. Push students: does this study prove the explanation, or make it more likely? What new evidence would test it further?
Source: ScienceDaily: Scientists May Have Finally Solved the Mystery of the Moon’s Two Faces (Science China Press; National Science Review, 2026)
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