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

A misplaced modifier is a word or phrase placed too far from what it describes. A dangling modifier describes something that isn’t in the sentence at all. Both can make a sentence say something you didn’t mean. Rewrite each sentence so its meaning is clear, and label the error as misplaced or dangling.

  1. Running down the hallway, the bell rang before I reached my classroom.
  2. She served sandwiches to the hikers on paper plates.
  3. After finishing the essay, the printer ran out of ink.
  4. He almost read the whole book in one night.
  5. Covered in mud, my mother made the dog stay outside.
Answer and teacher notes

1. Dangling: “As I was running down the hallway, the bell rang before I reached my classroom.” (The bell wasn’t running.)
2. Misplaced: “She served the hikers sandwiches on paper plates.”
3. Dangling: “After I finished the essay, the printer ran out of ink.” (The printer didn’t finish the essay.)
4. Misplaced: “He read almost the whole book in one night.” (He did read most of it, not nearly start it.)
5. Misplaced: “My mother made the dog, which was covered in mud, stay outside.” Also accepted: “My mother made the mud-covered dog stay outside.”

Quick test: ask “Who or what is doing this?” The answer should sit right next to the modifier. Opening phrases like “Running down the hallway” should be followed immediately by the person doing the running. Limiting words such as almost, only, just, and nearly go right before the word they limit. Other rewrites can be correct if the meaning is clear. Extension: write a funny sentence with a dangling modifier, then trade with a partner and fix it.

Math

On November 2, 1988, a self-copying program now known as the Morris worm began spreading across the early Internet. Commonly reported figures say it reached about 6,000 of about 60,000 connected computers within roughly a day. Suppose the infection began with 1 computer and doubled every d hours, so N(t) = 2t/d. (a) If N(24) = 6,000, find d to the nearest hundredth of an hour. (b) According to this model, when would all 60,000 computers be infected? (c) Give two reasons a real infection wouldn’t keep following this curve. (d) The program was written to copy itself onto a machine about 1 time in 7, even if the machine seemed already infected. If a machine received 20 such attempts, what is the probability that at least one succeeded?

Answer and teacher notes

(a) 224/d = 6,000, so 24/d = log2 6,000 ≈ 12.55 and d ≈ 24 ÷ 12.55 ≈ 1.91 hours. (b) t = d × log2 60,000 ≈ 1.912 × 15.87 ≈ 30.4 hours. Check: ten times as many computers takes log2 10 ≈ 3.32 more doublings, or about 6.4 more hours after hour 24. ✓ (c) Answers will vary: there are fewer uninfected machines left to reach, so growth slows; administrators disconnected and repaired systems. (d) P(at least one) = 1 − (6/7)20 ≈ 1 − 0.046 = 0.954, about 95%.

Point out the difference between exponential and logistic growth, which levels off as the population runs out. The 6,000 figure is itself a rough estimate: Wikipedia reports that it may have come from a guess of 60,000 total computers and a 10% infection rate, and another estimate was only “a couple thousand.” The doubling model and the starting value of 1 are assumptions, not measured data. In (d), the attempts are treated as independent. Common mistake: computing 20 × 1/7, which is the expected number of copies (about 2.9), not a probability. The worm slowed many computers, and it led to the creation of the CERT Coordination Center at Carnegie Mellon University to coordinate responses.

Sources: Britannica: On This Day, November 2 (date, about 6,000 machines, about a tenth of the Internet); Wikipedia: Morris Worm (one-in-seven rule, uncertainty in the estimate, CERT); Tom’s Hardware: On This Day in 1988 (60,000 systems, 24-hour time frame)

Science

Thousands of runners finished the New York City Marathon on Sunday. Late in a race, some marathoners “hit the wall,” a sudden, severe fatigue. A 2010 study in PLOS Computational Biology describes it as the result of nearly using up the carbohydrate stored in the leg muscles and liver. The body then must rely more on fat. The study notes that burning carbohydrate gives more energy for each mole of oxygen than burning fat does, and that the chance of hitting the wall peaks around mile 21. (a) Balance the equation for burning palmitic acid, a common fatty acid: C16H32O2 + __ O2 → __ CO2 + __ H2O. (b) Glucose needs 6 mol of O2 for its 6 carbon atoms. How many moles of O2 does palmitic acid need per carbon atom? (c) A runner can breathe in only so much oxygen per minute. Use this to explain why running out of carbohydrate forces a slower pace. (d) About what percent of a 26.2-mile race is complete at mile 21?

Answer and teacher notes

(a) C16H32O2 + 23 O2 → 16 CO2 + 16 H2O. Check oxygen: 2 + 46 = 48 on the left, and 32 + 16 = 48 on the right. ✓ (b) 23 ÷ 16 ≈ 1.44 mol O2 per carbon, compared with 6 ÷ 6 = 1 for glucose. (c) Oxygen supply limits how fast fuel can be burned. Since fat releases less energy per mole of oxygen, a runner relying more on fat produces less energy per minute from the same oxygen intake, and must slow down. (d) 21 ÷ 26.2 ≈ 80%.

The study also notes that muscle glycogen can be used only by the muscle cell that stores it, so the leg muscles must have their own supply. The chance of hitting the wall isn’t the same for everyone: the risk depends on pace, training, and fueling. The study reports that a 3:42:00 marathon takes about 1,500 kilocalories for a 75 kg runner. Extension: how many kilocalories is that per mile? (1,500 ÷ 26.2 ≈ 57 kcal per mile.) Keep the discussion on chemistry and performance, not on dieting or body size.

Source: Rapoport (2010), Metabolic Factors Limiting Performance in Marathon Runners, PLOS Computational Biology (definition, mile 21, oxygen per mole of glucose and palmitic acid, energy per oxygen, and the 3:42:00 example)

Social Studies

Marie Antoinette, the last queen of France before the French Revolution, was born on November 2, 1755, in Vienna, and died in 1793. Many people still believe she heard that the poor had no bread and said, “Let them eat cake.” Britannica says she probably never said it. The French phrase, about brioche, appears in Rousseau’s Confessions, written around 1767, where he credits it to “a great princess.” A German tale from the 1500s tells a similar story about a noblewoman. In 1843, the writer Alphonse Karr tied the line to Marie Antoinette, citing a book dated 1760. (a) How old was she in 1767? In 1760? How many years after her death did Karr connect her to the line? (b) What makes Rousseau’s text weak evidence that she said it? (c) Why might a false quotation stick to a person for centuries? (d) Britannica says her court spending was only a minor cause of France’s money problems. Why might people have blamed her anyway?

Answer and teacher notes

(a) In 1767 she was 11 or 12, depending on the month (1767 − 1755 = 12, with a November birthday). In 1760 she was 4 or 5. 1843 − 1793 = 50 years after her death. (b) It never names her. She was a child living in Vienna at the time, so the “great princess” was probably someone else. (c) Answers will vary: it is short and memorable; it fits what people already believed about her; it turns a complicated crisis into one person’s fault; and it gets repeated without being checked. (d) Answers will vary: she was a visible and wealthy royal; she was from Austria, which was unpopular in France; rumors spread about her; and a single person is an easier target than a whole financial system.

Use this as a sourcing exercise: who said it, when, how did they know, and how much time passed? Note that repeating a claim many times doesn’t make it stronger evidence. Britannica says some have suggested that revolutionaries spread the line about her, but that researchers have found no evidence of it in revolutionary publications. Extension: find a popular quotation credited to a famous person and try to trace it to its earliest source.

Sources: Britannica: Did Marie-Antoinette Really Say “Let Them Eat Cake”? (origins of the phrase, Rousseau, Karr); Britannica: Why Is Marie Antoinette So Famous? (probably never said it); Britannica: Marie-Antoinette (birth and death, reign, spending, Austria, rumors)

Current Events

On October 29, NASA astronaut Anil Menon and Canadian Space Agency astronaut Joshua Kutryk finished a 7-hour, 11-minute spacewalk that installed the seventh of eight new solar arrays on the International Space Station. It was the 100th U.S. spacewalk. The last array is scheduled to go up this Thursday, November 5. NASA says the arrays will raise the station’s power from 160 kilowatts to about 215 kilowatts, and also describes the gain as “up to 30%.” The original solar wings were installed starting in 2000 and were designed to last 15 years. (a) The spacewalk ended at 3:08 p.m. EDT. When did it start? (b) What percent increase is 160 kW to 215 kW? How does it compare with “up to 30%”? What questions would you ask NASA? (c) How many years past their 15-year design life are the oldest wings, as of 2026? (d) The station is planned to retire in 2030. Why spend the effort on new arrays so close to the end?

Answer and teacher notes

(a) 3:08 p.m. minus 7 hours is 8:08 a.m.; minus 11 more minutes is 7:57 a.m. EDT. (b) (215 − 160) ÷ 160 = 55 ÷ 160 ≈ 34%. A 30% increase would give only 160 × 1.30 = 208 kW, so the two figures don’t quite match. Answers will vary: Are the two numbers measuring the same thing? What baseline does each use? Is 215 kW a rounded value or a best case? (c) 2000 + 15 = 2015, and 2026 − 2015 = 11 years. (d) Answers will vary: Spaceflight Now reports that the old wings have lost power with age and that the added power is meant to carry the station through retirement in 2030, including its controlled deorbit.

This is a good chance to practice reading numbers critically. Don’t assume either NASA figure is wrong, since we can’t tell from the reports what explains the gap. Not all wings were installed in 2000; they went up between 2000 and 2009. Extension: follow Thursday’s spacewalk. Did the final array go up as planned, and did NASA update its numbers?

Sources: NASA: Spacewalkers Install Roll-Out Solar Arrays for Power Generation (date, crew, duration, power figures, November 5 plan, spacewalk count); Spaceflight Now: NASA Nears End of Space Station Solar Array Upgrade (original wings, 15-year design life, 2030 retirement)

Keep going

More bell ringers: Bell ringers for high school · Math bell ringers · Science bell ringers · Social studies bell ringers · Grammar bell ringers · 100 bell ringer questions

End of class: Exit tickets for high school · Math exit tickets · ELA exit tickets · Science exit tickets · Social studies exit tickets · Printable exit slips

Tools: Printable bell ringer sheet · Free AI bell ringer creator

Categorized in:

Grades 9–12