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 pronoun needs a clear antecedent, the noun it stands for. Each sentence below has a pronoun that is ambiguous or vague. Name the problem pronoun, explain why a reader could be confused, and rewrite the sentence so the meaning is clear. Do at least three.
- When Maya handed the folder to Jordan, she smiled.
- The coach told the player that he needed more rest.
- The museum closed its west wing for repairs, which upset visitors.
- They say the bridge will reopen next month.
Answer and teacher notes
1. She could be Maya or Jordan. Fix: Maya smiled as she handed the folder to Jordan. 2. He could be the coach or the player. Fix: The coach told the player, “You need more rest.” or The coach said that he himself needed more rest. 3. Which has no single noun to point to. Did the repairs upset visitors, or the closing? Fix: Visitors were upset that the museum closed its west wing for repairs. 4. They has no antecedent at all. Fix: City officials say the bridge will reopen next month.
Sentence 4 matters beyond grammar: a vague “they say” hides the source of a claim. Ask students why a reader should trust a claim more when the writer names who said it. Quick test for any pronoun: can you point to exactly one noun it replaces? If not, rewrite.
Math
Under the ADA accessibility standards, a wheelchair ramp can have a running slope no steeper than 1:12 (1 inch of rise for every 12 inches of horizontal run), and a single ramp run can rise at most 30 inches. A building’s entrance is 24 inches above the sidewalk. (a) What is the minimum horizontal run, in feet? (b) What angle does the ramp make with the ground, to the nearest tenth of a degree? (c) How long is the sloped ramp surface, to the nearest inch? (d) If the entrance were 36 inches high instead, why couldn’t one straight ramp run do the job?
Answer and teacher notes
(a) 24 × 12 = 288 inches = 24 feet.
(b) tan θ = rise/run = 1/12, so θ = tan−1(1/12) ≈ 4.8° (4.76°). Check: tan(4.76°) ≈ 0.0833 ≈ 1/12. ✓
(c) Pythagorean theorem: √(288² + 24²) = √(82,944 + 576) = √83,520 ≈ 289 inches, only about 1 inch longer than the run because the angle is so small.
(d) A 36-inch rise is more than the 30-inch limit for one run. The ramp would need at least two runs with a level landing between them. The total horizontal run would be at least 36 × 12 = 432 inches (36 feet), plus the landing.
Discussion: a 4.8° angle sounds tiny. Why do you think the limit is so gentle? (Someone pushing their own wheelchair has to move their body weight uphill, and a steep ramp is also harder to control going down.) The guide also requires level landings at the top and bottom of each run, at least 60 inches long.
Source: U.S. Access Board: Guide to the ADA Standards, Chapter 4: Ramps and Curb Ramps
Science
Cold weather is coming, and a space heater is labeled 1,500 watts. It plugs into a standard 120-volt outlet. Use P = IV and P = V²/R. (a) How much current does the heater draw? (b) What is the resistance of its heating element while it runs? (c) The U.S. Department of Energy estimates daily use as (watts × hours per day) ÷ 1,000 = kilowatt-hours (kWh). Suppose the heater runs 5 hours a day for 30 days and electricity costs $0.16 per kWh. What does it cost to run for the month? (d) Suppose the outlet is on a 15-amp circuit. Could you run a 1,000-watt hair dryer on the same circuit at the same time? Explain.
Answer and teacher notes
(a) I = P/V = 1,500 ÷ 120 = 12.5 amps.
(b) R = V²/P = 120² ÷ 1,500 = 14,400 ÷ 1,500 = 9.6 ohms. Check with Ohm’s law: V/I = 120 ÷ 12.5 = 9.6 Ω. ✓
(c) (1,500 × 5) ÷ 1,000 = 7.5 kWh per day. 7.5 × 30 = 225 kWh. 225 × $0.16 = $36.00 for the month.
(d) No. A 15-amp circuit at 120 volts can supply about 120 × 15 = 1,800 watts. The heater plus the hair dryer is 1,500 + 1,000 = 2,500 watts, which would draw about 20.8 amps and should trip the breaker.
The 15-amp circuit and $0.16 rate are assumptions for the problem; real rates and circuits vary, so students can check a home electric bill for the actual price per kWh. Extension: a heating element has low resistance on purpose, so it draws a large current and turns electrical energy into heat (P = I²R). Why might a manufacturer warn against plugging a space heater into an extension cord?
Source: U.S. Department of Energy: Estimating Appliance and Home Electronic Energy Use
Social Studies
Alfred Nobel was born on October 21, 1833, in Stockholm, Sweden. He became an inventor and industrialist whose inventions included dynamite and the blasting cap. On November 27, 1895, about a year before he died, he signed a will leaving most of his estate, more than 31 million Swedish kronor, to fund prizes for those who brought “the greatest benefit to humankind” in physics, chemistry, physiology or medicine, literature, and peace. The first prizes were awarded in 1901. His will also asked that “no consideration be given to nationality.” (a) Nobel died in December 1896. How many years passed before the first prizes? (b) The Nobel Foundation says 31 million kronor then is worth about 2.2 billion kronor today. By about what factor has the value grown? (c) Why might Nobel have insisted that nationality not matter? What problem could that rule prevent?
Answer and teacher notes
(a) 1901 − 1896 = 5 years. (b) 2,200,000,000 ÷ 31,000,000 ≈ 71 times. Note that this compares the money’s value in today’s terms, which reflects inflation as well as growth.
(c) Answers will vary; grade the reasoning. Strong answers note that without the rule, judges might favor their own country (Nobel was Swedish), which would make the prizes look biased and less respected worldwide. An international prize gains credibility when the best work can win no matter where it comes from. Extension: what does someone’s will tell historians about what that person valued? Why might a person whose fortune came from explosives choose to reward peace and science? (Students should treat this as a question to explore, not a known fact about Nobel’s motives.)
Sources: NobelPrize.org: Alfred Nobel’s will; NobelPrize.org: The Nobel Prize money; Britannica: Alfred Nobel
Current Events
Seismologists at the Alaska Earthquake Center described this week how a landslide on August 9, 2025, crashed into Tracy Arm, a fjord in southeast Alaska, near South Sawyer Glacier. It set off one of the tallest tsunamis ever recorded: water and debris reached 1,580 feet up the opposite fjord wall. No ships were nearby. Warning signs came first: the glacier below the slope had retreated more than a third of a mile in the two months before, heavy rain had been falling, and thousands of small seismic tremors were recorded in the days before the collapse. (a) Convert 1,580 feet to meters (1 ft = 0.3048 m). (b) Why would a glacier shrinking away from the bottom of a mountainside make the slope more likely to collapse? (c) The authors propose a three-level alert: yellow for risky weather and glacier conditions, orange for tremors, and red once a slide starts. What is one benefit and one drawback of issuing early (yellow or orange) alerts?
Answer and teacher notes
(a) 1,580 × 0.3048 ≈ 482 meters. (The article gives 481 m.)
(b) The glacier’s ice had been pressing against the base of the slope and helping hold it up. As the ice retreats, that support disappears. Rain adds water pressure inside rock cracks, which also pushes the rock toward failure. (c) Benefit: ships and visitors get time to leave the area before a slide happens. Drawback: early warnings can turn out to be false alarms, and too many false alarms can lead people to ignore later warnings. Strong answers weigh both. The authors note that once a slide starts, detection could take a couple of minutes, and that the U.S. does not yet have a landslide monitoring system like this at that scale. The research was published in Science.
Source: ScienceDaily: Alaska’s Monster Tsunami Sent Water 1,580 Feet Up a Mountain (Michael E. West and Ezgi Karasözen, Alaska Earthquake Center, via The Conversation)
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