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 restrictive clause is essential: it tells which one you mean, so it takes no commas (and in American usage often uses that). A nonrestrictive clause adds extra information about something already identified, so it is set off with commas (and uses which for things). For each sentence, choose the word, add commas if needed, and explain your choice.
- The book (that / which) I borrowed from you is on my desk.
- Mount Everest (that / which) sits on the border of Nepal and China is the highest mountain above sea level.
- The phone (that / which) I dropped in the lake no longer works.
- Compare: “Students who turned in the form get a parking pass” and “Students, who turned in the form, get a parking pass.” Who gets a pass in each?
- Compare: “My brother who lives in Denver is visiting” and “My brother, who lives in Denver, is visiting.” What does each version suggest about how many brothers the speaker has?
Answer and teacher notes
1. that, no commas. The clause identifies which book.
2. which, with commas: “Mount Everest, which sits on the border of Nepal and China, is…” There is only one Mount Everest, so the clause is extra information.
3. that, no commas. It specifies which phone (not the one in your pocket).
4. Without commas, only the students who turned in the form get a pass. With commas, the sentence says all students get a pass, and adds that they all turned in the form.
5. Without commas, the speaker likely has more than one brother and means the one in Denver. With commas, the speaker has one brother, who happens to live in Denver.
Quick test: if you can delete the clause and the sentence still points to the same thing, it is nonrestrictive and needs commas. Note that British writers often use which in restrictive clauses too; the commas, not the word, carry the meaning. Who works for people in both kinds of clauses. Extension: write a sentence whose meaning changes completely depending on whether you add the commas.
Math
On October 29, 1969, Charley Kline, a student programmer at UCLA, tried to send the word “login” over the brand-new ARPANET to a computer at the Stanford Research Institute, about 350 miles away. The receiving system crashed after two letters, so the first message ever sent on the network that grew into the internet was just “lo.” The full word went through about an hour later. Computers store text as binary numbers. In the ASCII code, capital L = 76, O = 79, G = 71, I = 73, and N = 78, and each lowercase letter’s code is exactly 32 more than its capital. (a) Write 76 (L) as a 7-bit binary number. (b) Find the code for lowercase “l” in decimal and binary. Which single bit changes between “L” and “l”? (c) If each character is stored in one 8-bit byte, how many bits are in “login”? What percent of them arrived in the first attempt? (d) How many different characters can a 7-bit code represent? An 8-bit code?
Answer and teacher notes
(a) 76 = 64 + 8 + 4 = 26 + 23 + 22, so 1001100.
(b) 76 + 32 = 108 = 64 + 32 + 8 + 4 = 1101100. Only the 25 (32s) bit changes, from 0 to 1. That’s why programs can switch case by flipping one bit.
(c) 5 characters × 8 bits = 40 bits. “lo” is 2 × 8 = 16 bits, and 16 ÷ 40 = 40%.
(d) 27 = 128 characters; 28 = 256 characters.
Check (a) by converting back: 1001100 = 64 + 0 + 0 + 8 + 4 + 0 + 0 = 76. ✓ For the full word, lowercase codes are l = 108, o = 111, g = 103, i = 105, n = 110. Common mistake: reading binary left to right as if the leftmost place were 1s; remind students the rightmost bit is the 1s place. Note that the ASCII values here are a modeling exercise; sources describe the message itself but not the exact encoding the 1969 machines used. Today is the 57th anniversary of the message (2026 − 1969). Discussion: why might engineers keep testing a network one character at a time rather than sending a whole file at once?
Sources: CBS News: 45 Years Ago, First Message Sent Over the Internet (date, people, “lo,” and the retry an hour later); Tom’s Hardware: This Week in 1969, the Internet Was Born and Immediately Glitched (distance); Wikipedia: ASCII (character codes)
Science
On October 29, 1998, 77-year-old John Glenn launched aboard the space shuttle Discovery on mission STS-95. According to NASA, the flight made 134 orbits and covered 3.6 million miles in 213 hours and 44 minutes. Use 1 mile = 1.609 km, Earth’s radius = 6,371 km, and g = 9.81 m/s² at Earth’s surface. (a) Find the average time for one orbit, in minutes. (b) Find the average speed in km/s. (c) Treat each orbit as a circle. From the distance per orbit, estimate the orbit’s radius and the shuttle’s altitude above Earth’s surface. (d) Find the centripetal acceleration v²/r and compare it with gravity’s strength at that radius, g(R/r)². What does this tell you about why astronauts appear “weightless”?
Answer and teacher notes
(a) 213 × 60 + 44 = 12,824 min; 12,824 ÷ 134 ≈ 95.7 minutes.
(b) 3,600,000 mi × 1.609 ≈ 5.79 × 106 km. Time = 213.73 h × 3,600 = 769,440 s. Speed ≈ 5.79 × 106 ÷ 769,440 ≈ 7.5 km/s (about 17,000 mph).
(c) Distance per orbit ≈ 5.79 × 106 ÷ 134 ≈ 43,200 km. r = C ÷ 2π ≈ 6,880 km, so altitude ≈ 6,880 − 6,371 ≈ 510 km (about 320 miles).
(d) v²/r = (7,530 m/s)² ÷ (6.88 × 106 m) ≈ 8.2 m/s². Gravity there: 9.81 × (6,371 ÷ 6,881)² ≈ 8.4 m/s². They nearly match: gravity is still about 85% as strong as on the ground, and it supplies exactly the pull needed to keep the shuttle curving around Earth. Astronauts and shuttle fall together, so they feel weightless. They are in free fall, not free of gravity.
Why the small mismatch in (d)? These are averages: the total distance includes the climb to orbit, the orbit was not a perfect circle, and the inputs are rounded. NASA’s mission page lists the orbit altitude as 310 nautical miles (about 574 km), so our estimate of about 510 km is in the right range for a simple model. Common mistake: forgetting to convert km to m before dividing v² by r. Extension: Glenn’s 1962 Friendship 7 flight made 3 orbits in about 4 hours 55 minutes. Was its average orbit time similar? (295 ÷ 3 ≈ 98 minutes, very close.)
Sources: NASA: John H. Glenn Jr. biography (orbits, miles, hours, and Friendship 7); NASA: STS-95 mission page (launch date, Glenn’s age, and altitude)
Social Studies
On October 29, 1923, the Grand National Assembly in Ankara amended Turkey’s constitution to read that the form of government “is a republic.” The same session elected Mustafa Kemal (later known as Atatürk) as the first president by a unanimous vote of 158 members. Two earlier steps set the stage: on November 1, 1922, the assembly had abolished the Ottoman sultanate, the monarchy that had ruled for centuries from Istanbul, and on October 13, 1923, a law made Ankara the capital. (a) How many years ago was the republic proclaimed? (b) About how much time passed between abolishing the sultanate and proclaiming the republic? (c) In a monarchy like the sultanate, where does a ruler’s authority come from? In a republic? (d) Why might new leaders choose a new capital instead of keeping the old one?
Answer and teacher notes
(a) 2026 − 1923 = 103 years. (b) From November 1, 1922, to October 29, 1923, is 362 days, just under one year. (c) In a monarchy, authority is usually inherited through a ruling family (often with religious or traditional backing). In a republic, the head of state is not a hereditary monarch; authority rests with the people and their representatives, here an elected assembly that chose the president.
(d) Answers will vary: a new capital marks a clean break with the old government and its symbols; Ankara had been the assembly’s base, so the new leadership’s institutions were already there; an inland city could be easier to defend than a coastal one. Remind students to support claims with evidence, not assumptions. Point out the sequence: dissolving the old system first and then defining the new one. Extension: compare this with another country’s shift from monarchy to republic. What steps did it take, and in what order?
Source: Wikipedia: Proclamation of the Republic of Turkey (date, amendment, vote, capital law, and abolition of the sultanate)
Current Events
When NASA’s uncrewed Artemis I mission flew around the Moon in late 2022, its Orion capsule carried two human-shaped mannequins packed with more than 10,000 tiny radiation detectors. A team at the Institute of Nuclear Physics of the Polish Academy of Sciences has now published results from one new type of detector, lithium fluoride crystals just a few millimeters across that record the tracks of individual particles (Radiation Measurements, reported October 28, 2026). Their readings agreed with older detectors to within 15%. A key finding: on the International Space Station, an earlier experiment found the radiation dose spread unevenly through a mannequin, because much of it comes from low-energy protons trapped in Earth’s Van Allen belts. Near the Moon, beyond the belts, high-energy particles from deep space dominated, and the dose was spread almost evenly through the body. The total dose near the Moon was higher than in low Earth orbit, but by less than many would expect. (a) Why would low-energy particles deposit most of their energy near the outside of a body, while high-energy ones spread it evenly? (b) Why use human-shaped mannequins instead of detectors on the capsule wall? (c) Why is agreeing with older detectors within 15% important for a new instrument? (d) What does this suggest about the protection Earth’s magnetic field gives astronauts on the space station?
Answer and teacher notes
(a) Low-energy particles are stopped quickly by material, so they dump their energy in the first layers they hit (the “skin” side of the mannequin). High-energy particles pass deep into or straight through the body, depositing energy all along their path. (b) The goal is to know the dose to organs inside a person. A human-shaped model with realistic shielding by the body itself shows how dose changes with depth and location. (c) Agreement with a trusted method is a calibration check: it gives scientists confidence the new, smaller detector measures correctly before relying on it, for example as a wearable badge for astronauts.
(d) Space station crews are inside Earth’s magnetic field, which deflects much of the high-energy radiation from deep space; their dose is dominated by trapped protons instead. Beyond that protection, deep-space particles take over, which matters for crews traveling to the Moon and Mars. Emphasize the hedged conclusion: the dose near the Moon was higher, but the gap was smaller than intuition suggests. The article gives no dose totals, so avoid inventing numbers. The detectors also register tracks too faint for earlier devices, and versions made with lithium-6 can detect neutrons.
Source: ScienceDaily: NASA’s Artemis I Mission Reveals Surprising Radiation Levels Near the Moon (Institute of Nuclear Physics, Polish Academy of Sciences; Radiation Measurements; October 28, 2026)
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