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 semicolon joins two closely related independent clauses, or separates list items that already contain commas. A colon comes after a complete sentence to introduce a list, an explanation, or an example. Decide whether each sentence needs a semicolon, a colon, or is correct as written. Fix the ones that are wrong.
- The forecast called for rain, we brought umbrellas.
- Pack three things for the trip: a jacket, a charger, and snacks.
- The tour stops in Austin, Texas, Denver, Colorado, and Portland, Oregon.
- My favorite subjects are: chemistry and history.
- She had one goal for the season; to make varsity.
Answer and teacher notes
1. Comma splice. Use a semicolon: The forecast called for rain; we brought umbrellas.
2. Correct. A complete sentence comes before the colon, and a list follows.
3. Use semicolons between items that contain commas: Austin, Texas; Denver, Colorado; and Portland, Oregon.
4. Remove the colon. “My favorite subjects are” is not a complete sentence, so no colon after a verb: My favorite subjects are chemistry and history.
5. Use a colon. “To make varsity” is not an independent clause, so a semicolon can’t introduce it: She had one goal for the season: to make varsity.
Test for a semicolon: could you replace it with a period and have two complete sentences? Test for a colon: is everything before it a complete sentence, and does what follows explain or list? Item 3 is the one most students miss; without semicolons, a reader can’t tell whether “Texas” is a separate stop. Extension: write one sentence using a colon to introduce an explanation, not a list.
Math
A stadium section has 20 seats in the first row, and each row behind it has 2 more seats than the row in front. (a) Write a formula for the number of seats in row n. (b) How many seats are in row 25? (c) How many seats are in the first 25 rows combined? (d) The planners want at least 1,500 seats in the section. What is the fewest number of rows they need?
Answer and teacher notes
(a) This is an arithmetic sequence with a1 = 20 and d = 2: an = 20 + 2(n − 1), or an = 2n + 18.
(b) a25 = 20 + 2(24) = 68 seats. Check: 2(25) + 18 = 68. ✓
(c) Sn = n(a1 + an)/2 = 25(20 + 68)/2 = 25(44) = 1,100 seats.
(d) Sn = n(20 + 2n + 18)/2 = n(n + 19). Solve n² + 19n ≥ 1,500. The quadratic formula gives n = (−19 + √6,361)/2 ≈ (−19 + 79.8)/2 ≈ 30.4, so round up to 31 rows. Check: 30 rows give 30 × 49 = 1,470 (not enough); 31 rows give 31 × 50 = 1,550. ✓
The sum formula is the “pairing” trick: row 1 + row 25 = 20 + 68 = 88, row 2 + row 24 = 22 + 66 = 88, and so on, so 25 rows make 12.5 pairs of 88. In part (d), stress why we round up: 30 rows fall 30 seats short. Common mistake: using an = 20 + 2n, which makes row 1 have 22 seats.
Science
In his pea-plant experiments, Gregor Mendel crossed plants that were hybrids for seed color. Yellow (Y) is dominant over green (y). In the offspring he counted 6,022 yellow and 2,001 green seeds. (a) Draw the Punnett square for Yy × Yy. What ratio of yellow to green do you predict? (b) Out of Mendel’s 8,023 seeds, how many of each color would you expect? (c) Compute chi-square: χ² = Σ (observed − expected)² / expected. The critical value for 1 degree of freedom at p = 0.05 is 3.84. Do the data fit the prediction? (d) Why does a large sample like Mendel’s make the result more convincing?
Answer and teacher notes
(a) Genotypes: 1 YY : 2 Yy : 1 yy. YY and Yy both look yellow, so the predicted ratio is 3 yellow : 1 green.
(b) Yellow: 8,023 × 3/4 = 6,017.25. Green: 8,023 × 1/4 = 2,005.75.
(c) Yellow: (6,022 − 6,017.25)² / 6,017.25 = 22.5625 / 6,017.25 ≈ 0.0037. Green: (2,001 − 2,005.75)² / 2,005.75 = 22.5625 / 2,005.75 ≈ 0.0112. χ² ≈ 0.015, far below 3.84, so yes: the difference is easily explained by chance. His actual ratio was 6,022 ÷ 2,001 ≈ 3.01 : 1.
(d) Random chance has a big effect on small samples (with 8 seeds, getting 4 green would not be surprising), but over thousands of seeds, the chance variations tend to even out, so the observed ratio gets close to the true probability. Degrees of freedom = number of categories − 1 = 1. Discussion: some statisticians have noted that Mendel’s results across all his experiments fit his predictions unusually well. What might explain data that are “too good”?
Source: Michigan State University, Biology Online: Mendel’s Monohybrid Crosses, Results and Ratios
Social Studies
Smallpox existed for at least 3,000 years and killed up to 30% of the people it infected. In 1967 the World Health Organization launched an intensified worldwide campaign to wipe it out. On October 26, 1977, a 23-year-old hospital cook named Ali Maow Maalin in Merca, Somalia, was diagnosed with what became the last known natural case. Health workers traced 161 of his contacts and vaccinated 54,777 people in the two weeks after he was isolated. He recovered, and WHO declared smallpox eradicated in 1980. (a) How many years did the intensified campaign take from launch to the last natural case? (b) Why might health workers vaccinate everyone around a case instead of vaccinating a whole country at once? (c) Smallpox is the only human disease that has been eradicated. What conditions might make a disease harder to eradicate?
Answer and teacher notes
(a) 1977 − 1967 = 10 years. Today is 49 years since the diagnosis (2026 − 1977). (b) Answers will vary. Strong ideas: vaccine, staff, and transport are limited, so focusing them where the virus actually is stops it fastest; a ring of immune people leaves the virus nowhere to spread; it works even in places hard to reach with a full national campaign. This approach depended on surveillance: finding every case quickly.
(c) Answers will vary. Smallpox had features that helped: it spread only between humans (no animal hosts), infected people showed a visible rash, and one vaccine gave lasting protection. Diseases are harder to eradicate if they hide in animals or insects, spread before symptoms appear, have many mild or invisible cases, or need repeated doses. After his recovery, Ali Maow Maalin worked as a vaccinator in the campaign against polio. Note: two later cases in England in 1978 came from a laboratory, not from natural spread.
Sources: World Health Organization: Smallpox; Gavi: The world’s last smallpox patient; Wikipedia: Ali Maow Maalin (date and contact figures); Britannica: When did the last known case of smallpox occur?
Current Events
Astronomers using the European Southern Observatory’s Very Large Telescope reported in Nature this week what they call the first plausible detection of an exosatellite, a moon outside our solar system. In the young system CD-35 2722, a brown dwarf (an object too small to be a star but bigger than a planet) of about 37 Jupiter masses orbits a star with about half the Sun’s mass. The team measured tiny back-and-forth shifts in the brown dwarf’s motion and concluded that something with at least one Jupiter mass is orbiting it. (a) What fraction of the brown dwarf’s mass is the candidate moon, at minimum? Compare it with our Moon, which has about 0.0123 of Earth’s mass. (b) How can a moon be detected by watching the object it orbits instead of the moon itself? (c) Should a gas giant orbiting a brown dwarf be called a “moon” or a “planet”? Defend one choice. (d) The authors call it “plausible,” not confirmed. What would confirmation require?
Answer and teacher notes
(a) 1 ÷ 37 ≈ 0.027, about 2.7% (a minimum, since the companion has at least one Jupiter mass). That is a little more than twice our Moon’s share of 0.0123 (0.027 ÷ 0.0123 ≈ 2.2). (b) The two objects orbit a shared center of mass, so the companion’s gravity makes the brown dwarf wobble. As it moves toward and away from us, its light shifts slightly bluer and redder (the Doppler effect). This is the radial velocity method.
(c) Answers will vary; grade the reasoning. “Moon”: it orbits a body that itself orbits the star. “Planet”: it is a gas giant at least as massive as Jupiter, and the brown dwarf is closer to a failed star than a planet. The researchers themselves say the system is hard to describe with solar-system words, and astronomers have no universally accepted definition of an exomoon. (d) Repeated observations that show the same signal, an independent method (such as direct imaging or watching for transits), and ruling out other causes like activity on the brown dwarf. Discussion: why do scientists publish results labeled “plausible”?
Sources: ScienceDaily: Astronomers May Have Discovered the First Moon Beyond Our Solar System (ESO; Nature); NASA Moon Fact Sheet (Moon and Earth masses)
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