Five warm-ups for grades 6–8. Each takes three to five minutes. Answers and teacher notes are in the collapsed box under each prompt.
ELA
Two words can share a dictionary meaning (denotation) but carry different feelings (connotation). In each pair below, tell which word feels more positive. Then rewrite this plain sentence two ways, once to make it sound pleasant and once to make it sound unpleasant: The smell from the kitchen filled the house.
- thrifty / cheap
- curious / nosy
- confident / cocky
- aroma / stench
Answer and teacher notes
More positive: 1. thrifty, 2. curious, 3. confident, 4. aroma.
Rewrites: Answers will vary. Pleasant sample: “The aroma from the kitchen drifted through the house.” Unpleasant sample: “The stench from the kitchen invaded the house.”
Point out that both rewrites describe the same event, so word choice alone changes the reader’s feeling. Common mistake: treating connotation as a different definition. The words still mean nearly the same thing. Have students notice that the verb can do as much work as the noun: “drifted” and “invaded” send very different signals. Extension: find a word with a neutral connotation for pair 2, such as “interested,” and explain why it fits in the middle.
Math
The Pythagorean theorem says that in a right triangle, a² + b² = c², where c is the longest side (the hypotenuse). Use it to answer each question. (These measurements are made up for practice.)
- A rectangular park is 60 meters wide and 80 meters long. How long is the straight path from one corner to the opposite corner? How many meters does that save over walking along the two edges?
- A 13-foot ladder leans against a wall with its base 5 feet from the wall. How high up the wall does it reach?
- A rectangular room is 7 meters by 10 meters. To the nearest tenth, how long is its diagonal?
- Could a triangle with sides of 6, 7, and 9 be a right triangle? Show how you know.
Answer and teacher notes
1. 60² + 80² = 3,600 + 6,400 = 10,000, and √10,000 = 100 meters. Along the edges: 60 + 80 = 140 meters, so the path saves 40 meters.
2. 5² + h² = 13², so h² = 169 − 25 = 144, and h = 12 feet.
3. 7² + 10² = 49 + 100 = 149, and √149 ≈ 12.2 meters.
4. No. 6² + 7² = 36 + 49 = 85, but 9² = 81. The two sides are not equal.
Check on #2: 5² + 12² = 25 + 144 = 169 = 13². ✓ Common mistake on #2: adding instead of subtracting. The ladder is the hypotenuse, so it is the c in the equation. Common mistake on #4: forgetting that c must be the longest side. Extension: 60-80-100 is a 3-4-5 triangle scaled up by 20. What is the scale factor for 5-12-13 if the shortest side is 15? (3, which gives 15-36-39.)
Science
Every magnet has a north and a south pole. Opposite poles attract, and like poles repel. Inside a material, tiny particles act like little arrows called spins. In a ferromagnet, such as iron, the spins line up in the same direction. In an antiferromagnet, they alternate up-down-up-down and cancel out. Scientists at SLAC recently reported strong evidence for a third type, altermagnetism, in a material called manganese telluride. (a) You push the north ends of two bar magnets together. What do you feel? (b) Draw eight arrows to show the spins in each of the first two types. Which drawing should make the stronger magnet? Why? (c) A compass needle’s north end points toward Earth’s North Pole. What kind of magnetic pole must be near there? (d) Altermagnets have no overall magnetic pull, but they can still push spins through a circuit. Why might that help a computer’s memory?
Answer and teacher notes
(a) The magnets push apart, because like poles repel. (b) The ferromagnet: all arrows point the same way, so their small effects add up. In the antiferromagnet, each arrow is canceled by its neighbor. (c) A magnetic south pole. Opposites attract, so the needle’s north end must be pulled by a south pole. (d) Answers will vary: memory that doesn’t create or feel a strong outside field may be less likely to be disturbed by nearby magnets.
Britannica concludes that Earth’s North Pole is “really a magnetic south pole,” which surprises most students, so it makes a good discussion point. The SLAC team used special X-rays to study the material. ScienceDaily quotes lead author Daniel Jost saying that “ferromagnets are too easily influenced by magnetic fields.” Keep the uses in the “could” column: the report says much more development is needed before these materials are widely used. Extension: why does a compass need a magnetized needle rather than a plain piece of plastic?
Sources: ScienceDaily: Proof of a Third Type of Magnetism (the three types, material, uses, quote); Britannica: Magnetism (poles, compass, Earth’s field)
Social Studies
In early November 1639, the Massachusetts General Court named Richard Fairbanks’s tavern in Boston as the place for letters arriving from overseas or being sent there. Fairbanks was allowed 1 penny for each letter. He kept the job until his death in 1667. (a) How many years ago was this? How many years did Fairbanks hold the job? (b) Suppose 60 letters passed through the tavern in one month. How much would Fairbanks earn? (This number is made up for practice.) (c) Why might a busy tavern be a smart place to collect mail? (d) Who in the colony might have needed to send letters across the ocean, and why? (e) What could go wrong for a letter on its way across the Atlantic in 1639?
Answer and teacher notes
(a) 2026 − 1639 = 387 years. 1667 − 1639 = 28 years. (b) 60 × 1 = 60 pennies. (c) Answers will vary: people already gathered there, it was easy to find, and news traveled through it. (d) Answers will vary: merchants doing business, officials reporting to England, and settlers writing to family. (e) Answers will vary: storms, shipwrecks, long delays, or lost and damaged mail.
Good source practice: the Smithsonian’s National Postal Museum dates the order to November 6, 1639, while Mystic Stamp’s history page says November 5. Ask students how they might check, such as finding the court record itself. Both agree on the penny fee. The Postal Museum says taverns as post offices copied European practice. Mystic Stamp says using the tavern was offered as a convenience, not required. Extension: how did this one mail stop differ from a post office today?
Sources: Smithsonian National Postal Museum: Richard Fairbanks’ Tavern and Post Office (November 6 date, court order, penny fee, 1667, European practice); Mystic Stamp: America’s First Postmaster (November 5 date, convenience)
Current Events
The Hubble Space Telescope launched in 1990 and was expected to last about 15 years. It orbits about 300 miles up, and it is slowly losing altitude because of atmospheric drag. It has no engine system of its own to climb back up. NASA predicts it will likely reenter the atmosphere in 2033 or 2034, so a rescue mission would need to happen by 2032. On October 29, NASA asked companies for ideas, with responses due November 30. The options include boosting Hubble higher, upgrading it, or safely retiring it. (a) In what year was Hubble expected to wear out? How many years past that is 2026? (b) How many years does NASA have until 2032? (c) How many days are left from today until responses are due? (d) Why can’t Hubble fix its own orbit? (e) If you ran NASA, which of the three options would you choose first? Give one reason.
Answer and teacher notes
(a) 1990 + 15 = 2005. 2026 − 2005 = 21 years past that. (b) 2032 − 2026 = 6 years. (c) November 30 − November 5 = 25 days. (d) It has no propulsion system, so it needs another spacecraft to push it. (e) Answers will vary: a boost keeps a working telescope going, upgrades add new abilities, and a safe retirement avoids an uncontrolled fall.
Stress that these are possibilities, not an approved mission. A Request for Information only asks what companies could do. Common mistake: thinking space has no air at all. At Hubble’s height a very thin atmosphere remains, and NASA says that drag affects all spacecraft in low Earth orbit. Extension: Hubble can’t be boosted forever. What would you want to know about the cost of a mission before choosing?
Sources: NASA: NASA Explores Potential Commercial Servicing for Hubble Telescope (drag, no propulsion, dates, options); NASA: Hubble FAQs (1990 launch, 15-year lifespan, altitude); ScienceDaily: NASA Is Racing Against Time to Save Hubble (summary)
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