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How to practice

~12 min

This is a short section with no new ideas about sentences. It is about how to use the rest of the course. The questions here are built on a pattern, and knowing the pattern makes practice go further.

The practice ladder, and answering with a reason

Think back to the fact-checker with the TRUE and FALSE stamps. A new fact-checker doesn't learn the job in one step. First they learn to spot a sentence that can be stamped at all. Then they stamp real ones. Then they write their own test cases. Finally, they learn to catch the sentence that looks stampable and isn't. This course trains you the same way. Every idea gets a ladder with four rungs:

  1. Recognize it. Someone names the idea. You pick out an example.
  2. Use it. You apply the idea to a case you haven't seen and get an answer.
  3. Build one. You make up your own example that fits the rules.
  4. Catch the look-alike. You tell the real thing from something that only resembles it.

Climb in order. If a rung feels impossible, go down one. The trouble is usually there.

For every item, give an answer and a reason. "It's a statement" is only half. "It's a statement, because 'That's false' is a sensible reply" is the whole thing. Then check the reason, not just the answer. A right answer for a wrong reason is luck, and luck runs out on the next question.

The page gives you three kinds of help. Check questions change each visit and get graded. They tell you where you stand. Practice sets stay the same every visit, in the same order, so you can work one again until it feels easy. Hints open one at a time and each costs a little credit. Try the item first, then take a single hint if you're stuck.

Last habit: slow down. Most mistakes here come from reading too fast, not from thinking badly. Before you answer, circle the small words that change what a sentence promises: some, all, no, only, or, not. Notice a question mark or an order. Then say the sentence back in your own words.

Each idea in this course is practiced on a ladder of four rungs, in order:

  1. Recognize. Identify an example of the idea when the idea is named for you. ("Which of these sentences is a statement?")
  2. Apply. Use the idea on a new case to reach an answer. ("Is 'Some seats are free' true if every seat is free?")
  3. Build. Produce your own example that meets stated conditions. ("Describe a scenario in which this claim is false.")
  4. Spot the look-alike. Tell the idea apart from a near miss that resembles it. ("Do 'Only members may swim' and 'All members may swim' say the same thing?")

The order matters. Building an example needs the ability to apply the idea, and spotting a near miss needs a firm grip on the idea itself. Section practice sets follow this order, and a rung that feels too hard usually means the rung below it needs more work.

Every item should be worked as answer, then justify: state the answer and the reason that settles it, then check the reason. A right answer with a wrong reason is a lucky guess, and it will fail on the next case. The reason is the part that carries over.

Three tools support this. Check questions are drawn at random on each visit and graded, so they measure. Practice sets are fixed and ordered, so they build; the same set can be reworked until it feels routine. Hints are revealed one at a time and cost a little credit each, so try the item first and take one hint at a time.

Most errors in this material are reading errors, not reasoning errors. Before answering, read the sentence slowly. Mark every word that fixes what it commits to: some, all, no, only, or, not, and any question mark or command. Then restate the sentence in your own words.

Which rung is this task on?

Each task practices the idea that “some” means “at least one.” Sort each task onto its rung of the ladder.

Loading interactive…

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Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

What this task checks

Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.

The compiler says

A model answer

Correct answer

Also accepted:

Why

Why

Picking out the “some” sentence only asks you to recognize the word. Judging the full bus asks you to apply what “some” means to a new case. Writing a situation where the shops claim fails asks you to build one. The last task is the look-alike: it sets two near-identical sentences side by side. “Some are taken” feels like part of the first message, but it is only a hint, and telling a hint from a promise is the near miss this rung trains.

Working one item

Put the steps for working a practice item in the order this section recommends.

Loading interactive…

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

What this task checks

Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.

The compiler says

A model answer

Correct answer

Also accepted:

Why

Why

Reading slowly comes first, because you can’t mark words you skimmed past. Marking the small words comes before restating, since those words decide what a faithful restatement must keep. Only then do you answer, and the answer always comes with its reason. The last step checks that reason, which is what separates an answer you understand from a lucky one.

Worked example

One item, start to finish

  1. 1

    Practice item: "A sign says 'Only seniors may park in Lot B.' A senior parks in Lot A. Does that go against the sign?"

    basic

  2. 2

    Read slowly and mark the small words: "only." Restate: "Everyone who parks in Lot B is a senior."

  3. 3

    Answer with a reason. No: the sign only limits who parks in Lot B. A senior parking somewhere else is not a case it covers.

  4. 4

    Check the reason. What would break the sign? A non-senior in Lot B. The senior in Lot A is not that case, so the reason holds up.

Worked example

Finding your rung after a miss

  1. 1

    Jae gets this item wrong: "Build a situation where 'Some of the tickets sold' is false." Jae wrote: "Most tickets sold, but a few didn't."

    using feedback

  2. 2

    Check the reason. Jae's situation has tickets that sold, so "some tickets sold" is still true in it. The build did not work.

  3. 3

    Go down a rung. The apply question underneath is: what does "some" commit to? At least one ticket sold. So it is false only if zero sold.

  4. 4

    Climb back up with that fixed. A situation that works: "The concert was canceled before sales opened, and not one ticket sold." Now the claim is false.

Check your understanding (counts toward your progress)

Which words should you mark when slow-reading “Not all of the buses or trains were late”?

Correct! 🎉 Not quite.

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Those words say what the sentence is about. The small words decide what it promises about them.

These words hold the sentence together, but they don’t change what it commits to.

“Not” matters, but so do “all” and “or.” Each one changes the promise.

Why

“Not,” “all,” and “or” each change what the sentence commits to. Marking them is how you avoid reading it too fast.

Look for the small words this section lists.

How do check questions differ from practice sets?

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It’s the other way around. Check questions are the graded ones.

They are separate collections with separate jobs: one measures, one builds.

Check questions are drawn fresh on each visit. Practice sets are the ones that stay the same.

Why

Check questions measure where you stand, so they are drawn at random and graded. Practice sets build skill, so they stay fixed and ordered and can be reworked.

Which one is meant to measure, and which one is meant to build?

Which answer follows the “answer, then justify” habit?

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That’s the answer without the reason. The reason is what carries over to the next item.

Adding “I think” shows doubt, but it still gives no reason to check.

This gives a reason, but the wrong one. Commands end in periods too, so the reason fails a check.

Why

A full answer names the result and the reason that settles it. The reply test is a reason that works on every sentence; “it has a period” is not.

Which choice gives a reason that would survive a check?

Why is a right answer with a wrong reason treated as a problem?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

An answer can be right by luck. The reason is what tells you whether you’ll get the next one right.

A multiple-choice grader can’t see your reason, which is exactly why you have to check it yourself.

Why

A lucky guess and a real understanding look the same on one item. The reason is what separates them on the next.

Picture the next item, where the lucky guess doesn’t line up.

Practice: Practicing well (5 problems · doesn’t affect your progress)

A task asks you to write your own “some” sentence and a situation that makes it false. Which rung is that?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

Recognizing means picking out an example someone else wrote. Here you write your own.

Applying means judging a given case. This task has you invent the case.

Spotting the look-alike compares two similar things. Nothing is being compared here.

Why

Making your own example that meets stated conditions is the build rung.

Who produces the example in this task?

Build

How should you use hints?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

Opening them all first skips the thinking the item exists for.

Hints cost a little credit, but a single hint when you’re stuck is often the fastest way to learn.

Why

Hints are revealed one at a time and cost a little credit each. Try first, then take the smallest nudge that gets you moving.

Hints open one at a time for a reason.

Try the item first, then take one hint at a time.

Slow-read this sentence and select the word that decides whether having both parts is allowed.

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

What this task checks

Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.

The compiler says

A model answer

Why

“Or” is the word to mark. With no “but not both,” careful reading takes it inclusively, so a trip using both is allowed.

Correct answer

Also accepted:

Why

Which small word joins the two ways to travel?

“or” (word 6)

Rina’s answer is right, but her reason is wrong. What should she do?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

A right answer for a wrong reason is luck. The next item may not line up so kindly.

Her answer was right. The reason is what needs to change.

Why

Checking the reason is the last step of every item. A corrected reason turns a lucky answer into one she understands.

Which part carries over to new items?

Fix the reason; she’ll need it on the next item.

Answer with a reason: is “Some of the windows are open” true if every window is open? Then say in one sentence how you checked your reason.

Correct! 🎉 Partially there. Not quite. Can you clarify? You chose to see the answer — this one earns no credit.

Explanation

Where this shows up later in the course

Where this goes next

This course

Every chapter's practice sets climb this ladder, and later chapters add rungs to it. Chapter 4 names common patterns of reasoning. For each one, its sections have you recognize the pattern and find it in ordinary English. Then you pick it out from its neighbors and complete it. Last, you catch the broken look-alike that tricks people. Chapters 5 through 7 use the same ladder for common reasoning mistakes. You name the mistake, find it in a passage, tell it apart from a near neighbor, and rewrite the passage.

The "answer, then justify" habit becomes a formal rule in Chapters 16 and 17. There, every line of a written proof must cite the rule that allows it. A line without a reason is marked wrong, even when the line happens to be true.

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