What does i+1 mean in Japanese learning?

i+1 is Stephen Krashen's shorthand for input just past your current level: everything you already know, plus one new thing. Applied to a flashcard example sentence, it means the sentence should be readable except for the single word the card is teaching you.

Why are example sentences in Japanese dictionaries so hard?

Dictionary example sentences are written to show how a word behaves, not to be readable by a beginner. They are drawn from corpora of natural adult Japanese, so they freely use vocabulary and grammar the learner has not met yet. That is correct for a dictionary and wrong for card two of your first study session.

Does Moji guarantee every example sentence has at most one unknown word?

No. The budget applies to a defined range of the study order. For slots 151 to 586, each example uses at most one word not yet taught at that slot, with katakana loanwords exempt. Slots 1 to 150 follow a looser band budget, and later cards are not budgeted this way.

How is a comprehensible input budget different from just using short sentences?

Short is not the same as comprehensible. A four-word sentence can contain three words you have never seen. The budget counts unknown words against the study order, so it depends on where a card sits in the sequence, not on sentence length.

Do all 7,435 words in Moji have example sentences?

Yes. All 7,435 entries carry a curated example sentence with an English meaning. The untaught-word budget is the extra constraint applied to the early part of the study order, where a single unknown word does the most damage.

Updated August 8, 2026

Why Japanese example sentences are too hard, and what i+1 fixes

Most example sentences fail beginners for one reason: they contain words the learner has not been taught yet. Not one word, which is useful, but three or four, which turns a vocabulary card into a decoding puzzle. Stephen Krashen’s term for the useful version is i+1, meaning input at your current level plus one new thing.

Moji - Learn Japanese Daily for iPhone enforces that as a hard constraint on part of its catalog. For study-order slots 151 through 586, every example sentence uses at most one word the learner has not yet been taught at that slot, with katakana loanwords exempt. Slots 1 through 150 sit under a looser band budget. That is a narrower claim than “all our sentences are easy”, and it is the one we can actually check.

What i+1 means, in one paragraph

Krashen’s input hypothesis argues that people acquire a language by understanding messages slightly beyond their current competence, which he wrote as i+1, where i is the level you have and +1 is the small step past it (Krashen, Principles and Practice in Second Language Acquisition, linked below). Input at i+0 teaches nothing new. Input at i+3 stops being input at all, because you cannot parse it, so there is nothing to acquire from.

An example sentence on a flashcard is the smallest possible unit of comprehensible input. The card is already teaching you one word. If the sentence around that word is made of things you know, you get the new word in context for free. If the sentence around it holds two more unknowns, you get a lookup chain instead.

Why most Japanese example sentences fail this test

Example sentences usually come from dictionaries and corpora, and they are doing a different job. A dictionary sentence exists to show how a word behaves grammatically for someone who already reads Japanese. It is written for reference, not for sequence, and a reference work has no idea which card you are on.

So a learner on an early card can meet words like 会議 (かいぎ, kaigi, meeting) or 値段 (ねだん, nedan, price) long before either is taught, purely because they happened to fit a natural sentence. Nothing is wrong with the sentence. It just was not written against a study order, and no sentence can respect an order that does not exist. That is the real gap: the budget only becomes possible once the catalog has a fixed, hand-checked sequence. See why word order matters for how that sequence is built, and how we curate Japanese vocabulary for the editorial rules behind entries.

The exact budget Moji applies

The precise definition, worth stating carefully because the loose version gets repeated wrongly:

Slots 151 to 586: each example uses at most one word the learner has not been taught by that slot.
Katakana loanwords are exempt from the count, since a beginner reads コーヒー (koohii, coffee) without being taught it.
Polite glue is exempt: です and ます are treated as known, because they are taught as a pattern rather than as vocabulary.
Particles are all taught before slot 151, so they never spend budget in that range.
Slots 1 to 150 satisfy a looser band budget of at most three untaught words, and were already inside it.
Kana-stage cards show a single word rather than a sentence, so they are outside this entirely.

The upper bound is not arbitrary. 耳 (みみ, mimi, ear) at slot 586 keeps a sentence using ので (node, because), which is taught three slots later at 589. That is one untaught word, inside budget, and it is where the audited range ends.

What the rewrite pass actually took

The budget was applied to the early catalog as an editorial pass, not a filter that ran once. A crude longest-match counter over catalog headwords produced a work list of 62 flagged cards. Every flag was then re-judged by hand, because that kind of counter is wrong in both directions. It over-flags: 休み inside 休む’s (やすむ, yasumu, to rest) own sentence is the card’s own word inflected, and しか inside 悲しかった (かなしかった, kanashikatta, was sad) is a substring, not a word. It under-flags too, since an inflected form of an untaught word can slip past a surface match.

Of the 62 flags, 48 sentences were rewritten and 14 were kept as false positives. Afterwards, genuine violations in the range went to zero, and the number of sentences using no untaught words at all rose from 92 to 115 out of 311. The rest sit at exactly one, which is the point.

A few conventions came out of that pass and now govern any future example work:

The order is frozen. If a sentence breaks the budget, you rewrite the sentence, never move the card. Reordering to make a sentence legal would trade a small win for a curriculum-wide side effect.
No fragments. One-word utterances would pass the budget trivially and teach nothing about placement, so they are not allowed as an escape hatch.
No new names. 田中 (たなか, Tanaka) is the only personal name in the catalog, used in the handful of sentences whose headword demands one.
Spend the budget forward. Where a sentence needs one unknown, prefer the word that is taught next. 料理 (りょうり, ryouri, cooking) at slot 181 spends its single allowance on 作る (つくる, tsukuru, to make) at slot 182, so the unknown becomes tomorrow’s card.
Vary the frame. Sentences stay situational instead of collapsing into a wall of これはXです.

Rewriting sentences also invalidated derived data. Example sentences feed Sentence Build, the mode where you arrange chunks into a sentence, and those chunks are cut so that particles stay on their own tile. Every chunked entry had to be re-swept against the new sentences before the change could merge, which moved coverage from 617 to 623 eligible entries and left nothing stale.

When we get it wrong: the に card

The budget is a claim, and claims should be audited. Reviewing this page’s material, we checked the に (ni, location and direction particle) card at slot 183 and found its example spent two untaught words, not one. It had been missed by the original pass.

The fix was a replacement sentence: 猫は家にいます (ねこはいえにいます, neko wa ie ni imasu, “The cat is at home”). Every word in it is taught by slot 70, so the card now spends zero untaught words while still showing に in its locative position. We would rather publish the correction than the tidy version.

What the budget does not do

It does not make Japanese easy, and it stops at slot 586. Beyond that range, sentences are curated for naturalness and usefulness but not held to the untaught-word count, on the reasoning that a learner 600 words in can absorb an unknown word or two without losing the thread. All 7,435 entries do carry a curated example sentence with an English meaning, but only the early range carries this extra constraint.

It also does not replace scheduling. Comprehensible input decides what a card can teach you in one look. Spaced repetition decides whether you still have it in three weeks, which is a separate machine: see how Moji uses FSRS and memory bands and retrievability. Worth noting too that Moji is iPhone-only, and that the catalog described here is editorial work layered on a dictionary base (JMdict), not a stock sentence bank shipped as-is.

If you want to see the effect, the first hundred cards are the honest test, since that is where a single extra unknown word does the most damage. The free tier covers the whole comprehension path, so example sentences, mnemonics and the study loop are all there without paying. Moji is on the App Store.

Sources

Stephen D. Krashen, Principles and Practice in Second Language Acquisition (input hypothesis and the i+1 formulation): https://www.sdkrashen.com/content/books/principles_and_practice.pdf
JMdict dictionary data, Electronic Dictionary Research and Development Group: https://www.edrdg.org