Playbook · First grade stretch · NC.1.OA & NC.1.NBT

When ten stops being the ceiling

Every tool in this suite is built against ten, deliberately and in several places at once. A child who has run out of kindergarten does not need bigger numbers. They need three specific ideas that only start in first grade — and two of the tools already on the glass are the right instruments for them.

01The ceiling is real, and it is in the code

Before deciding what an advanced step looks like, it is worth being precise about where the suite actually stops. An earlier version of this page described these limits by reading the code and got them wrong, so they are now measured — every row below is asserted in tests/representation-ceilings.js. Of the six ways a number is shown, five break past ten and four of those five break silently. Only the numeral survives.

A quiet failure in front of a confident child is worse than a locked door, and worse again when the quiet failure draws a plausible wrong picture rather than no picture at all. A ten frame showing ten when the answer is twelve is not a gap a child notices. It is something a child believes.

Where	The limit	What happens past it
Build the Number — target	`3 + random×8`, so 3–10	Never asks for more. The ceiling is the question, not the answer.
Tap to Count — total	Same range, 3–10	Same.
The Numeral	None	The only one that survives. Draws any number put in front of it.
The Word	`WORDS` holds eleven entries, zero–ten	Breaks at 11, loudly. Prints the text `undefined` on the card — wrong, and obviously wrong, which is the better kind.
The Ten frame	Ten cells, by definition	Silent, at 11. Draws ten and stops. Twelve renders identically to ten, byte for byte.
The Counters	Five to a row, in a box 92 units tall	Silent, at 11. The third row is drawn below the box and clipped away, so the count is simply short.
The Domino	Six spots a side, so twelve	Silent, at 13. Twelve is correct; thirteen needs a seven-spot half, which does not exist, so that half renders blank.
The Tally	Groups of five, 70 units apart in a 197-unit box	Silent, at 16. Fifteen just fits, with one unit to spare. The fourth group is drawn past the edge.
Number Worm	Ten stroke sets, 0–9	No concept of a second digit at all.
The jar	`JAR = 15` — five stars, three tiers	A full jar is the end of the road.

The four silent ones have to be fixed before the ceiling moves anywhere. None of them can fire today: every tool asks for 3–10, and there is no box anywhere for a teacher to type a bigger number — an earlier draft of this page said there was, and there is not. So these are not bugs waiting to bite a teacher on Monday. They are the work that has to land before any of section 04 is built.

The word representation is the cheap one and the least urgent, precisely because undefined on a card announces itself. The other four draw something that looks right, and a child has no way to tell. The ten frame is the worst of them, and also the most encouraging: what it needs is a second frame, which is exactly what NC.1.NBT.2 asks for. The fix and the feature are the same change.

02Three moves, not bigger numbers

Kindergarten maths is about cardinality and representation — how many, and how many ways can you show it. That is why six representations sit on the glass at once: NC.K.OA.1 asks for connections among them. First grade is a different subject wearing the same clothes. It is about operation, equality and place value. Three moves carry almost all of it.

Move one Ten stops being a ceiling and becomes a unit. NC.1.NBT.2 — a two-digit number is tens and ones, a ten is made of ten ones, and eleven to nineteen are a ten plus some more. This is the whole year in one sentence, and the ten frame is already the right instrument: a second ten frame is the entire idea.
Move two The equal sign stops meaning “the answer comes next”. NC.1.OA.7 — decide whether an equation is true. Nearly every first grader will say 8 = 3 + 5 is written backwards. It is the cheapest misconception to surface and the most expensive to leave alone.
Move three Numerals become two digits, so formation stops being the skill. NC.1.NBT.7 — read and write numerals to 100. Writing 21 for 12 is not a motor error. It looks identical to one in the data unless the tool is told the difference.

Everything else in NC.1.OA and NC.1.NBT hangs off those three. Strategies within 20 (NC.1.OA.6) are move one applied to addition — making ten is the ten-as-a-unit idea. Unknown addends (NC.1.OA.4, NC.1.OA.8) are move two with a gap in it. Ten more and ten less (NC.1.NBT.5) is move one with the ones column held still.

03Tier 4, and why it is the only hidden one

The maths tool already has the mechanism. Three tiers, five stars each, a fifteen-star jar, and tierForStars deciding what has been earned. Tiers two and three are visible while locked, and tapping a locked one says keep playing Tier 1 rather than doing nothing. That was a deliberate decision and it should not change.

Tier 4 — Stretch — extends the same ladder: five more stars, a twenty-star jar. But it should be the one tier that is hidden rather than locked, and the reason is worth stating because it looks inconsistent until you say it out loud.

A locked Tier 2 is an invitation: it is the next thing, it is close, and the child can see themselves getting there. A visible Tier 4 on a child's first morning is a different message entirely — there is a whole level above you that you will not be reaching. Lock what is nearly earned. Hide what is a grade away.

So Tier 4 appears for exactly two reasons: the child earned all fifteen stars, or the teacher opened it from behind the passcode. The second route matters as much as the first. The standing rule in this suite is that a child earns their climb and a teacher is never blocked from planning — a teacher who knows a child is a year ahead should not have to make them grind fifteen stars to prove it.

What it costs

Three numbers and one condition. JAR goes from 15 to 20, tierForStars caps at 4 instead of 3, the tier bar gains a fourth button that renders only when the child has opened tier 4 or the card carries a teacher override, and that override is saved next to tier on the card. The existing scratch allowance, star jar, treat and passcode gate all carry over untouched.

04What each tool becomes

This is the part worth arguing with. Six tools are built; two more are designed. Most of them have a first-grade version that is a change of question rather than a new piece of software, and the two cheapest are also the two most useful.

Tool	Serves now	Becomes	The actual change	Cost
Number Worm	NC.K.CC.3	NC.1.NBT.7	Two numerals in sequence, left digit first. Every one of the ten existing stroke paths is reused — no new art at all. Needs one new signal: wrote the ones digit first.	Cheapest
Build the Number	NC.K.OA.1	NC.1.NBT.2	Teens first, then twenty. A second ten frame; `WORDS` out to twenty; the domino becomes a full tile plus a partial one, which is the tens-and-ones idea living in the representation itself.	Low
Tap to Count	NC.K.CC.4	NC.1.NBT.1	Start the count from a given number rather than from one, and count on past a decade. The tool already enforces one-to-one; it just never starts anywhere but the beginning.	Low
Parallel Lanes	NC.K.OA.1	NC.1.OA.3	Hand two lanes the same total with the addends swapped — 7+5 and 5+7 — and let them notice across the panel. Commutativity found socially rather than told.	Medium
Draw and Tell	W.K.2	RF.1.4.b	The child reads their own sentence back, so the piece becomes a fluency sample on re-reading. Keep it recording pieces and words and never a score.	Medium
Sounds I Can Make	RF.K.4	RF.1.3.a RF.1.3.c	From single sounds to digraphs, then final-e and vowel teams. The gate before any of it is long versus short vowels, RF.1.2.a.	Medium
Pull-apart bond designed, not built	NC.K.OA.3 NC.K.OA.4	NC.1.OA.4 NC.1.OA.8	Put the gap anywhere in the bond and it is already the unknown-addend tool. Built once, it serves both grades — which is the strongest argument for building it next.	Serves both
Hundred chart designed, not built	NC.K.CC.1	NC.1.NBT.1 NC.1.NBT.5	Make it a 150 chart, because that is what the standard says. Then moving down one column is ten more and up is ten less — one grid, three standards.	Serves both

Two of these are free upgrades to things already designed. The number bond and the chart were both drawn up for kindergarten and both land on first-grade standards without a second build. If the question is what to do next, it is those two — not because of the stretch tier, but because the stretch tier makes them pay twice.

05Four tools with no kindergarten parent

Some of first grade has nothing to extend from, because kindergarten does not go near it. Four candidates, in the order their value per line of code suggests.

True or false — NC.1.OA.7. An equation appears; the child taps true or false. No canvas, no drag, no art, no animation. It is the smallest tool in the whole suite and the richest diagnostically, because the wrong answers sort themselves into named misconceptions: the child who calls 8 = 3 + 5 false reads the equal sign as an instruction, and the child who calls 4 + 3 = 7 + 2 true is adding everything they can see.
Ten more, ten less — NC.1.NBT.5. Built on the 150 chart rather than beside it. The error that matters is the child who counts ten squares one at a time instead of dropping a row, and a chart can see that happen where paper cannot.
Three categories — NC.1.MD.4. Organise and read data with up to three categories, including how many more. Draw and Tell is already filing thumbnails per child, so the class's own drawings are the data set and the question is about them rather than about nothing.
Hours and half-hours — NC.1.MD.3. Honestly the weakest of the four. A clock face is a good touch target and a real standard, but it is isolated — it connects to none of the three moves and teaches nothing else. Worth building when the list above is done, not before.

06What a board should not try

The suite has been honest elsewhere about standards software cannot serve — fine motor work is readiness and not a maths standard, and it says so. The same honesty applies here. Four parts of first grade are worse on glass than on a table, and listing them is more useful than pretending otherwise.

Leave on the table NC.1.MD.1 and NC.1.MD.2 — ordering by length and measuring with non-standard units. The entire point is iterating a physical unit end to end with no gaps. A screen removes the gaps for you, which removes the lesson.

NC.1.MD.5 — quarters, dimes and nickels. Real coins have weight, size and an edge you can feel. Pictures of coins are a vocabulary exercise wearing a maths hat.

NC.1.G.1 to NC.1.G.3 — attributes, composing shapes, halves and fourths. Pattern blocks already do this better than any drag target will, and a child's hands are the correct interface for turning a shape over to see whether it still counts.

07The data must not blur the two grades

This is the part the suite has already got wrong once and should not get wrong again. Number Worm originally recorded numeral tracing into rep.numeral — the same key Build the Number uses for recognising a numeral. The effect was that practising handwriting silently inflated a child's recognition score. Writing was given its own key and the bar started telling the truth.

Stretch work will do exactly the same thing if it is allowed to. A child answering within twenty is not demonstrating the kindergarten standard more strongly; they are demonstrating a different standard. Three rules keep them apart:

Leave stats.rep alone. It means the six representations within ten, and it should keep meaning that for every child in the class for the whole year. It is the only comparable number the record has.
Give stretch its own place: stats.ext, keyed by standard code — {'NC.1.NBT.2': {ok, miss}}. Keying by standard rather than by tool means two tools can feed one standard, which is exactly what the chart and the ten-more tool will do.
Record reversals as reversals. A two-digit mix-up belongs in conf as '12>21' — a place-value error, legible at a glance, and distinguishable from a representation mix-up because both sides are numeric. It must not land in the Worm's stray or wrongStart counts, which mean the hand went off the path and nothing else.

The record page then grows one more section, shown only when stats.ext has something in it. A child who never stretched shows no empty heading, and a teacher reading the record does not have to wonder whether a blank means not-yet or not-tried.

08Is this child actually ready?

The tier will open itself on fifteen stars, but fifteen stars in one lucky session is not evidence. What the record can already show, and what is worth looking for before opening Tier 4 by hand:

Signal	Where it lives	What good looks like
A full jar more than once	Stars, by day	Fifteen on three separate days, not three times in one afternoon
No weak representation	The six bars	All six above roughly seventy per cent, not an average that hides one at thirty
Not leaning on the scratch card	Mask fraction	Well under the allowance — getting there without rubbing much out
Clean numeral formation	Worm traces	Low strays and no wrong starts on the digits attempted
Range at Tier 3	Which reps were chosen	Picked several ways, not the same two every time

The counter-signal, which is the useful one. A child who is fast and accurate but chose the same two representations in every Tier 3 round has not outgrown kindergarten. They have found two ways that work and stopped. That child needs the narrow practice screen on the four they are avoiding — not a first-grade tier. Speed reads like readiness and often is not, and this is the one case where the stars will say yes and the record will say wait.

09Six weeks, on the day plan

The day plan already files tools by where they happen — at the board, one child at a time, you and one child — and shows which standards a day touches. Stretch items join the library as a third group, First grade stretch, marked so they never look like an ordinary choice for the whole class. A plausible arc for one child or a small group, fifteen minutes at a time:

Week	Move	Tool	Standard	Watch for
1–2	Ten as a unit	Build the Number, teens only	NC.1.NBT.2	Does the second frame get filled, or counted from one again?
2–3	Writing two digits	Number Worm, two numerals	NC.1.NBT.7	Ones digit written first — the reversal, not a stray
3–4	The equal sign	True or false	NC.1.OA.7	Is 8 = 3 + 5 called backwards?
4–5	Counting on	Tap to Count, from a given number	NC.1.NBT.1	Hesitation at the decade — 29 to 30, 109 to 110
5–6	Unknown addend	Pull-apart bond, gap anywhere	NC.1.OA.4	Counting up, or guessing and checking?
6	Ten more, ten less	150 chart	NC.1.NBT.5	One row down, or ten squares counted one by one?

The decade-crossing in week four is not invented. North Carolina's own formative task for NC.1.NBT.1 has children start at 100 and count on, then from 118 to 130, then from 137 to 150, and describes meeting expectations as crossing every decade without hesitation or omission. A tool that logs where the pause happened is doing the same assessment, continuously, for nothing.

10If only three things get built

Patch the four silent failures. A second ten frame, a third row of counters that stays inside its box, a domino that declines past twelve, and a tally that wraps. Add the words out to twenty while you are in there. An afternoon, not a week, and it is what stops the first stretch session going wrong in a way nobody can explain — because four of the six pictures currently lie quietly rather than break.
True or false. No art, no canvas, no drag. The whole of NC.1.OA.7, the misconception sorted into named categories, and it proves out stats.ext on the smallest possible tool before anything bigger depends on it.
Number Worm, two digits. Reuses all ten stroke paths, adds the one signal the data model is currently missing, and gives a child who has mastered numeral formation somewhere to go that is still obviously the same game.

Tier 4 itself can wait until there is something to put in it. The ladder is three numbers and a condition; the tools are the work.

—Two notes on the standards

There is no NC.1.OA.5. North Carolina dropped it in the 2017 revision of the Standard Course of Study, so the first-grade operations standards run 1, 2, 3, 4, 6, 7, 8, 9 with a gap. A pacing guide written against the common wording will send you looking for it.

NC.1.NBT.1 says 150, not 100. It is one of the places North Carolina diverges from the common wording, and it is the reason the chart tool should be built as a 150 chart from the start rather than extended later.

Standards as adopted June 2017, NC Standard Course of Study: K–8 Mathematics Standards and the first grade unpacking document. Reading foundational skills follow the common wording: RF Grade 1. The counting task referred to above is published on GoOpen NC.

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