Which number counts the groups

I can find the number that says how many groups, whatever word comes after it.

Flowers, lines, directions, puddles and pens are all doing one job: naming how many piles the animals go into. Deciding what counts as a group is the reader's job, not the book's.

The child collects the noun after the second number from six verses, says what all six have in common though no two are the same word, and builds three verses that share the number four.

First lesson. Read one verse aloud and ask how many plates the table will need, without saying the word groups yourself. Take every answer and ask what in the verse decided it.

The book almost never says the word groups where a reader needs it — it says flowers, lines, directions, puddles and pens instead.

Children underline the two numbers in a verse and circle the noun right after the second one, then read the six verse cards at their table and write that noun on a sticky note, one per note, putting all six notes together and reading them out.

Six nouns collected and read aloud, and the hummingbirds, the goats and the toads built — three verses that all use four, with the number on one plate written under each.

Children read the pelican verse, where the noun after the second number is fish and the fish are not a place the pelicans stand, deal fourteen counters onto two plates anyway, and say whether the number they get still answers the question the verse asks.

I can say what each, into, groups and round tell me to do, and show what changes when a word is swapped.

One word decides whether a question needs any arithmetic at all. Each sends you inside a single group; all sends you back to a number already printed on the page.

The child predicts what the underlined word tells them to do before dealing, writes an answer only once the counters agree, and says which single word was carrying the division in their verse.

Yesterday the noun said how many plates. Ask what the word each is doing in the same sentence, and hold the question open until the counters answer it.

The book's questions turn on four small words — groups, into, round and each — and never remark on any of them.

Children read four verse cards and underline each, groups, into and round where they find them, then for each verse say aloud what the underlined word tells them to do to the pile, deal the counters onto plates, read one plate, and write the answer only after the counters agree with what they said.

Four words tested on their own verses, each with a prediction made before the dealing and an answer written after it.

Children reread the turtle question with all the bails in place of each bail, try to build it, find there is nothing to deal, and say the answer to the swapped question and where in the verse that number was already sitting — then tell another pair which single word was carrying the division.

I can build a division as rows, draw it, and write the equation for what I built.

An arrangement and an equation are two records of one thing. The numbers in the equation each point at something on the desk — one counts the rows, one counts what a row holds.

The child builds, draws and writes the equation for three arrangements of the same fifteen, and says which number in each equation counts the rows.

The words have decided how many plates twice now. Lay fifteen circles out in five rows of three and ask what could be written down that would say exactly this.

Peter finds fifteen covered holes and counts them as five rows of holes in groups of three, which is the one place in the book where a division is already drawn.

Children lay fifteen paper circles flat in five rows of three and count by threes with one touch per number word, write the division that matches what is on the desk, slide each row into a heap to check that every heap holds three, then move the same fifteen into three rows of five and draw and write that one too.

Three arrangements of the same fifteen circles, each drawn and each with its own equation written underneath.

Children spread the fifteen circles so each one stands alone as its own group, draw the fifteen single circles in a line, write the equation for fifteen groups of one and ring the single hole the character kept, reading the equation aloud while a partner points at the ringed circle.

I can build two divisions of the same total and argue for one with both numbers in my sentence.

The same total divides more than one way, and choosing between them is an argument. An argument without a number in it is not one.

The child builds both results side by side, writes both equations, and completes the reason frame with both numbers while a partner argues the other divisor with its own numbers.

Fifteen was arranged three ways yesterday and nobody had to choose. Today the character chooses, and so does the class.

Peter says out loud that he could divide fifteen by five to get three holes, stops himself, and divides by fifteen instead, and one hole remains.

Children build fifteen counters as five groups of three on the left mat and the same fifteen as fifteen groups of one on the right, count what a single group holds on each, lift one group off each mat and set them side by side, and write both equations under the mats.

Both results built and left standing, both equations written, and the reason frame completed aloud with both numbers in it by each partner in turn.

Children build the same fifteen as three groups of five, count what one group holds, say where that result sits between the other two naming all three numbers, and decide with a partner whether it changes the argument they just made. Better, easier and faster may not be said without a number attached.

I can count off round a ring and end with teams that match.

There is more than one way to reach equal groups. The count-off gives one number word to each in turn, and the teams only come out matching if nothing was skipped and nothing took two numbers.

The child runs the count-off into two, three and four teams without losing the count and says both numbers — how many teams and how many on each — for every run.

Every group so far has been dealt onto plates. Ask how a class actually splits into teams in the playground, and try that on counters in a ring.

Three times the book says the same thing about how the teams got made: they counted off.

Children set twelve counters in a ring and go round saying one, two, one, two, sliding each counter to the plate whose number they just said with a partner watching that nothing is skipped and nothing takes two numbers, then return the counters and run it again into three teams and again into four.

Three count-offs run to the end, one plate counted after each, and both numbers said aloud for every run.

Children hold their plates beside the book's lines for the pool and the canoes, say whether the two agree, and say what happens to the size of a team every time a plate is added.

I can find how many groups a total makes at a stated size, and say what is left over.

Dealing at so many to a plate answers a different question from dealing onto a fixed number of plates: it tells you how many plates. And what the plates say can disagree with what the sentence says.

The child deals the six slices at two to a plate, counts the plates, reads the number of people out of the sentence, and states in one sentence who the phrase two friends leaves out.

Until now the sentence has said how many plates. Cut a paper pizza into six and say two slices each, and ask what the question has become.

The book gives the target pizza six equal slices and a sharing sentence naming two friends.

Pairs cut a paper circle into the six equal slices the book gives and deal them onto plates at two slices a plate until the slices run out, count the plates and write that number down without saying it aloud, then decide from the words alone how many people are at this pizza and point at the part of the sentence they used.

Three plates from the dealing set against the two people the sentence names, with the two-plate arrangement built as well and the slices left over counted.

Children who read two people set out two plates and say what happens to the slices left over, then each pair states in one sentence who the phrase two friends leaves out and why that person still eats, using the plates as the evidence.

I can produce a number a book never prints and read out the line that made it the only answer.

A produced number needs its evidence. The order matters: the sentence that fixes the answer is read aloud before the counters move, not after the answer is known.

The child works three verses in the read-then-deal order, saying the funding line aloud each time before the number is spoken or written.

Point out that nobody in this unit has ever found an answer printed in the book. Hand out four verse cards and ask the class to hunt for one anywhere.

Every one of the book's twelve questions goes unanswered: each card ends in a question and no card carries a third number.

Children read four verse cards and report that nothing is answered, then for the leatherback verse read aloud the sentence giving the animals and the sentence giving the groups with a finger on each in turn and say which number counts which — dealing nothing yet — before dealing ten counters onto five plates and reading one plate.

Three numbers produced for three verses, each written beside its verse with the funding line read aloud before it, and a partner's check that the order held.

Children repeat the read-then-deal order for the leopards and the gorillas, with a partner checking each time that the line was read aloud before the counters moved and that the written number sits beside the right verse.

I can find the phrase that says how many shares there are and show what changing it does.

The numerals alone cannot tell you how many shares there are. A phrase does it, and swapping that phrase changes the answer without changing a single numeral in the total.

The child deals the original and the swapped share, names the deciding phrase, and says in one sentence what the word changed and what the answer became.

The unit began with a noun deciding the plates. End it with a phrase doing the same job, and test it by changing the phrase rather than the numbers.

The book's sentence names three ways of splitting the prize, and prints two lines for the same thirty-six.

Pairs take thirty-six cubes and the sentence naming three ways, deal the cubes into three trays and count one tray, then underline the one phrase that says how many shares there are and say aloud why the numerals alone could not have told them.

Both deals of the same thirty-six cubes — three trays and six trays — with the deciding phrase underlined and both answers said in one sentence.

Children swap each for the in the payment sentence and say what the ticket would then cost one child, then say which of the two words they tested made the bigger difference to the answer and why.