Division: sharing into equal groups

I can deal a total into equal groups.

Dealing one at a time is what makes the sharing equal, and the answer is read off a single plate.

The child says a full sentence naming all three numbers.

First lesson. Put twenty counters and five plates in front of the class and ask what the question is. Take the answers and settle nothing yet.

The book hands a student both numbers a sharing needs and withholds only the answer: it prints the animals and it prints the groups.

Pairs count ten counters onto the mat and set five plates beside it, say aloud what each number counts, then deal one counter to a plate at a time until the pile is gone and count what sits on one plate.

A recording strip carrying the number on one plate for four different verses.

Each pair picks one verse and says a full sentence naming the total, the number of groups and the number on one plate; the partner checks the plates against the sentence.

I can say why the groups have to be equal.

An uneven split gives the question two answers, and the question asked for one.

The child makes an uneven split on purpose, finds two answers, and moves counters until there is one.

Yesterday every plate came out the same. Today you will split it wrongly on purpose and find out what goes missing.

The book asks how many in each twelve times and never once prints the word equal.

Pairs split sixteen counters onto two plates any way except evenly, answer the verse's question aloud and notice they have two answers, then slide counters across one at a time until both plates hold the same number.

The number of moves it took, and the word the table would add to the verse, written on the strip.

Pairs deal two more verses and check every plate holds the same number before writing anything down, dealing again from the start rather than moving one counter across if a plate is short.

I can hear which number the divisor counts.

Divided by three and into groups of three sound almost the same and build different arrangements, and the story's own result rules one of them out.

Both arrangements stand on the desk with an equation under each, and the child names the number that settles which is the book's.

You have dealt into a number of groups you were given. Today the sentence is going to be ambiguous, and only the story's own count will settle it.

Rumpelstiltskin's spells are two words and a number, and the two words decide whether the three counts the groups or what sits in one.

Pairs read the spell strip and the result strip aloud, count twelve counters into one pile, deal them onto three plates and write the equation, then sweep them up and deal them into plates of three and write that equation.

Two built arrangements side by side, each with its equation, and one plate pushed forward on each as the group that turns into frogs.

Pairs read the book's result strip with a hand on the plate that matches it, write one sentence naming which wording the book must have used, and circle the words that made the difference.

I can find the divisor.

When you are given the total and what one group holds, the number of groups is the thing to find.

The child writes the divisor with the equation that proves it.

Yesterday you decided which number the three was counting. Today that number is missing altogether.

What number the knights were divided by is never stated: twelve stood at the gate, four frogs appeared, and the rule is shown elsewhere on the kittens.

Pairs count twelve counters for the knights and four of another colour for the frogs, push four counters at a time into cups until the row is gone, count the cups and write the matching equation.

The cups on the desk with the divisor written and the equation that proves it.

Pairs check the rule on the kittens by dealing twelve into three cups, say which number the spell gives them, then test the rule on the smallest spell in the story and say whether it still holds.

I can say what happens when the total grows.

Hold the number of groups still and grow the total, and the share climbs by a predictable amount.

The child predicts a fourth answer before touching a counter and says what made them think so.

You can find any of the three numbers. Today two of the three are going to change on purpose, one at a time.

The book puts three verses into a student's hands that all divide into four groups, and never lines them up or remarks on them.

Pairs build all three verses on four plates each and write the number on one plate under each, then line the three answers up in the order they built them and say what happened across the three.

A row of three answers with the total that produced each written above it.

Given a fourth total that also makes four groups, pairs say what will be on one plate before touching a counter, say what made them think so, and then build it and check.

I can say what happens when more people share.

Hold the total still and add a sharer, and the share has to shrink, because the same amount is going further.

The child says the rule as a sentence and names what they would point at to convince somebody who did not deal the cubes.

Yesterday the total grew and the share climbed. Today the total stays put and the number of sharers grows instead.

This is the book's one place where the same amount is shared twice with different numbers of sharers and both results are printed.

Pairs deal thirty-six cubes into three trays and count one tray, then put every cube back into one pile, add a fourth tray and deal the same thirty-six again.

Two recorded shares from one unchanged total, with both printed lines set beside them.

Each pair says in one sentence what happens to one person's share when more people join and the prize stays the same, and says what they would point at as the evidence.

I can say what is left over and what it is not.

When the sharing does not come out even, the leftover is part of the answer, and the book stops without saying what happens to it.

The child keeps the four spare bags visible and can point at all four numbers of the share.

Every share so far has come out even. Today it will not, and the leftover is not going to be tidied away.

Twenty-four bags meet twenty kids at the campout and four bags do not fit the share.

Pairs count twenty-four cubes as the bags and set out twenty counters as the kids, give one bag to each kid until every kid has one, and count what nobody received without putting the extras away.

The leftovers tray holding four, with all four numbers of the share pointed at on the printed line.

Pairs say aloud that the book stops here, then say one thing they would need to be told before they could work out what each person got from those four spare bags.