Equal parts of one whole

I can name a part from the number of equal parts.

Cut into so many equal parts, divided into the name for that many — and the word equal in the middle is what children skip.

The child moves between the cut object, the count of its parts and the name of one part in any direction.

First lesson. Hold up a circle cut into three pieces that do not match and ask whether these are thirds. Take the answers and cut nothing yet.

Eight times this book says the same sentence with two numbers swapped in, and the word equal sits in the middle of every one.

Pairs hear one of the book's cutting sentences, fold a circle into exactly that many matching parts, cut and stack to check, then fill the two blanks of the book's frame with the count word and the name word and read the finished sentence aloud.

A cut circle with the finished naming sentence written beside it, the two blanks filled with different words.

Each pair is handed a circle already cut into three pieces that do not match, stacks them, decides whether thirds may be used, and writes the word the pieces do deserve.

I can say which slice is bigger and why.

When the top number is the same, more parts means each part is smaller, and the pieces show it before the numbers do.

The child predicts before cutting and then checks against the stack.

Yesterday the name came from the number of parts. Today two names are set against each other and the bigger bottom number is going to be the smaller piece.

The book ends by asking which of two slices a child would rather have, and every one of its four pairs has the same number on top.

Pairs fold two circles of the same size into three parts and into four, cut and stack one piece from each with their points meeting, and say which hangs out past the other; then predict for sixths against eighths before cutting.

Four cut pieces lined up from largest to smallest with their bottom numbers read aloud in that order.

Each pair states in one sentence what happens to the size of a slice when a pizza of the same size is cut into more slices, and two pairs settle any disagreement by restacking.

I can show two names for the same amount.

An equals sign between two fractions is earned by paper lying flat on paper.

The child can point at the covering that makes their written equation true.

You can say which of two pieces is bigger. Today two different names turn out to describe exactly the same piece.

The book states three equivalences and proves none of them.

Each student folds a disk in half three times and cuts eight equal wedges, checking them by stacking, then lays two eighth wedges over one fourth wedge so no paper shows at any edge.

A record strip carrying the written equivalence with the covered shape drawn round it.

Pairs put six wedges together, write how much of the disk they make in eighths, then group them into pairs against the fourth template and write the same amount a second way on the same line.

I can take a fourth away from a whole.

Four fourths and one whole are the same amount, which is what gives the subtraction something to take from.

The child writes the subtraction using the numbers and can point at the fourth that was set aside.

Yesterday two names covered one amount. Today the whole itself gets a second name so that a piece can be taken off it.

The book gives a recipe that names one part and hides the other: a whole cup of mix, one fourth of it blue, and the red left only as the rest.

Pairs pour four one-fourth measures into one cup to fill it exactly, say the count as fourths and write both names for the full cup, then set one fourth aside as the blue and count what is left.

A recipe card carrying the whole in both forms and the subtraction written in numbers.

Pairs measure the red three times into the pitcher saying the running total, check it against a three-fourths measure, then copy the finished recipe and trade cards with another pair to make it without speaking.

I can repeat a half until it makes whole pounds.

A half is a quantity of weight that can be repeated, not only a piece of a cut-up shape.

The child pairs the bags into pounds and counts the pounds rather than multiplying.

So far a fraction has been a piece of paper. Today it is a weight, and it is going to be laid down ten times.

The fisherman gives the book's one clean unit-fraction fact, that a dozen shells weighs one half pound, and then states the ten-dozen total himself.

Pairs balance one bag of twelve shells against half-ounce weights and read the weight, then lay out ten bags, touch each saying one half, and slide every two together calling that pair one pound.

A strip of paired bags with the pounds counted and set against the fisherman's printed answer.

Each pair tells a partner what one dozen weighs and what ten dozen weigh in one sentence, then changes the fisherman's sentence so a dozen weighs a whole pound and says what ten dozen would weigh then.

I can hear which words fix the weight.

Three words in one sentence each fix a number, and not one of them is a numeral.

Both balance arrangements stand side by side and the child names the word that moved between them.

Yesterday you built the half-pound and repeated it. Today one word in the sentence changes and the whole row has to be rebuilt.

A dozen weighs one half pound holds three words that each fix a number, and Alice's enough is a fourth that is a verdict rather than a quantity.

Pairs weigh a dozen and say the fisherman's sentence over their own balance, lay ten bags in a row and pair them into pounds, then replace half with whole and rebuild the row under the new word.

Two balance arrangements standing side by side with both totals said aloud.

Pairs say what enough means for the rabbit, using the pounds on their row, and decide aloud whether five pounds meets what he said he needed.

I can say what the fraction is a fraction of.

One eighth is always one eighth of something, and until the something is named the words have not said an amount.

The child completes the sentence one eighth of ___ is ___ for all three sharings, or says why it does not fit.

Every fraction so far has had one whole behind it. Today the whole changes three times and the words do not.

The book uses the same wedge to mean an eighth of a cup on one page and a whole cup on another, and says so plainly.

Groups share four cups among four people and write the division; share one cup among eight pots and write what fraction of a cup each holds; then share eight cups among the same eight pots and write what each holds now.

A record row carrying the three sharings in order, each with what was shared and among how many.

For each of the three sharings, students write the sentence one eighth of ___ is ___ or say why it does not fit, then explain to another group why a wedge meant a fraction of a cup in one sharing and a whole cup in another.