How heavy, and how much it holds

I can build a balance and say which of three things it did.

A balance compares and does not count. Its whole vocabulary is heavier, lighter and level, and every one of those is about two things at once.

The child says each result as one sentence naming both sides, and relevels the board between objects.

First lesson. Hold up two objects and ask which is heavier. Take the answers, then ask how they would settle it without a scale.

Walt has no scale and makes one out of a plank and a rock, and from then on every weight judgement in the book is made by watching which end goes down.

Children lay a board across a block so both ends can drop, level it with a matching can on each end and mark where the block sits, then put the reference bag on one end and set one test object on the free end before letting go of both together.

Six objects each run once against the reference bag, with the result said aloud as a sentence naming both sides.

Children put two of their test objects together on the free end against the bag, swapping one if the board tips, and say what a level board tells them about those two together that it does not tell them about either alone.

I can record what the balance said in the right column.

A chart is a record of results, not of opinions. The middle column is the hardest to earn because level is the rarest thing a board does.

The child says each entry aloud as a whole sentence while writing it, and nothing appears on the chart that has not been on the board.

Yesterday the board gave you sentences. Today the sentences go somewhere, and the chart has a rule about what may enter it.

The book finishes with a page it calls a weight chart, four rows comparing things to a box nobody opens.

Children fold a sheet into three columns headed lighter, the same and heavier, say what has to have happened on the board before a name can go into each, then run six objects one at a time and write each name into the column its result earned.

A three-column chart filled only from the pair's own board results, and a second chart holding the book's four rows in their earned columns.

Children look at their chart of the book's rows and say what the box could weigh and what it could not, then say whether the chart settles what is inside it and, if not, which row they would need changed and what it would have to say.

I can find two objects that balance a marked bag and say what they weigh together.

The board cannot count, but a number can be carried across it. If one end holds a weight you already know and the board sits level, the other end weighs the same — and no more than that can be said.

The child writes the weight of the level pair and says the reason they are allowed to write it, then says why neither half of the pair can be given a number.

The board has given comparisons for two lessons. Today it gives a number, and the class has to work out where the number came from.

Walt's plank cannot count, and yet he walks away from it knowing his fishing gear and his backpack come to twenty pounds. The number is Patch's, and the level board is what carries it across.

Children put the bag marked with its weight on one end, run objects one at a time on the free end and keep the ones the board calls lighter, then take two from that pile and swap one at a time until the board sits level.

A card carrying the weight of the level pair, with the reason for writing it said aloud.

Children split the level pair, put one of the two back on alone, say what the board shows now and whether they can put a number on that object, and say what would have to happen for them to know it.

I can weigh something in grams and write the number with its unit.

A scale answers a different question from a board: it gives one number about one object. The number is only a reading once the unit is written beside it.

The child writes object, number and unit for every row, and writes both readings when a repeat weighing disagrees.

The board never gave a number. Today the machine does, and the class finds out that it does not always give the same one.

The book names the scale as the tool and never shows a reading, so this lesson supplies the part the text asserts and skips.

Groups weigh a paperclip, a pencil and a glue stick in turn, waiting for the number to settle, reading it aloud and writing it beside the object's name with the word grams after it — nobody writing a number without its unit.

A record sheet with three rows of object, number and unit, plus a second reading for one object and a fourth row the group chose and weighed themselves.

Groups take the glue stick off and put it straight back on, read the number again, write both numbers if it changed and same if it did not, and say aloud what they saw.

I can put objects in order by weight and say what a new one sits between.

An order can be built from stated weights and then tested where the objects are small enough to hold. Placing a new object means naming both of its neighbours.

The child slides an unlisted object into the line and says one sentence naming what it is heavier than and what it is lighter than.

Single readings are on the sheet. Today four weights get put in order, and two of them get checked by hand.

The back matter prints four objects each with a weight — a paperclip about a gram, a slice of bread about an ounce, two pears around a pound, a giraffe about a metric ton — and they are already in order.

Groups read the weight printed on each of four picture cards aloud, lay the cards from lightest to heaviest, then hold the real paperclip and the real slice of bread one in each hand, say which hand is pulled down harder and check that against both scale readings.

A ladder of five objects including one the book does not list, with a two-part sentence naming its neighbours.

Groups read the finished line of five aloud from lightest to heaviest touching one object per name, read it back the other way, and say which two objects swapped places in their mouths when the direction changed.

I can find out which container holds more by pouring.

How tall a container looks does not tell you how much it holds. Pouring settles it, and pouring in both directions is what turns a result into a proof.

The child pours in both directions, says the result of each as it happens, and marks their own prediction right or wrong.

Weight has been the question for four lessons. Today two containers are the question, and they will not go on a balance.

The book settles an argument by pouring: Lulu is sure the big pitcher holds more, and Martin fills one, empties it into the other, and the water comes right up to the top.

Children look at a tall narrow container beside a short wide one and write a three-word prediction, then fill the tall one to the very top and pour all of it into the wide one, watching whether the water lands short of the top, right at the top or over it.

A recording strip carrying the prediction, both pour results and the sentence the pouring settled.

Children write one sentence saying which container holds more with the words because I poured, then mark their own prediction right or wrong and say their partner's aloud and mark that one too.

I can put the capacity units in order and compare two of them.

The units come in an order, and the order can be discovered rather than recited. Where the book gives no numbers, pouring settles which is bigger.

The child orders all six lines, checks the two smallest by pouring, and writes one comparison sentence carrying both unit names and an ounce number.

Yesterday two containers were compared by pouring. Today six named amounts have to be put in order, and only four of them have numbers.

The recipe lists six amounts and the book happens to print them from largest to smallest: half a gallon, quart, pint, cup, tablespoon, teaspoon.

Children cut the recipe strip into its six lines and lay them out biggest first, read the row aloud by unit name, then check the two smallest by pouring a teaspoon and a tablespoon side by side into the measuring cup where no ounce number is given.

The six units written in order, with one comparison sentence carrying both unit names and at least one ounce number.

Children point at the largest line and say how many ounces it is, then at the smallest line with an ounce number, and say how many of the small one it would take to make the large one — working it out from the ounce rows rather than guessing.