The unit decides the number

I can measure so that somebody else gets my number.

A measurement is a number, a unit and a procedure anyone can repeat, and the evidence is that two pairs measuring one object agree.

Two pairs measure the same object without seeing each other's number, and the two numbers match.

First lesson. Ask two children how tall the bookcase is and let them answer however they like. Write both answers up and leave them there.

The book shows two friends settle a contest badly, by standing beside their suitcases and reporting a chest and a knee, and then shows Sebastian do it properly.

Pairs first report both objects against their own bodies and swap with another pair to hear the same object reported differently, then find the 1 and the 36 on a yardstick and run the book's four moves in order on the taller object.

A record sheet carrying one object's height as a number and a unit, with a second pair's independent number beside it.

Pairs put the body report and the two yardstick numbers side by side and say which report another class could check and why, each finishing with one sentence naming their object, number and unit.

I can measure one thing three ways.

Changing the unit changes the number without changing the object; changing the attribute can change which object wins.

The child says which contest the tall object won and which it lost, and says it was the same object every time.

Yesterday two pairs got the same number. Today one pair gets three different numbers for one object, and none of them is wrong.

The book measures the same two suitcases three times over: in inches, in centimetres, and on the scale.

Pairs measure both objects in inches and write both numbers with the unit, turn the yardstick to its centimetre side and measure the same unchanged objects again, then weigh two packed bags and read the pounds off the dial.

A three-line record, each line carrying two numbers and a unit word, with the winner of each contest named.

Each pair reads their three lines aloud, says what each pair of numbers is a measurement of, and names the contest the tall object won and the one it lost.

I can read to the half inch and compare it with a foot.

The comparison is settled by two fingers on one tape, not by taking one number from another.

The child finds the long mark halfway between two numbers and says the length as a whole number and a half.

You can read a whole number off a tool. Today the object stops between two of them.

Dad's foot measures eleven and a half inches, and the book says the foot is less than a foot, which is a joke and a genuine comparison at once.

Pairs find the half-inch mark between 11 and 12, and between two other pairs of numbers, then measure a paper slipper cut to exactly eleven and a half inches with its heel flush at the start of the tape.

A record card carrying the slipper's length as a whole number and a half, and a sorting mat with four slippers placed above or below the foot line.

Pairs measure three more slippers, place each above or below the one-foot line, and say a full sentence for each naming its inches and whether it is less than a foot; a slipper landing exactly on twelve goes on the line.

I can choose a unit that fits the thing.

A unit has a size you can feel, and choosing one is a judgement about the object rather than a rule to recall.

Every object on the tray sits on a unit card, and the child can name the reference object that decided it.

You have been given the unit all week. Today you choose it, and the choice has to be defended.

The book gives four objects whose weights are each about one unit: a paperclip, a slice of bread, two pears, a walrus.

Pairs hold each of eight objects against the reference object on each unit card and lay it on the card it feels closest to, weighing nothing; then check the two lightest against a real scale and compare the reading with what the book claimed.

Four unit cards holding eight sorted objects, with two of them checked on a scale.

Each child picks one object and says a sentence naming the unit they chose and the reference object that decided it; the partner holds both and says whether they agree.

I can build the relation between two units.

Sixteen is reached by counting sixteen slices beside one, so the relation is seen rather than calculated, and it has two true sentences.

The child says both sentences with both numbers in each, pointing at the stack for one and the single slice for the other.

Yesterday you chose between units. Today two of them are set against each other and the counting says by how much.

The book puts a slice of bread at about an ounce and two pears at about a pound, four lines apart, and sets them against nothing.

Pairs read the two object sentences, count sixteen paper slices into a stack and stand one more beside it, then weigh two real pears on the ounce scale and say whether the reading is near the pound the book claims.

A counted stack of sixteen standing beside one slice, with the pears weighed on the same table.

Each child says one heavier-than sentence and one lighter-than sentence with both numbers in each, and a partner says whether the second sentence said the same thing as the first.

I can build the ladder of capacity units.

Each customary capacity unit is twice the one below it, so the ladder can be built by doubling rather than remembered.

Each row is built by doubling the row beneath it, and the child says what they did each time.

Yesterday sixteen ounces made a pound. Today four units are going to line up and each one is twice the one under it.

The recipe at the back prints four liquids with both a unit name and an ounce number, and each number is twice the one below it.

Pairs read the four ounce numbers aloud with both name and number, then build the smallest row in ounce tokens and make each next row by making a second row just like it and pushing the two together.

Four rows of ounce tokens built by doubling, with the unit cards laid beside the rows they name.

Pairs write the four pairs on a strip, largest first, and write one sentence saying what happens to the ounce number each time you go down a line.

I can find two names for one amount.

The same bottle is two cups in the story and one pint in the recipe, and nothing in the book says they agree.

The child says one sentence using both names and the ounce number.

Yesterday you built the ladder. Today two rungs of it turn out to be describing the same bottle.

In the kitchen Martin finds about two cups of soda left; in the recipe at the back the same soda is one pint.

Pairs read the two cards and say why they do not look like they agree, then pour one measuring cup into the empty container and mark where it stops, pour a second, count the ounces to sixteen and set the pint card at the line.

The container marked at one cup and at two, with the pint card set at the second mark.

Each pair writes the soda amount twice, once as the story says it and once as the recipe says it, with the ounce number beside each, and joins them with a line marked same.