Measuring with a unit you lay end to end

I can line things up to see which is longer.

A comparison can be settled by lining up at one end and looking at the other, and the word longer needs two things while shortest needs all of them.

The child covers one feather and says why the shortest can no longer be named.

First lesson. Hold two strips up at different heights and ask which is longer. Take the answers, then lay them on the desk from one line and ask again.

The book asks which snake is longer and, four sentences later, which feather is the shortest, and the two are not the same question.

Pairs lay two snake strips with both left ends on one line and say which is longer and which is shorter without moving either, then line up three feathers from the same end and order them to name the shortest.

Three feathers in order from a common line, and the two snakes with both sentences said about them.

One child covers a feather with a hand and asks whether the shortest can still be named, then uncovers it and says why all three were needed and only two snakes were.

I can measure by moving one unit along and counting.

A length is produced, not read: you move one unit, keep track of every move, and the count is the answer.

The counting strip has one box filled for every ruler length, and the number matches the book's.

Yesterday you settled which was longer without any number. Today you need a number, and one ruler is going to have to do all the work.

The book hands over its own unit and its own conversion in one printed line and then prints the ostrich at six feet without ever showing the six rulers.

Pairs lay the ruler along the ostrich strip starting flush, mark where it stops, move it to the mark and go again, filling one box on the counting strip for every move and saying the number aloud.

The counting strip with one box filled per ruler length, and the height said twice, once in rulers and once in the book's word.

Pairs measure the paper snake the same way and say how many rulers long it is, then say it again in feet, and say why the snake needed so many fewer.

I can say what my number is a number of.

Two people can measure the same mat honestly and get two different numbers, because the count is a count of somebody's unit.

The child says a full sentence naming the object, the number and the unit, and hears a different number for the same mat without deciding either is wrong.

Yesterday everybody's ruler was the same length and everybody got six. Today the unit is your own foot, so hold on to your number.

Arzo has no sword and no cow, and he wins the contest by putting one foot in front of the other and counting.

Each child lays paper copies of their own foot end to end along the mat, then walks the mat heel to toe counting aloud; partners measure the same mat with their own feet and both numbers go on it side by side.

One mat carrying two different numbers, and each child's sentence naming the object, the number and the unit.

Each child says the sentence about the mat, hears a partner's sentence with a different number in it, and says whether both can be true at once.

I can show why the sticks have to match.

A count only settles a length when every unit is the same size, and a mixed set can be made to give two answers for one ribbon.

The child has four numbers on the page and can say which pair of them can be trusted.

Yesterday two people got two numbers with two different feet. Today one person gets two numbers with one set of sticks, and that is a different problem.

The contestants measure with swords and sickles and goats, and a watching voice says the flaw out loud: those swords are all different sizes.

Pairs measure one ribbon twice with six mixed sticks, rearranging between the goes, and write both numbers; then measure the same ribbon twice with six matching sticks and write those two.

Four numbers on one page, two from the mixed sticks and two from the matching set.

Each child tells a partner which set can be trusted to settle the length, and the reason has to name all four of their own numbers.

I can hear which unit the order is asking for.

Counting to ten twice can produce two different lengths, so the number is only half the answer.

The child holds two cut strips both made by counting to ten and names the word that made them different.

Yesterday the sticks had to match. Today they match, and the trouble is that the order does not say which stick.

Drapes are ordered ten spoons long and a door fourteen sausages high, and nothing fits; the tailor's failure is not a failure of arithmetic.

Each child hears the drape order and lays ten spoons end to end along a paper strip, cutting where the tenth ends; then hears the same order with one word changed and does it again with ten paper sausages.

Two cut strips per child, both made by counting to ten, held up side by side.

Each child gives a partner a measuring order of their own for a named object; the partner must fill it without asking anything, and any order that fails is said again with the missing word put in.

I can fill one foot with inches and count them.

A big unit is made of a countable number of small ones, and which unit to speak in is a judgement about the object.

The count lands on twelve, and any pair that got eleven or thirteen has found the gap and closed it.

Yesterday two units gave two lengths. Today the two units are related, and you can find out by how much.

The book prints the question and its own answer in the same breath, so the number twelve is given and nothing about it is done.

Pairs lay paperclips end to end along a measuring tape from the very beginning, counting each aloud, and stop when the clips reach the end of one foot.

A row of clips filling one foot with the count said aloud, and the number checked against the book's.

Pairs take three paper strips one at a time and decide out loud whether to give each length in inches or in feet, laying the strip against the football to check before committing.

I can say how close is close enough.

About is not vagueness; it is the word that makes a benchmark sentence true, and deciding whether it applies takes an object in each hand.

The child says a whole sentence about each object with about, more than or less than, and names what the pans did.

Yesterday twelve clips filled one foot exactly. Today nothing is going to come out exactly, and the sentence is going to be true anyway.

A loaf of bread is about a pound, a football is about a foot long, a paperclip is about an inch long — and that one word is what makes all three true.

Pairs weigh the loaf against a one-pound weight and watch the pans tip, then hear the sentence with about removed and say whether the shortened version is true; then sort six objects into about, more than and less than, saying the whole sentence as each lands.

Three labelled areas holding six objects, each placed after its sentence was said aloud.

Each pair chooses the object they found hardest to place, says to another pair why it went where it did, and the two pairs settle it on the balance rather than by talking.