Making a graph somebody else can read

I can sort my collection and label what I did.

A sort means nothing to anyone else until the two groups are named on the page.

Another pair can say what the graph shows from the cards alone, without asking.

First lesson. Put a pile of buttons in the middle and ask two children to split it. Then ask a third child what the two piles mean.

Gonk is handed a pile of rocks and nothing else, and the first thing he does is decide what to look at.

Pairs turn a button pile over, choose one attribute that splits it in two, move every button onto one of two paper squares saying why for any that are hard, and write a label for each square and a title for the whole thing.

Two labelled squares holding every button, with a title card a stranger can read.

Pairs hand their graph to another pair, who say what it shows from the cards alone, then find the pair whose two squares look closest to the same and say what they would have to do to be sure.

I can sort by two things at once.

Once the labels are written, a card's own two answers fix where it goes, and no card is placed by how it looks or where there is room.

Every card is on the mat and every region survives the rule-card check.

Yesterday one attribute split the pile in two. Today two attributes are in force at the same time, and some cards will answer no to both.

The back of the book hands over the whole procedure in four sentences and adds that some shapes will belong in neither circle.

Pairs draw a rectangle with two overlapping circles, write both labels before any card moves, then turn over each of twelve cards and ask it both questions, sending two yeses to the middle and two noes inside the rectangle but outside both circles.

A completed mat with all twelve cards placed, checked region by region against the rule cards.

Pairs hold up each rule card in turn and sweep the region it names, sending any card that breaks its rule back to be asked the two questions aloud.

I can check that nothing is missing.

The four region counts have to rebuild the set they came from, so a total that is wrong names an error rather than hiding it.

The four numbers add to the size of the deck, and any pair whose total is wrong finds the card they double-counted.

Yesterday every card went somewhere. Today you prove it by counting the regions and adding them back up.

A finished diagram carries four numbers: the two crescents, the middle, and the ground outside both circles.

Pairs count each of the four regions with one touch per card and write each count in its box, add the four and write the total, then count the deck itself and compare.

A four-box recording strip with a total that matches the deck.

Pairs swap to the second pair of labels, sort the same twelve cards again and fill a fresh strip, then check each other's addition.

I can build a graph with a fair unit.

Height stands for number only if the pieces are the same, and a taller stack can hold fewer things.

The child catches the thick block and can say what rule would stop it.

You have counted your regions. Today the counts turn into height, and height can lie.

Beezy stacks each kind of cookie separately so height stands in for number, and the book gives the condition that makes it honest.

Pairs decide the three kinds in their tray, build one stack per kind straight up from a common base line with every counter in a stack, and read the tallest by looking across the tops before counting it.

Three stacks on one base line with the tallest read by eye and then counted.

Two thick blocks are added to the shortest stack. Pairs look across the tops again, count all three, and say whether the tallest stack really holds the most and what rule would stop it.

I can number the side and say what one square is worth.

A bar means an amount because a numbered side and a stated key make it mean one.

The child says the key aloud with a finger on a single square before colouring anything.

Yesterday the stacks were real objects. Today the objects go away and squares on paper have to carry the count.

The book stops the story to narrate how Marco makes his graph, and gives four moves in order.

Pairs put the four move cards in the book's order, number a grid nought to ten up the left side, say the key aloud touching one square, name four columns, then colour Marco's three dollars counting each square as it fills.

A grid with a numbered side, four named columns and one bar coloured to a stated key.

Partners name an amount for another column each, colour it, then trade grids and read each other's bars by running a finger across to the numbered side.

I can say what changes when the key changes.

Nothing about the numbers says how tall a bar should be; the key sentence does, and changing it changes the picture without changing the data.

Two grids stand side by side, and a listening pair can say which key built which by looking at the bars alone.

Yesterday you said what one square was worth. Today you say it again with a different number in it and rebuild.

This book says out loud the thing most graphs leave implicit: one square stood for each dollar.

Pairs build the book's grid to a key of one dollar a square, then take the changed key sentence, say it aloud, and plot the same three amounts on a second grid, dealing with the amount that will not fill whole squares.

Two grids of the same three amounts under two keys, with the awkward amount handled and explained.

Pairs lay the two grids side by side and say one sentence naming something that changed and something that did not, using a number from each grid.

I can say which question a graph can answer.

A graph answers the question its survey asked and no other, so two graphs of the same children can disagree without either being wrong.

The child finds the two pairings a graph cannot answer and gives a reason from the columns.

You have changed the key and watched the picture move. Today the picture stays and the question changes.

Marco makes two graphs of the same classmates, and because the questions differ his own column is the shortest on one and the tallest on the other.

Pairs write the two questions Marco asked, match each to a finished untitled graph and say what told them, then take three questions in turn and decide for each graph whether it can be answered, giving the reason from the columns.

Two graphs matched to their questions and six can-or-cannot judgements, two of which are cannot.

Pairs say to each other what the second graph showed that the first could not, using a number from each, and listen for whether the partner's reason names a bar or only a feeling.