Doubling: making a second group that matches

I can build a second group that matches the first.

Doubling means make another one just like it, and the second group is built against the first so the matching is visible before any total is said.

Both rows of the doubling mat hold the same number, checked cube for cube, before the total is counted.

First lesson. Put one cube on the mat and ask the class what to do to double it. Take the answers and do nothing yet.

Jordan makes one sign, then makes a second, and the book says outright that two signs were twice as good as one.

Pairs put one cube in the left row and match it in the right, push and count and say two; then slide all into the left row and match again for four, then eight, then sixteen, touching the cube being matched as they go.

The four totals said in order — two, four, eight, sixteen — with the mat showing the last one built.

Pairs look back along their four totals, say them in order, and say how many cubes they added at each step.

I can tell a double from a pair that only looks like one.

A double is two equal groups, and the check is physical: if any cube sticks out past its partner, it is not a double.

Six tower pairs are sorted correctly, and every repaired pair is described by what the child did to it.

Yesterday you built matching rows yourself. Today somebody else built them and two of them cheat.

Albert's plan only works because Leo's share always equals his own, and the mathematics under double the fun is two equal groups.

Pairs match six ready-made tower pairs side by side cube against cube and sort them into doubles and not-doubles, then repair each cheat twice over, once by adding to the short tower and once by taking from the tall one.

Two sorted piles of tower pairs and every cheat repaired, with the repair described.

Each child holds up one repaired double and says it in a full sentence with the equality inside it, then says its total.

I can name the double and say its total.

Two rows that match with nothing left over at either end are what makes an addition a double.

The child runs a finger down both rows and finds nothing left over before saying any number.

Yesterday you repaired the pairs that were not doubles. Today every pair matches and the job is to name it.

The book supplies two clean doubles and names the strategy on the second: five horses with five riders, and ten porcupines with ten children.

Pairs build five and five as two rows one under the other, run a finger down both to find nothing left over, count straight through to ten and say the sentence; then build ten and ten and count through to twenty.

Two matched double-rows built and named, with the sum said as one sentence over each.

The book asks which number doubles to make ten and does not answer it. Children go back to the horses and riders, put a finger on the two rows of five, and say the answer with the rows in front of them.

I can show one double three ways.

Cubes, a drawing and a written sentence are three records of one double, and all three have to say the same thing.

A partner can count the drawing, read the sentence and rebuild the towers, and all three agree.

You have built doubles and named them. Today the double gets written down so somebody who was not here can read it.

The book says its arithmetic out loud, four plus four equals eight, and this is where students become the ones who write it.

Each child builds two equal towers of three, draws them as two columns of squares one square per cube, writes the plus sentence underneath, then does a second double of their own choice the same way.

A page holding two complete triples of towers, drawing and sentence.

Partners trade pages and check each triple: count the drawing, read the sentence, rebuild the towers if the two disagree.

I can hear whether the rule doubles or adds two.

The number two appears in both versions of the rule; the word each is what decides whether it is asked of the group or of every member of it.

The child has two runs of numbers written down and can point at the round where they stop being the same.

Every double so far has been announced. Today the rule sounds the same both ways and only the cards will tell you which one you followed.

Jordan asks whether each child could get two more friends, and delete each from the sentence and the plan collapses into adding two.

Each child starts with one sign card, runs the book's rule so every card on the desk asks two more, and counts; then clears to one card and runs a rule that adds only two more each round, counting after every round.

Two runs of numbers said aloud in order, with the desks holding the last round of each.

Children say both runs, point at the round where they part, and say in a whole sentence which single word made the difference.

I can find the number that built a double.

Halving runs the doubling machine backwards, and the fair share of a double is the number that built it.

The child predicts the fair share before dealing and says both directions about one pair of numbers.

All week doubling has gone one way. Today twenty arrives already doubled and you have to find what built it.

Twenty action figures land for two friends, and the machine that made twenty has already been taught: ten and ten.

Pairs deal twenty counters onto two mats one at a time and count each mat, repeat with eight, then predict the fair share for each of the story's doubles before dealing to confirm.

Each double's fair share predicted and then confirmed by dealing, with the pattern said aloud each time.

Each child takes one number pair and says both directions without dealing. Asked for half of seven, they deal it and report the leftover rather than forcing an equal split.