Taking away, and what is left

I can say the three numbers of a take-away.

A take-away has a start, a part that goes and a part that stays, and the one you are asked for is what your hand did not touch.

Every sentence the child says has all three numbers in it.

First lesson. Put seven counters on the mat and take three off without saying anything. Ask what just happened, and collect answers that name only one number.

The book hands over two clean take-away scenes with every number printed: seven bulldogs with three scared off, and thirteen hornets with ten buzzing away.

Pairs count seven onto the mat and say the number, slide three into the cup one at a time saying take away, count what stays and say the three numbers in order; then run the hornets the same way before checking the book.

Two scenes built, and each child's spoken three-number sentence for each.

Each child points at the mat and says the start, the part that left and the part still there, once for the bulldogs and once for the hornets.

I can take away again and again without starting over.

The mouth says what stays while the hand takes only what is refused, so the pile can be emptied a few at a time.

The child never sweeps the mat and recounts from one, and reaches zero two different ways.

Yesterday one removal, three numbers. Today the same pile is taken down over and over and the count never goes back to the start.

Once Albert's pile reaches eleven the book runs the whole climb backwards, and every difference is said aloud down to zero.

Pairs load eleven, slide one off for the puzzle and say ten, then one and then two, then one and one and then two, lining the removed counters at the edge so every take stays visible.

A line of removed counters at the mat's edge showing every take, and the mat emptied to zero.

Pairs take the last three off in one sweep and say zero, then put them back and take them off one at a time, and say which way emptied the mat in fewer moves.

I can write down what I did.

The written line records the three numbers, and the word in the middle claims that the two sides are worth the same.

The card line matches the mat, number for number, and the child can say what the middle word is doing.

Yesterday the takes were spoken. Today the same take gets written down, and every number on the line has a job on the mat.

The book writes two subtraction sentences in symbols and then stops to explain its own equals sign.

Pairs stand ten counters as pins, sweep eight over, count what stands, and lay number cards to match the mat, pointing at each card as the line is said back; then roll the second ball and build the line for that.

Two card lines matching two mats, with the last number said aloud when nothing is standing.

Each child points at the middle of the card line, says what that word is doing, then says the line again swapping is for equals and checks nothing about the pins changed.

I can hear how much the sentence takes away.

The amount removed can be named by a word rather than a number, and one word is the difference between one leaving and all of them.

Two mats stand side by side, one nearly full and one bare, and the child names the word that emptied the house.

So far every removal has come with a number. Today the sentence has no number in it at all, and the word has to do the work.

Every quantity in the story is a group that arrives and stays, and the only thing that ever reduces the pile is the word all in the ramp sentence.

Pairs build the running pile of cubes from the arrival sentences, then run the swapped sentence by moving one cube to the truck and saying the number left, rebuild, and run the book's sentence by loading the whole train.

Two mats visible at once, with the number standing on each said aloud.

Partners each say one sentence naming the word that emptied the house and the number left, then test the same word in Penelope's refusal and say why the pile did not change there.

I can use a clue to send exactly one away.

A stated condition can do the removing, and the count is what says whether it removed the right number.

After every clue the row has gone down by exactly one, and the cleared pile has grown by one.

Yesterday a word decided how much left. Today a whole sentence decides who leaves, and the count is going to check it.

Duck's clues each name a single feature and each clears exactly one baker, and the book prints the resulting count every time.

Pairs match each clue to the card it names, decide whether it clears that baker, move only the cards the clue clears, and count the row after every removal, checking the number went down by one.

The row counted after each clue, with the cleared pile counted against it.

When one card remains, the child names the animal and says why every other baker was sent home, naming two of the clues.

I can find the pile I cannot see.

A whole splits many ways and the pieces always rebuild it, which is what makes a missing part findable rather than guessable.

The child says how many must be hiding before uncovering the pile, and is right.

Yesterday you watched cards leave one at a time. Today both piles are counted, and then one of them is hidden.

The book keeps a whole and two parts on the table at every moment, and never once counts the cleared side.

Pairs count twelve into the row, move four to the cleared space and count both, slide them back and count the whole again, then fill two ten frames with the two piles and say what pouring them together would give.

Both piles counted with the twelve rebuilt, and the ten frames filled and read.

One partner hides the cleared pile and says only how many are left in the row. The other says how many must be hiding, then uncovers and counts.

I can find how many arrived between two totals.

When the start and the finish are both known, the change is the number you are looking for.

The child counts what left the cup, not what is on the mat, and says the whole trip in the frame.

All week the question has asked what is left. Today both ends are given and the middle is missing.

What the pile held before each of Albert's trips and after is stated, but never how many things he carried in.

Pairs set the mat at three, move counters from the cup one at a time until the mat holds five, and count what left the cup; then clear, set seven, and fill to ten in groups of two and one.

Two completed trips with the number that left the cup counted and said, checked against the book's equation strips.

Each partner takes one of the book's one-thing trips, builds it, and tells the other the whole trip in the frame; the listener rebuilds the mat from the telling alone.