What a coin is worth

I can say how many cents each coin is worth.

A coin's name carries its value. The nickel is bigger than the dime and worth less, so looking at a coin cannot tell you what it is worth.

The child names a coin from a number of cents without looking at the strip, and can say the sentence where the smaller coin is worth more.

First lesson. Hold up a nickel and a dime and ask which is worth more. Take the answers and let the disagreement stand.

The book stops the story to print its four coin values one after another, each as a plain equation with the coin on the left and a number of cents on the right.

Children line the four coins up in the order the book names them, read the four printed sentences aloud touching each coin as they say its value, then write each coin's name and cents on a strip, copying the value from the book's sentence rather than from memory.

A four-line cent strip with the actual coin sitting on each line, read top to bottom as four sentences.

One partner says a number of cents and the other picks up the coin that equals it and names it without looking at the strip; a disagreement is settled by putting the coin on the book's own sentence.

I can build each coin's worth in pennies and put the coins in order by worth.

Worth is a count. A pile of pennies under a coin is what makes the number checkable, and the piles put the coins in an order that the coins themselves do not.

The child orders the four coins from least worth to most using the penny piles, and recounts rather than looking at the coins when a partner disagrees.

Yesterday the values came off the page. Today they get built out of pennies so the numbers can be checked.

The book prints a worth line for all four coins and promises the reader will know each one before it ends.

Children lay one penny under the penny, five under the nickel counted one by one, ten under the dime, and twenty-five under the quarter laid five to a row, counting each pile aloud and saying its cents before moving on.

Four counted penny piles with a worth card beside each coin, checked by a partner against the pile.

Children put the four coins in order from least worth to most using the piles and not the coins, and where two children disagree both recount the piles rather than looking at the coins again.

I can trade a handful of coins for one coin worth the same.

Fairness in a trade is decided by cents on both sides. The number of coins in your hand gets smaller and the money does not change.

The child says out loud, after each swap, whether they have more money than before, less, or exactly the same — and says the same.

The piles showed that five pennies and a nickel are the same worth. Today that becomes something you can do rather than something you can see.

Three times the book answers Albert's question with a trade rather than an amount: five pennies become a nickel, two nickels a dime, and two dimes with a nickel a quarter.

Children put five pennies on the mat, count them aloud, swap all five for one nickel and say what the nickel is worth, then run the two-for-one and three-for-one trades in the book's own order, holding each result before the next trade begins.

Three completed trades with the cent value said at every swap, and a count of how many coins were held before and after.

The teacher offers one dime for four pennies. Children use the strip and the coins to decide whether to take it, say the two cent numbers that made up their minds, and say what would have to be added to make it fair.

I can add each payment to my total and say the new total.

A running total is the number you are standing on. The next payment is added to it, and saying your own answer before reading the page is what makes it arithmetic rather than copying.

The child says the new total aloud before the printed line is read, every time, and the chart carries their number first.

Trades kept the money the same. Today the money grows, one payment at a time.

Albert is paid four times and the book prints the running total in cents after each payment, each addition written out as a sentence.

Children start with the nickel Albert holds, add the second nickel, trade the pair for a dime and add a second dime — saying what the two dimes are worth together and writing it on the chart before the book's sentence is read.

A wall chart carrying four running totals, each in the child's own number with the book's printed line written after it.

Children read the line where Albert is given the second quarter, put it on the mat, say the total in cents before writing it, and say the one number both they and the book ended on.

I can put the jar lines in order and build the whole chain.

Six lines about one jar lock together because each one starts on the number the last one ended on. That rule alone puts them in order, without adding anything up.

The child orders the six cards by that rule alone and can say why the first card goes first — its starting number is nobody's answer.

Yesterday's totals were in cents and arrived in order. Today they arrive shuffled, in dollars, and the order has to be worked out.

Every chapter closes with a line of arithmetic about the same jar, and the six lock together: the numbers they start with run one, two, five, eight, eleven, sixteen, and the last ends on twenty.

Groups put the six shuffled cards in order using one rule — a line goes after the line whose answer it starts with — reading each card aloud as it is placed and saying the number it ends on, without adding anything up.

The six cards in order, and the chain built once on a mat that is never cleared, counted aloud after every line and matched to that line's stated answer.

Children turn the cards face down and say the whole chain of totals from memory, then write the seven totals along a strip, cover one, and say which is hidden with the totals either side of it as the proof.

I can find how many dollars are still needed to reach the goal.

A gap is a count of what is not there. Build the total on a frame of twenty and the empty squares answer the question without any subtraction.

The child counts the empty squares to reach the gap and checks the method against the one gap the book works out before trusting it on the others.

The chain ended on twenty because twenty was the price all along. Today the class measures how far away it was at each stop.

The book fixes a goal on its first page — the ball costs twenty dollars — measures the distance to it twice in Ella's voice, and leaves it unmeasured at four more stops whose totals it prints.

Children lay eleven dollar cards on the twenty-frame, one to a square, count the squares that stay empty and say whether their count and the book's nine agree, then clear the frame and do the same at eight and at sixteen.

A recording strip carrying the gap at each of the book's stops, with the book's own nine used as the check on the method.

With sixteen dollars on the frame, children read what grandma paid and lay that many cards into the empty squares one at a time, saying whether the frame came out exactly full, over or short.

I can take ten dollars off a price and say whether a price has already had it taken off.

A discount is a rule printed once and used twice. The hard part is not the subtraction but deciding whether it has already been done to the price in front of you.

The child sorts the shop's two prices by whether the ten has come off yet, and can point at the words that decide it.

Totals have gone up all unit. Today one comes down, and the amount is fixed by a coupon rather than by a payment.

The coupon is a rule the book prints in a single line and then uses twice without ever printing either result.

Children read the coupon and the price aloud, point at the word telling them the thirty-eight is what the shoes cost before any coupon, build thirty-eight from three tens and eight ones, slide one ten out under the coupon, and count and write what is left.

The written answer to the book's question, and the shop's two prices sorted by whether the ten has come off, with the wrong move tried aloud and refused.

Children put the build and the answer side by side, say how many one-dollar cards they started with and how many are there now, then take a ten off thirty-eight with their eyes shut and say which part of the amount they had to think about and which they did not.