Money Math

$Money Math book cover$

Grade 2
4 skill lessons

Math

Skill lessons

The mathematics the book carries, taught directly. Printable workbook pages and teacher keys are not available for this book yet.

1What Stays on the Desk
2Eleven on the Page, Twelve on the Desk
3Greatest First, Then Down the Line
4Do It on Paper, Prove It in Coins

Math + reading

Math through the reading

The same book, entered through a sentence it prints. Change one word in the reading and the numbers change with it.

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Reading

Reading and language lessons

The same book read as a text. What a word means in its sentence, how a character is shown, how the writing is put together - no mathematics.

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Skill lessons

4 lessons on the mathematics the book carries. Printable workbook pages and teacher keys are not available for this book yet.

1. What Stays on the Desk Application · Finding change by removing named coins and counting what stays

A shopper pays seventy-five cents for a fifty-nine cent chocolate bar, and the book works the change out by naming every coin on both sides: the seventy-five it starts with, the fifty-nine that leaves, and the dime, nickel and penny that remain. Then it sets three more subtractions the same way and answers none of them. Students lay out the named coins, lift out the named coins, and read the answer off what stays behind. The application is that change is not something you are told, it is what is left, and the coins on the desk settle it before any number sentence is written.

Full lesson — 20 minutes

1. Set out seventy-five cents the book's way (4 min)
Read the candy-store line aloud and set the price card in front of you. Build seventy-five cents on the KEEP side using exactly the coins the book names — two quarters, a dime, two nickels and five pennies — and count them to seventy-five before you touch anything else. Say the two amounts out loud, what you are holding and what the bar costs.
Word preview: change
At a candy store, you might pay 3 quarters, 75 cents, for a 59 cent chocolate bar.
You paid more than 59 cents, the cost of the chocolate bar.
Begin with 75 cents, 2 quarters, 1 dime, 2 nickels, and 5 pennies.
2. Take out fifty-nine cents and count what stays (6 min)
Slide across to the PAID side exactly the coins the book names — two quarters, one nickel, four pennies — counting them to fifty-nine as they go. Do not touch the KEEP side while you do it. Now count what is still sitting on the KEEP side and say the amount. Read the book's line and check it against your desk, coin for coin.
Word preview: remain
Take out 59 cents, 2 quarters, 1 nickel, and 4 pennies.
1 dime, 1 nickel, and 1 penny remain, 16 cents remain.
You expect the clerk to give you change.
3. Answer the three the book leaves open (6 min)
Take the three problem cards. For each one, build the coins the book names on the KEEP side, slide across the coins the book names as taken out, and count what stays. The book asks the same question after all three and answers none of them, so your desk is the only place the answer is. Write each answer in cents on your strip and say which coins are still sitting there.
Word preview: remain
For the first problem, 50 minus 29 begin with 1 quarter, 2 dimes and 5 pennies. Take out 29 cents. 1 quarter and 4 pennies. How much money remains?
For the second problem, 73-67 begin with two quarters, one dime, two nickels, and three pennies. Take out 67 cents, two quarters, one dime, one nickel, and two pennies. How much money remains?
For the third problem, 25-19 begin with one dime, two nickels, and five pennies. Take out 19 cents, one dime, one nickel, and four pennies. How much money remains?
4. Write the taking-away as a number sentence (4 min)
Now write down what your hands already did. Copy the book's sentence for the chocolate bar onto your strip, then write one of your own for each of the three cards, in cents, with the amount that stayed on the desk on the right of the equals. Read one aloud with a finger resting on the coins it describes.
Word preview: difference
Giving change is money subtraction.
The answer to 75 minus 59 is 16.
75 cents minus 59 cents equals 16 cents.

Short version — 9 minutes

1. Take out fifty-nine cents and count what stays (5 min)
Build the seventy-five cents the book names on the KEEP side. Slide across the two quarters, nickel and four pennies it names as paid, counting to fifty-nine as they go. Count what stays and say the amount, then check it against the book's line.
Word preview: remain
Begin with 75 cents, 2 quarters, 1 dime, 2 nickels, and 5 pennies.
Take out 59 cents, 2 quarters, 1 nickel, and 4 pennies.
1 dime, 1 nickel, and 1 penny remain, 16 cents remain.
2. Answer the three the book leaves open (4 min)
Take the three problem cards. Build the coins named, slide across the coins named as taken out, and count what stays. Write each answer in cents and name the coins still sitting there.
Word preview: remain
How much money remains?

Three levels

Support: Run the third card only, and run it in two goes. First lay out the twenty-five cents the book names — a dime, two nickels, five pennies — and count it. Then slide across just the dime and the nickel, count what stays, and say it. Only then slide the four pennies across and count what stays again. Nineteen cents leaves the desk in two loads instead of one, and the amount left is said out loud after each load.
At Grade: Run the chocolate-bar change with the book's named coins, then all three cards, counting what stays each time and writing the subtraction in cents with the remaining amount on the right of the equals.
Extension: On the second card, seventy-three take away sixty-seven, nothing on the desk ever gets broken open: every coin that leaves was already there to lift. Say why that is, using the two coin lists, and then build a card where it would not work — an amount to take away that forces you to trade a coin in before you can lift it — and say what you had to trade.

English learners

Taking coins away is the same act in every classroom, and children who have shopped anywhere have done it. English is what multiplies here: this book calls one act four things. Money is taken out, an amount remains, the clerk gives change, and the number itself is the difference. Difference is the hard one, because outside this book a difference is a way two things are unalike, and here it is a number of cents you can pick up. Put the four words on the desk mat where the act happens — taken out on the PAID side, remains on the KEEP side, change and difference on a card between them — and say each one as the coins move. Rehearse the frame that carries both amounts: I paid ___ cents, it cost ___ cents, so ___ cents remain. Children may talk the coins through in their strongest language while the sliding happens, then give the frame in English with the remaining coins under one hand.

Materials

Coin trays per pair: eight pennies, four nickels, three dimes, four quarters
A desk mat with a KEEP side and a PAID side
Three problem cards carrying the coin lists the book prints for each subtraction
Recording strips ruled for a subtraction sentence in cents
Pencils
Word cards: remain, change, difference

Standards & curriculum

These lessons are being matched against curricula now.

2. Eleven on the Page, Twelve on the Desk Reasoning · Finding and organising every way to make twenty-five cents

The book asks how many ways there are to make twenty-five cents without using a quarter, then prints eleven of them and asks the reader how many they found. Eleven is not all of them. Using only pennies, nickels and dimes there are twelve, and the one the book does not print is a dime, two nickels and five pennies. Students build the eleven, sort them so that a gap becomes visible rather than lucky, and find the twelfth. The reasoning is that a list is only finished when it is organised: you cannot know what is missing from a heap, and you can from a sorted board.

Full lesson — 20 minutes

1. Build the book's eleven ways (6 min)
Split the eleven ways between the pairs at your table and build the ones you are given, one way per build card. Count each card to twenty-five before you leave it — every card has to be worth exactly twenty-five cents, no more, no less. Bring all eleven cards together in the middle of the table and read them off against the book's lines to check that no way got built twice.
Word preview: way
A quarter is 25 cents.
How many other ways can you make 25 cents?
Here are 11 ways to make 25 cents.
One dime and 15 pennies are 25 cents.
Two nickels and 15 pennies are 25 cents.
One nickel and 20 pennies are 25 cents.
25 pennies are 25 cents.
2. Sort them so nothing can hide (5 min)
The eleven cards arrive in the book's order, which is no order at all. Move every card onto the sorting board by how many dimes it uses: two, one, or none. Inside each column, put the card with the most nickels at the top and work down to the card with none. Read your board out loud from the top and listen for a step that is missing.
Word preview: sort
2 dimes and 1 nickel are 25 cents, 2 dimes and 5 pennies are 25 cents, 1 dime and 3 nickles are 25 cents, 5 nicles are 25 cents, 4 nickles and 5 pennies are 25 cents, 1 dime 1 nickel and 10 pennies are 25 cents.
3 nickels and 10 pennies are 25 cents.
3. Hunt the gap (5 min)
Look down the ONE DIME column. The cards there run three nickels, then one nickel, then none — count the nickels aloud and say the number that is not there. Build the missing card with real coins and count it to twenty-five to prove it belongs. Then check the whole board the same way, column by column, and say whether any other step is missing.
Word preview: missing
How many did you find?
4. Say your way in the book's own sentence (4 min)
The book writes every way in one sentence shape. Take a strip and write your new way into that same shape, naming the coins in the order the board puts them. Read it aloud to another pair, who build it from your words alone without looking at your card. If what they build is not twenty-five cents, fix the sentence, not the coins.
Word preview: way
You can practice by solving coin puzzles.

Short version — 9 minutes

1. Build the book's eleven ways (5 min)
Split the eleven ways across the table and build the ones you are given, one per card. Count each card to twenty-five before you leave it, then bring all eleven together and check that none got built twice.
Word preview: way
How many other ways can you make 25 cents?
Here are 11 ways to make 25 cents.
2. Hunt the gap (4 min)
Line the cards up by how many dimes they use, then by how many nickels. Count the nickels down one column aloud and say the number that is not there. Build that card with coins and count it to twenty-five.
Word preview: missing
How many did you find?

Three levels

Support: Work the NO DIME column on its own, and start it already sorted: five nickels, four nickels and five pennies, three nickels and ten pennies. Build those three with coins, count each to twenty-five, and say what happens to the pennies each time a nickel leaves. Then carry the pattern down two more rows without a card to copy. One column, the same reasoning, and the nickel count going down by one at every step.
At Grade: Build all eleven of the book's ways, sort them onto the board by dimes and then by nickels, find the missing twelfth from the gap in a column rather than by guessing, and write it in the book's sentence shape for another pair to build.
Extension: The book says eleven and the board says twelve. Say how the sorted board proves there is no thirteenth, using the columns to do it — what makes each column stop where it stops. Then answer the book's harder question about thirty-five cents: sort the four sums it prints the same way and say which column each belongs in, and whether they are the whole of any one column.

English learners

This is the friendliest language in the book, because the book writes eleven sentences to one pattern and never varies it: a coin count, and, another coin count, are 25 cents. Eleven near-identical models is exactly what a child assembling English needs. Cut the eleven printed lines into strips and let children match each strip to the card they built, so the sentence and the coins arrive together. Rehearse the frame with the numbers left open: ___ ___ and ___ ___ are 25 cents. The plurals are the only real trap — one nickel against two nickels, one dime against 2 dimes — and they are audible in the book's own lines, so read them aloud rather than pointing at them. A child may sort and count in their strongest language; the frame is what has to come out in English, and it comes out with a card in hand.

Materials

Coin trays per pair: twenty-five pennies, five nickels, two dimes, one quarter
Twelve blank build cards per pair, each ruled with an empty coin frame
Pencils
A sorting board with three columns headed TWO DIMES, ONE DIME, NO DIME
Sentence strips printed with the frame ____ and ____ are 25 cents.
Word cards: way, sort, missing

Standards & curriculum

These lessons are being matched against curricula now.

3. Greatest First, Then Down the Line Fluency · Counting a mixed handful of coins to a total in cents

The book prints one procedure and then runs it three times: put the coins in order by worth, start with the biggest, and count on. It shows the work once in words — a quarter, then a nickel, then three pennies, thirty-three cents — and then hands two more handfuls over with only the order named. Students count the same three handfuls with coins on a mat, saying the running amount out loud at every coin. What they are getting fast at is the count itself: not naming a coin, but carrying a total across coins of different worth without losing it.

Full lesson — 20 minutes

1. Build the book's thirty-three cents (5 min)
Lay out one quarter, one nickel and three pennies in a left-to-right row on the mat, biggest first. Put a finger on the quarter and say twenty-five, slide to the nickel and say thirty, then touch each penny and say thirty-one, thirty-two, thirty-three. Say the total once more with your hand flat over all five coins. Write the amount on your strip in cents.
Word preview: value
What is the value of the coins below?
Add the quarter to the nickel, then add the three pennies.
The value of the coins is 33 cents.
2. Say the rule the book counts by (5 min)
Read the four order lines aloud with your partner, one line each. Then scramble your five coins and put them back in the book's order without being told which comes first. Point at the coin you would count first and say why it goes there — the reason is its worth, not its size. Do it twice, swapping who scrambles.
Word preview: greatest, order
The easiest way to find the total value of the coins is to count them in order.
Begin with the coin of greatest value.
With these coins, you would first count the quarter.
Next count the coin with the second highest value, and so on.
3. Rebuild fifty-eight cents from the order line (5 min)
The book names the order for this handful but not the coins. Take two quarters, one nickel and three pennies, lay them in the order the line gives, and count on: fifty, fifty-five, fifty-six, fifty-seven, fifty-eight. Check your total against the book's. If you land somewhere else, count again with one finger on one coin at a time.
Word preview: total
What's the total value of these coins?
Start with the quarters, then the nickel, then the pennies.
The value of the coins is 58 cents.
4. Count a handful nobody has told you about (5 min)
Open the sealed envelope and tip out the coins. Sort them by worth first, greatest at the left. Count on aloud while your partner keeps a finger on the coin you are saying. Write the total in cents, then hand the envelope to another pair and count theirs. Two pairs who get different totals for the same envelope count it again together, one coin at a time.
Word preview: value
Before you count, you need to know the value of each bill and coin.
Counting money is money addition.

Short version — 9 minutes

1. Build the book's thirty-three cents (5 min)
Lay out a quarter, a nickel and three pennies in a row, biggest first. Count on aloud — twenty-five, thirty, thirty-one, thirty-two, thirty-three — touching one coin per number. Say the total with your hand over all five coins.
Word preview: value
Add the quarter to the nickel, then add the three pennies.
The value of the coins is 33 cents.
2. Rebuild fifty-eight cents from the order line (4 min)
Take two quarters, one nickel and three pennies and lay them in the order the book's line gives. Count on aloud to the total, then check it against the book.
Word preview: total
Start with the quarters, then the nickel, then the pennies.
The value of the coins is 58 cents.

Three levels

Support: Work the thirty-three-cent handful only, and take the quarter out of it. Count the nickel and three pennies on their own — five, six, seven, eight — so the whole count runs in ones from a single starting number. When that is steady, put the quarter back at the head of the row and start the same count from twenty-five instead of five. Same coins, same order, one bigger first number.
At Grade: Count all three of the book's handfuls on the mat, greatest coin first, saying the running amount at every coin, and write each total in cents. Then count a sealed handful nobody has named for you and agree the total with a second pair.
Extension: Count the thirty-three-cent handful backwards — pennies first, then the nickel, then the quarter — and say what the total came to. It is the same thirty-three. So say what the book's order is actually buying you, given that both orders land in the same place, and find a handful where counting smallest first makes you lose your place.

English learners

The coins are the same objects in any language, and a child who counts by fives at home counts by fives here. The snag is one English word doing a job it does not do in ordinary speech: value. In this book value is a number of cents, so a handful has two different counts — five coins and thirty-three cents — and the book means the second one every time. Put a five-coin handful under two labels, HOW MANY COINS and HOW MANY CENTS, and have children fill both before any counting-on starts. Rehearse the frame that keeps them apart: this is ___ coins and it is ___ cents. Children may count on in their strongest language while their finger moves along the row, and say the two-part frame in English at the end with the coins still under their hand.

Materials

Coin trays per pair: ten pennies, six nickels, six dimes, four quarters
A counting mat ruled into one left-to-right row
Recording strips, one per child
An order card reading GREATEST FIRST, one per pair
Sealed handfuls, one envelope per pair, each holding coins worth under one dollar
Word cards: value, total, greatest

Standards & curriculum

These lessons are being matched against curricula now.

4. Do It on Paper, Prove It in Coins Representation · Checking a two-digit sum by building both addends in coins

The book takes an ordinary addition problem, tells you to work it the way you always would, and then makes you count it out in coins to see whether the paper was right. It does this twice with the answers printed — twenty-seven and twelve, then eighteen and thirty-four — and then hands over three more with the answers blank. Students write the sum, build both amounts in coins, push them together and count the pile. The representation is the point: the same number appears as a written total and as a heap of coins, and the two have to agree or one of them is wrong.

Full lesson — 20 minutes

1. Do the book's first sum on paper (4 min)
Write twenty-seven plus twelve down the page, ones under ones, and work it the way you always work an addition. Do not touch a coin yet. Put your answer in a box and turn the paper face down so nobody changes it once the coins come out.
Word preview: check
If you can count money, you can use coins to help you practice addition.
Here's an addition problem.
27 plus 12 equals blank.
First, do the problem as you would any addition problem.
2. Count out both amounts and push them together (6 min)
Build twenty-seven cents on the left mat and twelve cents on the right, counting each one out loud as you build it. Push both piles across the join line into one pile. Sort the joined pile biggest coin first and count it on to a total. Turn your paper over. If the two answers disagree, count the pile again before you touch the paper.
Word preview: total
Now check your answers using Money Math.
Count out 27 cents.
Count out 12 cents.
Now put the coins together and find their total value.
27 cents plus 12 cents equals 39 cents.
3. Run the harder one, where the ones spill past ten (6 min)
Write eighteen plus thirty-four on paper and work it out, then build both amounts in coins the same way. Watch what happens to the pennies when the piles join: there are more than ten of them, and on paper that is the ten you carried. Trade ten pennies for a dime and count the pile again. Say whether the total moved.
Word preview: check
18 plus 34 equals blank.
18 cents plus 34 cents equals 52 cents.
4. Take the three the book leaves blank (4 min)
The book sets three more sums and prints no answers. Work each one on paper first, then build it in coins and count. Write both answers side by side on your sheet and ring the pair that agree. Bring any pair that does not agree to the table and count it out again with another pair watching.
Word preview: check
Here are some addition problems.
First do them as math problems.
Then use money math to check your answers.
36 plus 19 equals blank.
51 plus 12 equals blank.
76 plus 23 equals blank.

Short version — 9 minutes

1. Count out both amounts and push them together (4 min)
Work twenty-seven plus twelve on paper and turn it face down. Build twenty-seven cents and twelve cents on the two mats, push them together, sort the pile biggest first and count it on. Turn the paper over and see whether the two agree.
Word preview: total
Count out 27 cents.
Count out 12 cents.
Now put the coins together and find their total value.
27 cents plus 12 cents equals 39 cents.
2. Run the harder one, where the ones spill past ten (5 min)
Do eighteen plus thirty-four on paper, then build both in coins. When the piles join there are more than ten pennies. Trade ten of them for a dime, count the pile again, and say whether the total moved.
Word preview: check
18 plus 34 equals blank.
18 cents plus 34 cents equals 52 cents.

Three levels

Support: Stay with twenty-seven and twelve, and build both amounts out of dimes and pennies only — two dimes and seven pennies, one dime and two pennies. Push them together and count the dimes first, then the pennies: ten, twenty, thirty, thirty-one, and on to thirty-nine. No coin has to be traded and nothing crosses ten, so the whole check is one count in dimes and then one count in ones.
At Grade: Work both of the book's printed sums on paper and check each one in coins, trading ten pennies for a dime when the joined pile carries more than ten. Then take the three blank sums, do each on paper and in coins, and ring the pairs that agree.
Extension: The book uses the coins to check the paper. Turn it round: count out a pile of coins first, say its total, and write the addition sentence that the pile is an answer to. Then find two different piles that give the same total and say what is the same about them and what is not. Seventy-six and twenty-three is the one sum here whose ones never pass ten — say how you could have known that before you added.

English learners

Column addition is written the same way in most of the classrooms these children have come from, so the arithmetic here is often already familiar and it is the English wrapped round it that is new. Check is the word that misleads: it is a tick on a page in one use and a whole second method in another, and this book means the second. Say it as a two-part instruction every time — do it once on paper, do it again with coins — so check is heard as doing the sum twice rather than looking at it twice. Rehearse the frame that reports both: on paper I got ___ and with the coins I got ___, so they agree. Children may run the count in their strongest language and say the frame in English with both answers visible, the paper on one side and the pile on the other.

Materials

Squared paper and pencils, one sheet per child
Coin trays per pair: twelve pennies, four nickels, eight dimes, three quarters
Two count-out mats side by side with a join line between them
Problem cards carrying the three sums the book leaves blank
Word cards: check, total

Standards & curriculum

These lessons are being matched against curricula now.