Follow Your Money

$Follow Your Money book cover$

Grade 4
5 skill lessons · 5 math-through-reading

Math

Skill lessons

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

1What's Left: Reading a Price Down to the Last Line
2Same Jeans, Double the Price: Where the Extra Forty Dollars Goes
3The Parts Line: Six Prices That Have to Add Up
4Four Prices for One Shirt: Reading a Markdown Line
5One Piece Out of Ten: What the Cashier Adds

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.

6The Word That Tells You to Subtract
7Four Prices, One Debt: Telling the Shirt's Story in Order
8The Number the Cashier Says
9Would You Pay the Extra Forty?
10Twice as Much, Half as Much: Saying the Jeans Both Ways

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.

11Who the book thinks you are
12Where the book stops to explain
13One link in the chain
14Where the book takes a side
15Three kinds of question

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Skill lessons

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

1. What's Left: Reading a Price Down to the Last Line Fluency · Adding a column of money amounts and subtracting to find what is left

This book prints the same table more than forty times, and every one of them balances: a price on the top line, a column of costs beneath it, and a last line that is exactly the price minus the costs. Students work three of those tables by hand. They add a column of dollars-and-cents amounts with regrouping across the decimal point, subtract the total from the price, and then lift the cover from the book's own last line to see whether their answer and the authors' agree. The two moves become automatic and the checking becomes a habit: a ledger that does not balance means a line was dropped, and the student goes back to find which one rather than accepting the number. Nothing is estimated and nothing is invented; every figure a student handles is printed in the book.

Full lesson — 20 minutes

1. Read one whole ledger aloud and name its three parts (4 min)
Partners read the pencil ledger aloud, one line each, all the way to the last line. Point to the price on the top line, then run a finger down every cost line, then stop on the last line and say what is left. Say aloud to your partner: fifteen cents came in, three cents went out, twelve cents stayed.
Word preview: price, cost, what’s left
PENCIL: $0.15 Less: Wood: $0.01 Graphite: 0.01 Eraser, paint, etc.: 0.01 What’s left: $0.12
So the price you pay minus the cost of materials must be the profit. But, no! There are other costs to pay.
2. Add the cost column on the notebook ledger (6 min)
Take the notebook ledger and add only the cost lines, top to bottom, writing each running total in the margin beside the line you just added. Do not touch the six dollars yet. Stop when you have added the last cost line and circle your total. Two students in a pair add the same column separately and then compare circled totals before anyone goes on.
Word preview: column, total
NOTEBOOK: $6.00 Less: Cardboard cover: $0.02 Paper inside: 2.50 Spiral binding: 0.01 Other manufacturing costs: 1.47 Profit to manufacturer: 0.20 Store costs (wages, storage, rent): 1.50 Store profit: $0.30
3. Subtract to find what is left, then check the book (6 min)
Subtract your circled cost total from the six-dollar price and write the answer at the bottom of your card. Now uncover the book's last line and set your number beside it. If the two agree, write agrees; if they do not, add the cost column a second time and find which line you dropped. Say aloud which line it was.
Word preview: subtract, agrees
MILK: $3.00 Less: Paid to farmer: $1.50 Processing: 0.70 Transportation: 0.30 Storing/packaging: 0.20 What’s left: $0.30
4. Run the same two moves on a ledger you have not seen (4 min)
Take the pet food ledger face down, turn it over, and run the same two moves without being told: add the cost column, subtract from the price on the top line, and write what is left. Check against the book's last line. Tell your partner the two moves in order, using the words add and subtract.
Word preview: add, subtract
PET FOOD: $20.00 A BAG Less: Ingredients: $12.50 Manufacturing costs: 2.50 Profit to manufacturer: 1.50 Store costs: 2.50 What’s left: $1.00

Short version — 9 minutes

1. Read one whole ledger aloud and name its three parts (4 min)
Partners read the pencil ledger aloud, one line each, to the last line. Point to the price, run a finger down the cost lines, stop on the last line and say what is left.
Word preview: price, cost
PENCIL: $0.15 Less: Wood: $0.01 Graphite: 0.01 Eraser, paint, etc.: 0.01 What’s left: $0.12
2. Add the cost column on the notebook ledger (5 min)
Add only the cost lines of the notebook ledger, top to bottom, writing each running total in the margin. Circle your total, then subtract it from six dollars and check your answer against the book's last line.
Word preview: column, total
NOTEBOOK: $6.00 Less: Cardboard cover: $0.02 Paper inside: 2.50 Spiral binding: 0.01 Other manufacturing costs: 1.47 Profit to manufacturer: 0.20 Store costs (wages, storage, rent): 1.50 Store profit: $0.30

Three levels

Support: Stay on the pencil ledger and the milk ledger, which have three and four cost lines and no amount above three dollars. Add the cost column with the amounts already lined up on a decimal grid so the cents columns cannot drift. Do both moves on the pencil ledger first with the book's last line uncovered, so the target is visible while the procedure is still new, then cover it for the milk ledger and check afterwards.
At Grade: Work the pencil, notebook and pet food ledgers in that order, adding each cost column, subtracting from the price, and checking against the book's last line before moving on. Find and name the dropped line whenever a ledger does not balance.
Extension: Take the backpack ledger, which is the one table in this book that states a middle total in the prose as well as the ends. Add its cost column, subtract, and confirm the last line as usual. Then find the sentence after the table that says what the manufacturer spends and what the store pays, and say which lines of the column add to that middle number and which lines fall outside it. You are splitting one balanced ledger into two smaller balanced ones, and the whole column still has to total the same.

English learners

Adding and subtracting money transfers completely and a learner produces every total correctly with no English at all. The hard part for a learner is the ledger's shape as a piece of reading. English writes the price on top and the leftover at the bottom, and marks the middle with Less, a word that here means subtract everything that follows rather than fewer. A learner who reads Less as a comparison word will read the column as a list of things that are smaller. The second trap is that what's left is three words doing the job one word does in most languages, and it names a result rather than a leftover scrap. Rehearse the whole ledger once as a spoken frame with a finger travelling down the card: ____ came in, ____ went out, ____ is left. Students may add and subtract in their strongest language, and say the frame in English pointing at the three lines it names.

Materials

Pencil ledger card, one per pair
Pencil per student
Notebook ledger card with a wide margin, one per student
Ledger answer strip, one per student
Pet food ledger card, one per student
Decimal grid strip, one per student
Backpack ledger card, one per student
Word cards: ledger, cost, what’s left

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

2. Same Jeans, Double the Price: Where the Extra Forty Dollars Goes Reasoning · Comparing two tables line by line and subtracting to find a difference

The book prints two ledgers back to back whose cost columns are identical, line for line, and whose prices differ by forty dollars. Fabric is three dollars in both. Equipment and shipping is four in both. Store costs are seventeen in both. Only the top line and the bottom line move. Students match the columns by hand, discover for themselves that only two of the eight lines change, and subtract each of those pairs to find that both differences are forty. The reasoning is the point: because every cost line matches, the whole of the extra forty dollars a buyer pays arrives at the last line and nowhere else. This is a comparison the book sets up deliberately and then never completes with arithmetic, so the subtraction and the conclusion are the students'.

Full lesson — 20 minutes

1. Lay the two ledgers side by side and mark every line that matches (5 min)
Put the regular jeans card on the left and the designer jeans card on the right, cost line against cost line. Read the two fabric lines aloud together, then the two equipment lines, and keep going down the column. Draw one line joining each pair that carries the same amount. Count how many joining lines you drew.
Word preview: match, same
The way jeans are made doesn’t differ much between one company and another, but the cost of those jeans depends a lot on the name that’s stitched on the pocket.
REGULAR JEANS: $40.00 Less: Fabric: $3.00 Equipment, shipping: 4.00 Other manufacturing costs: 1.00 Profit to manufacturer: 2.00 Store costs (wages, rent, etc.): 17.00 What’s left: $13.00
DESIGNER JEANS $80.00 Less: Fabric: $3.00 Equipment, shipping: 4.00 Other manufacturing costs: 1.00 Profit to manufacturer: 2.00 Store costs (wages, rent, etc.): 17.00 What’s left: $53.00
2. Find the two lines that do not match and subtract each pair (6 min)
Two lines on your cards have no joining line. Find them and say them aloud. Subtract the smaller price from the larger and write the difference. Subtract the smaller leftover from the larger and write that difference too. Set the two differences beside each other and say what you notice.
Word preview: difference, subtract
REGULAR JEANS: $40.00 Less: Fabric: $3.00 Equipment, shipping: 4.00 Other manufacturing costs: 1.00 Profit to manufacturer: 2.00 Store costs (wages, rent, etc.): 17.00 What’s left: $13.00
DESIGNER JEANS $80.00 Less: Fabric: $3.00 Equipment, shipping: 4.00 Other manufacturing costs: 1.00 Profit to manufacturer: 2.00 Store costs (wages, rent, etc.): 17.00 What’s left: $53.00
3. Say where the extra forty dollars went (5 min)
Point at the cost column and say aloud, to your partner, how much more the designer jeans cost to make. Then point at the last line and say how much more is left over. Finish the sentence on your strip: the buyer paid forty dollars more and the making cost ____ more, so ____ more is left. Your partner checks that both blanks carry a number from your cards.
Word preview: more, left over
DESIGNER JEANS $80.00 Less: Fabric: $3.00 Equipment, shipping: 4.00 Other manufacturing costs: 1.00 Profit to manufacturer: 2.00 Store costs (wages, rent, etc.): 17.00 What’s left: $53.00
4. Test the claim on a second pair of tables (4 min)
Take the cheap earrings and diamond earrings cards and run the same test: join the lines that match, name the lines that do not, and subtract each unmatched pair. Say aloud whether these two ledgers behave the way the jeans did, and name one cost line that changes here but did not change on the jeans.
Word preview: changes
CHEAP EARRINGS: $8.00 Less: Fake gems: $0.50 Metal: 0.50 Cost to make (wages, equipment): 2.00 Profit to manufacturer: 0.75 Store costs (wages, rent, etc.): 3.25 What’s left: $1.00

Short version — 9 minutes

1. Lay the two ledgers side by side and mark every line that matches (4 min)
Put the regular jeans card beside the designer jeans card, cost line against cost line. Read each pair of cost lines aloud and draw a joining line wherever the two amounts are the same.
Word preview: match, same
REGULAR JEANS: $40.00 Less: Fabric: $3.00 Equipment, shipping: 4.00 Other manufacturing costs: 1.00 Profit to manufacturer: 2.00 Store costs (wages, rent, etc.): 17.00 What’s left: $13.00
DESIGNER JEANS $80.00 Less: Fabric: $3.00 Equipment, shipping: 4.00 Other manufacturing costs: 1.00 Profit to manufacturer: 2.00 Store costs (wages, rent, etc.): 17.00 What’s left: $53.00
2. Find the two lines that do not match and subtract each pair (5 min)
Name the two lines with no joining line. Subtract the smaller price from the larger, subtract the smaller leftover from the larger, and set the two differences beside each other. Say aloud what you notice.
Word preview: difference, subtract
DESIGNER JEANS $80.00 Less: Fabric: $3.00 Equipment, shipping: 4.00 Other manufacturing costs: 1.00 Profit to manufacturer: 2.00 Store costs (wages, rent, etc.): 17.00 What’s left: $53.00

Three levels

Support: Work with the two jeans cards only, printed one directly above the other with the cost lines already aligned in a shared grid so matching pairs sit in the same row. Draw the joining lines and name the two that do not match; the subtraction is eighty minus forty and fifty-three minus thirteen, both stated as a written number sentence to fill in rather than set up from scratch. The spoken sentence in the third step is supplied with the first blank filled.
At Grade: Match the two jeans columns line by line, name and subtract the two unmatched pairs, state where the extra forty dollars ends up, and then run the same test on the earrings ledgers and report whether they behave the same way.
Extension: You showed that when every cost line matches, the whole price difference lands on the last line. Now build the case where that does not happen. Take the regular jeans ledger and write a second ledger for an eighty-dollar pair whose leftover is thirteen dollars, exactly as on the regular pair, by raising cost lines instead. Your column must still total sixty-seven and every line must be a plausible cost the book names somewhere. Then say what a buyer would be paying for in your version that they are not paying for in the book's.

English learners

Matching two columns and subtracting transfers completely, and the two differences of forty come out with no English. The language work is the conclusion sentence, and it is genuinely hard. English says forty dollars more twice in this lesson to mean two different things, once about a price and once about a leftover, and the noun after more is what tells you which. A learner may hear the repeated number as the same fact stated twice rather than as two separate subtractions that happened to agree, which is the discovery of the lesson. The second trap is that left over here means remaining, not departed, and a learner reading left as the past of leave will read the last line backwards. Rehearse with a finger on the two rows of the strip: the price is ____ more, and what is left is ____ more. Students may compare and subtract in their strongest language, then say the frame in English touching the two rows it names.

Materials

Regular jeans ledger card and designer jeans ledger card, one pair per two students
Pencil per student
Comparison strip with a price row and a leftover row, one per student
Sentence strip with two blanks, one per student
Cheap earrings and diamond earrings ledger cards, one pair per two students
Aligned two-ledger grid sheet, one per student
Blank ledger form with a printed price line and leftover line, one per student
Word cards: difference, cost line, left over

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

3. The Parts Line: Six Prices That Have to Add Up Concept · Adding a list of whole-dollar amounts to test a total stated elsewhere

The computer ledger says Parts: $240.00 and moves on. Three lines later the book prints six computer parts with a price on each, and never once says that the two go together. They do: the six prices add to exactly two hundred forty. Students add the six whole-dollar amounts, set their total against the book's parts line, and reach a conclusion the book leaves unwritten — that these six parts account for the entire parts figure, so any seventh part would have to be paid for out of a different line. The concept is that a single line in a summary table can be a total in its own right, with its own column hidden elsewhere on the page. The arithmetic is addition of six two- and three-digit whole numbers with no decimal work at all, which is why this module carries the conceptual weight rather than the computational weight.

Full lesson — 20 minutes

1. Read the big table and find the one line that hides a list (4 min)
Read the computer ledger aloud and find the cost line that names a whole group of things instead of one thing. Say its name and its amount to your partner. Then read the six-part list on the facing card and say how many separate prices it carries. Predict aloud, before adding anything, whether the six prices will come to more than the line, less than it, or exactly it.
Word preview: parts, list
COMPUTER: $600.00 Less: Parts: $240.00 Labor: 20.00 Manufacturing equipment: 100.00 Research: 100.00 Profit to manufacturer: 40.00 Store costs: 70.00 Store profit: $30.00
SIX MAJOR PARTS OF A COMPUTER: Monitor: $100 Speaker: $35 Mouse: $20 Processor that runs the computer: $25 Keyboard: $20 Modem: $40
2. Add the six part prices (6 min)
Add the six prices from the list. Work in whole dollars, adding two at a time and writing each running total, so a wrong step can be found later. Circle your answer. Each student in a pair adds in a different order and the two circled answers are compared before anyone speaks.
Word preview: add, total
SIX MAJOR PARTS OF A COMPUTER: Monitor: $100 Speaker: $35 Mouse: $20 Processor that runs the computer: $25 Keyboard: $20 Modem: $40
3. Set your total against the book's parts line (5 min)
Write your circled total directly under the two hundred forty on the computer ledger and say aloud whether they are the same number. Then say what that means in words: the six named parts account for the whole parts line, so a seventh part would have to come out of some other line. Point at the line it would have to come out of.
Word preview: same, account for
COMPUTER: $600.00 Less: Parts: $240.00 Labor: 20.00 Manufacturing equipment: 100.00 Research: 100.00 Profit to manufacturer: 40.00 Store costs: 70.00 Store profit: $30.00
4. Do the same reading on the shoe list (5 min)
Read the shoe sentence, which names five materials and then gives a total. Add the two amounts the sentence states and check the total it gives. Say aloud which of the five materials the sentence prices on its own and which ones it does not, and why you cannot find the price of the rubber alone from anything printed.
Word preview: total, alone
The other materials in the shoe—cloth, rubber, metal, foam, plastic— come from other sources. Those materials add up to another $8 or so per pair of shoes, so the total per-pair cost for the materials is now about $10.

Short version — 9 minutes

1. Read the big table and find the one line that hides a list (4 min)
Read the computer ledger aloud and find the cost line that names a group of things instead of one thing. Say its name and its amount. Then read the six-part list and predict whether the six prices will come to more than that line, less, or exactly it.
Word preview: parts, list
COMPUTER: $600.00 Less: Parts: $240.00 Labor: 20.00 Manufacturing equipment: 100.00 Research: 100.00 Profit to manufacturer: 40.00 Store costs: 70.00 Store profit: $30.00
SIX MAJOR PARTS OF A COMPUTER: Monitor: $100 Speaker: $35 Mouse: $20 Processor that runs the computer: $25 Keyboard: $20 Modem: $40
2. Add the six part prices (5 min)
Add the six prices from the list, two at a time, writing each running total. Circle your answer, write it under the two hundred forty on the ledger, and say aloud whether the two numbers are the same.
Word preview: add, total
SIX MAJOR PARTS OF A COMPUTER: Monitor: $100 Speaker: $35 Mouse: $20 Processor that runs the computer: $25 Keyboard: $20 Modem: $40

Three levels

Support: Add the six prices with the list already arranged from largest to smallest, so the hundred is placed first and the running total never falls. Add in three pairs — the two twenties, then the thirty-five and the twenty-five, then the hundred and the forty — and add the three subtotals. The parts line stays uncovered on the ledger throughout, so the comparison at the end is a matching rather than a reveal.
At Grade: Predict before adding, add the six part prices, set your total against the parts line on the computer ledger, and say in words what it means that the two agree. Then read the shoe sentence and say which materials it prices separately and which it does not.
Extension: The book prices a monitor at one hundred dollars and prices the whole computer at six hundred. Work out how much of the six hundred is not parts at all, using the ledger's own lines, and say which single line is the largest of those. Then take the ink cartridge ledger, which the book says is thirty-five dollars for about ten dollars of ink, and say why its parts line and its price cannot be read the way the computer's were — name the line that makes the difference and say what it is for.

English learners

Adding six whole-dollar prices transfers completely and the total of two hundred forty comes out with no English. The language work here is the word parts doing two jobs on one page. On the ledger it names a single amount, the way a bill has a line called tax; on the list it names six separate objects. English lets one plural noun be both a group and a total and marks the difference only by where it sits, which is exactly the ambiguity the lesson turns on, and a learner may reasonably read the ledger line as meaning the parts cost two hundred forty each. The second trap is that add up to and account for both mean the same arithmetic here but neither says add. Rehearse the frame with a finger moving from the list to the ledger line: these six come to ____, and the line says ____, so they are the same. Students may add and check in their strongest language, then say the frame in English touching the list and then the line.

Materials

Computer ledger card, one per pair
Six-parts list card, one per pair
Recording strip with six blank rows, one per student
Pencil per student
Shoe materials sentence card, one per pair
Ordered six-parts strip, largest first, one per student
Ink cartridge ledger card, one per student
Word cards: parts, total, account for

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

4. Four Prices for One Shirt: Reading a Markdown Line Application · Finding successive differences in a falling sequence and comparing each to a fixed amount

The book tells one shirt's price four times over — fifteen, then twelve, then ten, then eight — against a ten the store owes the whole way through. Every number is stated. What the book never does is subtract any of them. Students lay the four prices out in the order the story gives them, find the drop between each neighbouring pair, and then compare each price to the fixed ten to see what would be left. Two of those answers fall below zero, and naming that is the application: the same subtraction that yields a leftover at fifteen dollars yields a shortfall at eight, and the arithmetic does not change when the answer becomes uncomfortable. The book supplies its own ending — the store takes the eight dollars anyway and spends it — so the last step asks students to say why using their own numbers rather than the book's assertion.

Full lesson — 20 minutes

1. Build the price line in the order the book gives it (5 min)
Read the shirt story aloud, stopping at every price. Write each price on a card as you hear it and lay the cards left to right in the order the book says them: fifteen, twelve, ten, eight. Underneath, on a separate card, put the ten the store owes, and keep it out of the line. Say aloud which cards are prices the shopper would see and which one is not.
Word preview: price, owes
A store buys a shirt for $10 and agrees to pay the supplier later. The store has 90 days to sell the shirt so it can pay back the supplier the $10. The store plans to sell the shirt for $15.
The store cuts the price to $12, hoping to have $2 left over. But let’s say that doesn’t work either. After another month, the store drops the price to $10.
2. Find the drop between each pair of neighbours (5 min)
Subtract each price from the one before it and write the drop between the two cards. Do all three. Then read your three drops aloud in order and say whether the price falls by the same amount every time or not. Point at the largest drop.
Word preview: drop, falls
The store cuts the price to $12, hoping to have $2 left over. But let’s say that doesn’t work either. After another month, the store drops the price to $10.
3. Work out what is left at each price (6 min)
For each of the four prices, subtract the ten the store owes and write what would be left. Two of your answers will be less than zero; write those as a loss with the word under and the amount, and say aloud what under means here. Say which price is the first one where nothing is left.
Word preview: left, under, loss
A store buys a shirt for $10 and agrees to pay the supplier later. The store has 90 days to sell the shirt so it can pay back the supplier the $10. The store plans to sell the shirt for $15.
It will sell the shirt for $8—yep, even less than it owes for the shirt. Why? Because this strategy brings in $8. The store can use that $8 to purchase something else and then mark up that item to $12.
4. Say why the store took the last drop anyway (4 min)
Read the last part of the story aloud. Using your own numbers, tell your partner what the store gets at eight dollars and what it does with that money next, naming both amounts from the passage. Then say what the store still owes after selling at eight, using a number you worked out yourself.
Word preview: brings in, mark up
It will sell the shirt for $8—yep, even less than it owes for the shirt. Why? Because this strategy brings in $8. The store can use that $8 to purchase something else and then mark up that item to $12.

Short version — 9 minutes

1. Build the price line in the order the book gives it (4 min)
Read the shirt story aloud, stopping at every price. Write each price on a card and lay the cards left to right in the order the book says them. Keep the ten the store owes on a separate card, out of the line.
Word preview: price, owes
A store buys a shirt for $10 and agrees to pay the supplier later. The store has 90 days to sell the shirt so it can pay back the supplier the $10. The store plans to sell the shirt for $15.
The store cuts the price to $12, hoping to have $2 left over. But let’s say that doesn’t work either. After another month, the store drops the price to $10.
2. Find the drop between each pair of neighbours (5 min)
Subtract each price from the one before it and write the drop between the two cards. Read your three drops aloud in order, say whether the price falls by the same amount each time, and point at the largest drop.
Word preview: drop, falls
The store cuts the price to $12, hoping to have $2 left over. But let’s say that doesn’t work either. After another month, the store drops the price to $10.

Three levels

Support: Lay out the four price cards and find the three drops, which are three, two and two, all within ten and all on whole dollars. For the leftover work, stop at the first two prices only, where fifteen and twelve both leave something above the ten, so every answer is a positive amount. The two prices that fall below the ten are read aloud together as a class rather than computed alone, and the word under is supplied with the sentence around it.
At Grade: Order the four prices, find the three drops and say whether they are equal, subtract the ten owed from each of the four prices, name the two that fall short and say what under means, and then explain in your own numbers why the store sold at eight anyway.
Extension: The book stops at eight dollars and one replacement item marked up to twelve. Carry it further with the book's own rule. If the store buys a second item with the eight dollars and marks it up to twelve, work out what the store has after that sale and whether the ten is settled. Then say what would have to be true of the second item for this to fail, and give the price at which it would fail, defending your figure from the numbers in the story rather than from a guess.

English learners

Ordering four prices and finding three drops transfers completely and needs no English. The hard language here is that this book uses at least four different expressions for the same subtraction and a learner has to hear them as one idea: cuts the price to, drops the price to, what's left, and less than it owes. The one that misleads most is drops the price to twelve, because to names the arrival and not the amount removed, so a learner may write twelve as the drop where three belongs. The second trap is that owes is a debt in one direction only and English does not mark that direction on the verb. Rehearse the frame with a finger travelling between two neighbouring cards: it went from ____ to ____, so it dropped by ____. Students may order, subtract and decide in their strongest language, then say the frame in English touching the two cards and the slip between them.

Materials

Price cards, blank, five per pair
Marker per pair
Drop slips, three per pair
Left-over recording sheet with four price rows, one per student
Pencil per student
Positive-only leftover strip with two price rows, one per student
Continuation sheet with a blank second-item row, one per student
Word cards: drop, owes, left

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

5. One Piece Out of Ten: What the Cashier Adds Representation · Finding one tenth of a whole-dollar amount and reading it as ten percent

The book states a ten percent tax on a thirty dollar hat and gives the answer, three dollars, without showing a single step. Students build the step the book skipped, and they build it as a physical cut rather than a rule: a strip marked in thirty single dollars folded and cut into ten equal pieces, one piece counted. The representation is the whole lesson — ten percent is one piece out of ten, and on this strip that piece holds three dollars. Only once the cut has been made and counted do students take one tenth of a price the book never taxes, so the method has to travel. The final step sets the tax sentence beside the bank's one percent sentence to establish that a percent always acts on a stated amount, and that the same operation can add to what you owe or add to what you hold.

Full lesson — 20 minutes

1. Find the sentence where the price on the tag is not the price you pay (4 min)
Read the cap passage aloud and find the sentence that says the number on the tag changed at the till. Say the two amounts in that sentence to your partner: the price and the tax. Then say the third number, the one the shopper actually hands over, which the book does not print. Write all three on your strip.
Word preview: tax, tag
Did you notice that the price on the cap, or on those back-to-school jeans, got higher when the cashier rang up the sale? Why? Taxes.
Let’s say there’s a 10% sales tax on the $30 hat. That means you pay an additional $3 in tax.
2. Cut a thirty into ten equal parts and take one (6 min)
Fold and cut a paper strip marked in thirty single dollars into ten equal pieces, checking that each piece carries the same number of dollars before you cut. Count what is on one piece. Say aloud that one piece out of ten is what ten percent means, and that on this strip one piece is three dollars, which is the number the book printed.
Word preview: ten percent, equal parts
Let’s say there’s a 10% sales tax on the $30 hat. That means you pay an additional $3 in tax.
3. Take one tenth of a price the book never taxes (6 min)
Take the cap's last line, one dollar twenty, and the jeans price of forty dollars. Find one tenth of the forty using your strip method or by dividing, and write it. Then say aloud what the shopper would hand over for the jeans at the same tax rate. Say which of your two numbers came from the book and which is yours.
Word preview: one tenth, rate
BASEBALL CAP: $30.00 Less: Fabric, cardboard, thread: $2.00 Labor: 0.40 Equipment, storage, gas: 8.00 Designer’s fee: 2.00 Logo rights: 5.00 Profit to manufacturer: 1.40 Store costs (wages, rent, etc.): 10.00 What’s left: $1.20
4. Read a second percent sentence and say what is different (4 min)
Read the bank passage aloud. Find the percent, the amount it acts on, and the answer, and say all three to your partner. Then say aloud what makes this one different from the tax: the tax was added to what you pay, and this one was added to what you already had. Point at the word in each passage that told you which.
Word preview: percent, earn
Suppose the bank pays you 1% interest per year. If you put $100 in your bank account for one year, you would earn $1 from the bank for letting it use your money during that time.

Short version — 9 minutes

1. Find the sentence where the price on the tag is not the price you pay (4 min)
Read the cap passage aloud and find the sentence saying the number on the tag changed at the till. Say the price and the tax aloud, then say the third number the book does not print, and write all three on your strip.
Word preview: tax, tag
Did you notice that the price on the cap, or on those back-to-school jeans, got higher when the cashier rang up the sale? Why? Taxes.
Let’s say there’s a 10% sales tax on the $30 hat. That means you pay an additional $3 in tax.
2. Cut a thirty into ten equal parts and take one (5 min)
Fold and cut a strip marked in thirty single dollars into ten equal pieces, checking each carries the same number of dollars first. Count one piece and say aloud that one piece out of ten is ten percent, and that here it is the three dollars the book printed.
Word preview: ten percent, equal parts
Let’s say there’s a 10% sales tax on the $30 hat. That means you pay an additional $3 in tax.

Three levels

Support: Cut the thirty-dollar strip into ten pieces with the fold lines already printed, so the equal-parts check is a matter of confirming the marks rather than establishing them. Count one piece, say what it holds, and set it against the book's three dollars. The second price is twenty dollars rather than forty, so the tenth is a whole two dollars and the strip can be cut again the same way instead of divided on paper.
At Grade: Name the three amounts in the tax sentence including the one the book does not print, cut the thirty-dollar strip into ten equal pieces and count one, take one tenth of the forty-dollar jeans price and say what a shopper would hand over, then read the bank sentence and say what a percent acts on in each case.
Extension: Your strip gives one tenth by cutting. Now use it to reach a rate it was not cut for. The book prices a fancy chocolate bar at two dollars and a hot chocolate at four. Using tenths you can count, find five percent of one of them and say what you did to the tenth to get there, and say why that move works. Then find a price in this book where a ten percent tax would not come out in whole cents, name it, and say what the cashier would have to do.

English learners

Cutting a strip into ten equal pieces and counting one transfers completely and a learner reaches three dollars with no English. The language work is the word percent, and the trap is specific: English says ten percent of thirty with of, which everywhere else in mathematics class signals multiplying and here signals a piece being taken, and a learner who reads it as a multiplication will look for a bigger number. Many languages mark this differently or word the rate before the amount. The second trap is that tax is added and interest is earned, and both are described as what you get, though one leaves your hand and one arrives in it. Rehearse the frame with a finger on the cut pieces: ten percent of ____ is ____, because one piece out of ten holds ____. Students may cut, count and compute in their strongest language, then say the frame in English touching the whole strip and then the one piece.

Materials

Three-box strip labelled price, tax, paid, one per student
Pencil per student
Dollar strip marked in thirty single dollars, one per student
Scissors, one pair per two students
Blank tenths strip, one per student
Percent sentence card, bank passage, one per pair
Pre-marked ten-fold strip, one per student
Twenty-dollar strip, one per student
Chocolate bar and hot chocolate ledger cards, one per student
Word cards: percent, tenth, tax

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

Math through the reading

The mathematics is reached through a sentence the book prints: change one word in the reading and the numbers change with it. These carry their own standards, matched against these lessons rather than inherited from the skill ones.

6. The Word That Tells You to Subtract Integrated · Students find the one word that turns a column of prices into a subtraction, swap it for its opposite, and show the table stops balancing while every digit stays the same.

Students find the one word that turns a column of prices into a subtraction, swap it for its opposite, and show the table stops balancing while every digit stays the same.

Full lesson — 20 minutes

1. Hunt for the instruction in a table with no signs (5 min)
Read the pencil table aloud line by line with a partner. Look for a plus, a minus or an equals sign anywhere on the card and say aloud that there is none. Then find the one word that tells you what to do with the three cost lines, put a finger on it, and say to your partner what it is ordering you to do.
2. Work the table the way the word says (5 min)
Add the three cost lines and write the total. Subtract it from the fifteen cents on the top line and write your answer beside the book's last line. Say aloud whether they agree.
3. Swap the word and work the table again (6 min)
Lift the word strip off the operation line and lay the Plus strip in its place. Change no digit anywhere. Work the table again exactly as the new word instructs and write the new answer under your first one. Subtract the smaller from the larger and circle the gap. Say aloud whether the book's printed last line is still true.
4. Say what the word was doing (4 min)
Tell your partner, in one sentence, what changed and what did not: name the word, say which operation it called for, and give both answers. Then write that sentence. Your partner checks that your sentence carries two numbers and the name of the word.

Short version — 9 minutes

1. Hunt for the instruction in a table with no signs (5 min)
Read the pencil table aloud line by line with a partner. Look for a plus, a minus or an equals sign anywhere on the card and say aloud that there is none. Then find the one word that tells you what to do with the three cost lines, put a finger on it, and say to your partner what it is ordering you to do.
2. Swap the word and work the table again (6 min)
Lift the word strip off the operation line and lay the Plus strip in its place. Change no digit anywhere. Work the table again exactly as the new word instructs and write the new answer under your first one. Subtract the smaller from the larger and circle the gap. Say aloud whether the book's printed last line is still true.

Three levels

Support: Stay on the pencil table, whose three cost lines are one cent each, so both totals are found by counting on and the two answers are twelve cents and eighteen cents. The word strip is a two-sided card so the swap is a flip rather than a search. The final sentence is spoken with a finger travelling from the word to the first answer to the second, using the frame supplied aloud, and written only if there is time.
At grade: Find the operation word in the pencil table, work the table as it instructs, swap the word for its opposite, work the table again without altering a digit, find the gap between the two answers, and write one sentence naming the word, the operation and both results.
Extension: You showed the word carries the instruction on a three-line table. Now find where that stops being enough. Take the backpack table, which has six cost lines and a sentence after it that mentions two more amounts, seventeen and eighteen dollars, that appear nowhere in the column. Work the table under Less as usual, then say what the word cannot tell you: which cost lines the seventeen is made of, and where the eighteen comes from. Name one more word the book would need to print on the card for a reader to find those two numbers without the paragraph.

English learners

Adding a column and subtracting a total transfers completely, and a learner produces twelve cents and eighteen cents with no English at all. The whole difficulty here is that this lesson's register words are all common English words wearing a second meaning, which is harder than a new technical term would be, because nothing signals that the familiar meaning is wrong. Less is the sharpest case: every learner meets it first as a comparison word, smaller in amount, and that meaning fits the pencil table plausibly enough to be read straight past — three small costs, all less than the price. The word is being used as a command here, and English does not mark that anywhere. What's left has the opposite problem, since its everyday sense of scraps carries a judgement the mathematical sense does not, and bottom line is an idiom in ordinary speech before it is a position in a column. Rehearse the operation word alone, three times, with a hand sweeping down the cost lines and then away from the card: Less means take all of these away. Then rehearse the whole frame with a finger on each answer in turn: with ____ the answer is ____, with ____ the answer is ____. Students may add, subtract and decide in their strongest language, and say the frame in English pointing at the word and then at the two answers it produced.

Materials

Pencil ledger card with the operation line left blank, one per pair
Word strips reading Less and Plus, one pair of strips per pair of students
Two-answer recording slip, one per student
Pencil per student
The pencil table enlarged with its operation line covered, kept up for the whole lesson
The sentence about price minus the cost of materials, with the words that follow it shown only after segment three

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

7. Four Prices, One Debt: Telling the Shirt's Story in Order Integrated · Students order the shirt's seven events, compute the gap between price and debt at each stage, and retell the story so that every step names the number it changed.

Students order the shirt's seven events, compute the gap between price and debt at each stage, and retell the story so that every step names the number it changed.

Full lesson — 20 minutes

1. Put the seven events in the order the book tells them (5 min)
Take the seven event cards face down and shuffled. Read the shirt paragraph aloud with your partner, and each time you hear an event, find its card and lay it next in the line, left to right. When all seven are down, read your line back against the paragraph and move any card that is out of place.
2. Write the gap under every price (6 min)
Four of your cards carry a price. Under each one, write what is left after the ten the store owes is taken away. Two of your four answers will be below zero; write those as short by and the amount. Read your four gaps aloud in order.
3. Find the card that cannot move (5 min)
Look at your four gaps and find the one that is neither left over nor short. Put a finger on that card. Try moving it one place earlier and say aloud what goes wrong with the numbers, then try moving it one place later and say what goes wrong then. Leave it where the book put it.
4. Retell it so every step carries its number (4 min)
Tell the whole story to your partner from your card line, using first, then, after that and finally, and naming the amount at every step. Your partner follows along the cards and stops you at any step where you say what happened without saying the number.

Short version — 9 minutes

1. Put the seven events in the order the book tells them (5 min)
Take the seven event cards face down and shuffled. Read the shirt paragraph aloud with your partner, and each time you hear an event, find its card and lay it next in the line, left to right. When all seven are down, read your line back against the paragraph and move any card that is out of place.
2. Write the gap under every price (6 min)
Four of your cards carry a price. Under each one, write what is left after the ten the store owes is taken away. Two of your four answers will be below zero; write those as short by and the amount. Read your four gaps aloud in order.

Three levels

Support: Work with five cards rather than seven, dropping the ninety-day card and the replacement-item card, so the line is the four prices and the opening purchase. The gaps are written only for fifteen and twelve, where both answers are above zero, and the ten and the eight are placed on the line and read aloud together as a class. The retelling is spoken one card at a time with the connective supplied on the card itself, so the student produces the event and the number and the card produces the joining word.
At grade: Order all seven event cards from the paragraph, write the gap under each of the four price cards including the two that fall short, identify the card where the gap is exactly zero and say what breaks if it moves either way, and retell the whole sequence aloud with a connective and an amount at every step.
Extension: Your line ends with a second item priced at twelve. Carry the story one step further with the book's own rule and say whether the debt is settled, giving the number. Then build a version that fails: keep the same opening purchase and the same debt, and choose four prices of your own that make the store's final decision unreasonable rather than reasonable. Say which of your prices does it and why, and be ready to defend that the store in your version would not have dropped as far as it did.

English learners

Ordering cards and subtracting ten from each price transfers completely, and a learner produces all four gaps with no English. The language work is sequencing and it carries two real traps here. English marks order with words that sit outside the clause — first, then, after that, finally — and also with tense inside the verb, and this paragraph uses both at once, so a learner who tracks only the connectives will miss that but no one buys it and let's say that doesn't work either are each marking a passage of time with no connective attached. The second trap is the word for the pivot: the store drops the price to ten, and to names where the price arrived, while by would name how far it fell. Learners routinely produce dropped by ten for this, which is a different and much larger fall. Rehearse two frames with a finger moving between neighbouring cards: first the store ____, then the store ____. And separately: it went to ____, so it dropped by ____. This lesson's spoken retelling is the assessment, so learners tell it from the card line with the connectives available on a strip, and may plan the telling in their strongest language before speaking it in English.

Materials

Seven event cards, one set per pair
Gap slips, four per pair
Connective strip reading first, then, after that, finally, one per student
Pencil per student
The shirt paragraph enlarged, kept up for the whole lesson
A blank seven-place line drawn where every pair can see it, filled in together only after all pairs have laid their own

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

8. The Number the Cashier Says Integrated · The book prints the price and prints the tax and never adds them; students find the total the shopper actually pays and prove it is the only answer the page allows.

The book prints the price and prints the tax and never adds them; students find the total the shopper actually pays and prove it is the only answer the page allows.

Full lesson — 20 minutes

1. Find the question the book asks and refuses to answer (4 min)
Read the cap passage aloud with a partner. Find the sentence where the book asks you a question and the word it gives as the answer. Say aloud whether that word is a number. Then hunt the whole passage for the amount the shopper handed over and say aloud that it is not there.
2. Underline the word that decides which way to go (5 min)
Write the two amounts the book does give into the first two boxes on your strip. Now find the one word in that sentence telling you whether the tax joins the price or comes out of it, and underline it. Tell your partner what the answer would be if that word meant the other thing, and say both numbers aloud.
3. Add the two amounts and say the number out loud (5 min)
Fill the third box on your strip. Say the sentence aloud to your partner with all three numbers in it: the tag said ____, the tax was ____, so the shopper handed over ____. Then write that sentence.
4. Do it again where the book gives you less (6 min)
Take the jeans price of forty dollars. The book gives no tax amount for it, only the same rate. Cut a forty-dollar strip into ten equal pieces, count one piece, and write it as the tax in the second box of a new strip. Then fill the third box. Say aloud which of your two totals the book could have printed and which one it never came close to.

Short version — 9 minutes

1. Find the question the book asks and refuses to answer (4 min)
Read the cap passage aloud with a partner. Find the sentence where the book asks you a question and the word it gives as the answer. Say aloud whether that word is a number. Then hunt the whole passage for the amount the shopper handed over and say aloud that it is not there.
2. Add the two amounts and say the number out loud (5 min)
Fill the third box on your strip. Say the sentence aloud to your partner with all three numbers in it: the tag said ____, the tax was ____, so the shopper handed over ____. Then write that sentence.

Three levels

Support: Work the cap alone, where both amounts are printed and the arithmetic is thirty plus three. The three-box strip arrives with the first two boxes already carrying their labels and a place value line under the third. The word additional is circled on the passage rather than hunted for, and the student's job is to say what it tells you to do and then do it. The sentence in the third segment is spoken with the frame supplied aloud and a finger on each box, and written only if there is time.
At grade: Find the question the book leaves unanswered in numbers, underline the word that fixes the operation and say what the other reading would give, add the tax to the price and write the total in a sentence naming all three amounts, then repeat the whole thing on the jeans where the tax must be found before it can be added.
Extension: You found a total the book never prints. Now find the price where the method needs care. Hunt this book for a marked price whose ten percent tax would not come out in whole cents, name the price and the tax it would carry, and say what the cashier would have to do with the extra part of a cent. Then take the cap's last line of one dollar twenty and say whether the tax the shopper paid is larger or smaller than everything the store had left, giving both numbers, and say what that comparison shows about who receives the most from a thirty-dollar sale.

English learners

Adding thirty and three transfers completely and needs no English at all. Everything difficult in this lesson is in one word, and it is worth naming precisely. Additional is a Latin-rooted formal word a fourth grader may never have met, and its everyday paraphrase in this sentence would be more, which is a comparison word. A learner who substitutes more reads the sentence as saying the price is more, which is true and useless, and the instruction to add disappears. Worse, the surrounding sentences are all about the price going higher, so the wrong reading is supported by context. The second trap is that tax is a noun here and pay is the verb, while many languages express the whole thing with one verb, so learners produce you tax three dollars and lose track of which amount moves. Rehearse the word alone against a hand gesture of joining, three times, before any arithmetic. Then rehearse the frame with a finger on each of the three boxes in turn: the tag said ____, the tax was ____, so you hand over ____. This lesson's evidence is written, so learners may say the frame aloud until it is fluent and copy it into the written sentence, and may reason about the operation in their strongest language first.

Materials

Three-box strip labelled price, tax, paid, two per student
Cap passage card with the tax sentence printed whole, one per pair
Dollar strip marked in forty single dollars, one per student
Scissors, one pair per two students
Pencil per student
The cashier question and the tax sentence enlarged side by side, kept up for the whole lesson
A blank three-box strip drawn large, filled in only after every pair has filled their own

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

9. Would You Pay the Extra Forty? Integrated · Students match two identical cost columns, compute the forty-dollar gap twice, and argue aloud to the shopper the book addresses about whether that gap is worth paying.

Students match two identical cost columns, compute the forty-dollar gap twice, and argue aloud to the shopper the book addresses about whether that gap is worth paying.

Full lesson — 20 minutes

1. Join every line that matches (6 min)
Lay the two ledger cards side by side with the cost lines level. Read each pair of cost lines aloud together and draw a joining line wherever the two amounts are the same. Count your joining lines and say the number aloud. Then name the two lines you did not join.
2. Find the gap twice (5 min)
Subtract the smaller price from the larger and write it on the top row of your strip. Subtract the smaller leftover from the larger and write it on the bottom row. Read both rows aloud and say whether they are the same number and why that is surprising.
3. Decide what the extra forty buys (4 min)
Look at the six joined lines and say aloud, to your partner, everything the forty dollars did not go to, naming three of them with their amounts. Then say what is left for it to have gone to, using the words the book uses. Choose the position you will argue.
4. Argue it to the shopper with a number in it (5 min)
Your partner is the shopper standing in front of both pairs. Tell them which pair to buy and why, naming one number from your strip and saying what that number is the difference between. Then swap and listen to a partner who chose differently, and afterwards say aloud which number they used.

Short version — 9 minutes

1. Join every line that matches (6 min)
Lay the two ledger cards side by side with the cost lines level. Read each pair of cost lines aloud together and draw a joining line wherever the two amounts are the same. Count your joining lines and say the number aloud. Then name the two lines you did not join.
2. Argue it to the shopper with a number in it (5 min)
Your partner is the shopper standing in front of both pairs. Tell them which pair to buy and why, naming one number from your strip and saying what that number is the difference between. Then swap and listen to a partner who chose differently, and afterwards say aloud which number they used.

Three levels

Support: Work with the two ledgers printed on a single shared grid so matching cost lines already sit in the same row and the joining is a matter of confirming rather than aligning. Both subtractions are set out as written number sentences with the two amounts filled in, eighty take away forty and fifty-three take away thirteen, so the arithmetic is the taking away and not the setting up. The spoken position is given as a frame with the first blank filled and a hand resting on the strip row that supplies the second.
At grade: Match the two cost columns line by line and count the matches, subtract both unmatched pairs and notice the two differences agree, name what the extra forty dollars did not buy using amounts from the joined lines, and argue a position aloud to the shopper naming a number you computed and saying what it is the difference between.
Extension: Your case rests on six lines being identical. Test how much weight that carries. The book says a worker assembling these jeans is paid about three cents a pair, and both ledgers charge one dollar for other manufacturing costs. Say what fraction of a single joined line the worker's share could be, in words rather than in symbols, and whether your position survives knowing it. Then argue the position you did not choose, using a real number from your own strip, and say what would have to be different about one of the six joined lines for that position to become the stronger one.

English learners

Matching columns and subtracting twice transfers completely, and a learner reaches forty both times with no English. The language work here is argument, and this book's version of it has a particular difficulty: the strongest evidence is an absence — six lines that are the same — and English states absences awkwardly, with negatives stacked up, as in the extra money does not go to any of them. A learner may produce the positive form and be heard as arguing the opposite of what they mean. The second trap is that worth it is an idiom carrying no arithmetic at all while sounding like it does, and a learner who reaches for it may find they have said nothing checkable, which is exactly what the specification refuses. Rehearse the frame twice with a finger travelling from the joined lines to the strip: I would buy the ____ pair, because the extra ____ does not go to ____. Students may compare, subtract and decide in their strongest language, then say the frame in English touching the joined lines and then the row of the strip that carries their number.

Materials

Regular jeans and designer jeans ledger cards, one pair per two students
Two-row difference strip labelled price and leftover, one per pair
Position frame card, one per student
Pencil per student
Both ledgers enlarged side by side with the cost lines level, kept up for the whole lesson
The two sentences about being a smarter consumer and appreciating a thing more, shown together only at segment three

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

10. Twice as Much, Half as Much: Saying the Jeans Both Ways Integrated · Students build two bar strips for the two jean prices, discover the longer folds exactly onto the shorter, and say the relation in both directions using words the book never uses.

Students build two bar strips for the two jean prices, discover the longer folds exactly onto the shorter, and say the relation in both directions using words the book never uses.

Full lesson — 20 minutes

1. Build the two prices as strips (5 min)
Take the two jeans cards and read the top line of each aloud. Build a strip of ten-dollar units for each price, laying them on the shared baseline so both start at the same edge. Count the units on each strip aloud and say which is longer.
2. Fold one onto the other and say what you found (6 min)
Fold the longer strip in half and lay it against the shorter one. Check that it covers exactly, with nothing sticking out and no gap. Say aloud what you have shown. Then unfold, lay the shorter strip along the longer, and say how many units are left standing and what they are worth.
3. Say it both ways round (5 min)
Say the relation to your partner starting with the designer jeans, using a doubling word. Then say the same relation starting with the regular jeans, which will need a different word. Do it again using the difference instead of the doubling. Your partner checks each sentence against the strips and stops you if a sentence is true of a different pair of strips than the ones on the desk.
4. Try the same two moves on the leftovers (4 min)
Build strips for thirteen dollars and fifty-three dollars from the last lines of the same two cards, using single-dollar units. Fold and check as before. Say aloud whether the doubling sentence still works for this pair, and if it does not, say which of your two sentence types still does.

Short version — 9 minutes

1. Build the two prices as strips (5 min)
Take the two jeans cards and read the top line of each aloud. Build a strip of ten-dollar units for each price, laying them on the shared baseline so both start at the same edge. Count the units on each strip aloud and say which is longer.
2. Fold one onto the other and say what you found (6 min)
Fold the longer strip in half and lay it against the shorter one. Check that it covers exactly, with nothing sticking out and no gap. Say aloud what you have shown. Then unfold, lay the shorter strip along the longer, and say how many units are left standing and what they are worth.

Three levels

Support: Build both price strips from ten-dollar units only, four and eight, so the fold is a count of units rather than a measurement, and do the fold with the two strips already on the shared baseline. Say the two doubling sentences first, one in each direction, with the frame supplied aloud and a hand on the strip named first. The leftover pair is set aside and the difference sentences are said about the prices instead, where the answer is a whole four units.
At grade: Build both price strips, fold the longer onto the shorter and confirm it covers exactly twice, find the difference from the units left standing, say the relation in both directions with a doubling word and again with a difference word, then build the two leftover strips and say which of your sentence types survives and which does not.
Extension: You found one pair where doubling works and one where it does not. Now find where it works in this book that nobody set up. Take the earrings prices, eight dollars and a thousand, and say why a fold cannot settle that pair and what you would have to count instead. Then find a pair anywhere in these tables that is close to doubling but not exactly, name both amounts and say how far off it is, and say which of your sentence types you can still say truthfully about it and which you cannot.

English learners

Building strips, folding and counting transfers completely, and a learner establishes the doubling with no English. The language is the entire difficulty and it is worth being exact about which part. English marks the direction of a comparison in three separate places at once — the order of the two things, the comparative word, and the little word than — and a learner may reverse one without reversing the others, producing regular jeans cost twice as much as designer jeans while pointing correctly at the strips. The sentence is then heard as a mathematical error when it is a word-order error. The second trap is that half is a noun elsewhere in this book and a comparison word here, and twice has no everyday meaning at all for a learner to fall back on. Rehearse both directions as a pair, always together and always with a hand moving from the strip named first to the strip named second: ____ costs twice as much as ____, and ____ costs half as much as ____. This lesson's evidence is spoken, so learners may fold, count and decide in their strongest language and then say both sentences in English with a hand on each strip in turn.

Materials

Regular jeans and designer jeans ledger cards, one pair per two students
Ten-dollar unit strips, twelve per pair
Single-dollar unit strips, seventy per pair
Shared baseline card, one per pair
Sentence frame card with both directions printed, one per student
The two jeans tables enlarged with their top lines and last lines highlighted
One pair of built strips shown folded, displayed only after every pair has folded their own

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

Reading and language lessons

5 lessons on the reading and language the book carries - what a word means in its sentence, how a character is shown, how a text is built. No mathematics: these are matched against the English language arts curricula, which are a different and smaller set than the mathematics ones.

11. Who the book thinks you are Author's craft · Identifying who a text speaks to and what it assumes about them

Almost every section of this book opens by grabbing the reader — waking them up, shouting past their headphones, telling them their pocket is buzzing. Each opening smuggles in an assumption about who is reading. Students mark the address, name the assumptions and quote what carries them, strip the address out of one opening to see what it was doing, and find the one place the book starts without it.

Full lesson — 20 minutes

1. Circle every word aimed at the reader (5 min)
Read these two openings aloud. Circle every you, your and I in them. Say who the author means by you, and say what the author is pretending is happening in each one.
Word preview: address
Wake up, sleepyhead, it’s time for breakfast! What better place to start exploring the money web than at the beginning of your day?
Hey! Hey, you! Yes ... I’M TALKING TO YOU! Oh, sorry. I guess you didn’t hear me. I didn’t see your headphones.
2. Say what the author has decided about the reader (5 min)
These openings assume things about you before you have said a word. Read them and list, in your notebook, three things the author has decided is true about the reader — where they are, what they own, what time of day it is. Quote the words that carry each assumption.
Word preview: assume
Your butt is buzzing. Yes, it’s the sound of the cell phone, an everyday (every minute?) part of life.
Shoes aren’t just great for your feet, they also tell us a lot about the money web. Yes, a lot more goes into shoes than your smelly old socks! Let’s say you paid 65 bucks for a good pair of leather running shoes.
3. Rewrite one opening with the reader removed (5 min)
Take one of these openings and rewrite it in your notebook without any you or your, saying the same information about the world. Read both versions aloud. Say what your version gains and what it loses.
Word preview: rewrite
Your butt is buzzing. Yes, it’s the sound of the cell phone, an everyday (every minute?) part of life.
4. Find the one opening that drops the you (5 min)
Here is how the whole book begins. Read it aloud and say whether it talks to a reader the way the section openings do. Then read the line that ends the same opening and say exactly where the author switches into talking straight to you.
Word preview: switch
Money. Money. Money. Everybody wants it. Some people have a lot of it. Most don’t have enough.
So where does your money go? Turn the page and find out.

Short version — 9 minutes

1. Circle every word aimed at the reader (5 min)
Read these two openings aloud and circle every you, your and I. Say who the author means by you and what the author is pretending is happening.
Word preview: address
Wake up, sleepyhead, it’s time for breakfast! What better place to start exploring the money web than at the beginning of your day?
Hey! Hey, you! Yes ... I’M TALKING TO YOU! Oh, sorry. I guess you didn’t hear me. I didn’t see your headphones.
2. Say what the author has decided about the reader (4 min)
These openings assume things before you have said a word. Name three things the author has decided is true about the reader, and quote the words carrying each.
Word preview: assume
Your butt is buzzing. Yes, it’s the sound of the cell phone, an everyday (every minute?) part of life.
Shoes aren’t just great for your feet, they also tell us a lot about the money web. Yes, a lot more goes into shoes than your smelly old socks! Let’s say you paid 65 bucks for a good pair of leather running shoes.

Three levels

Support: Work with the breakfast opening only. Circle each you and your, then answer one question aloud: does the book think the reader is a grown-up or a kid, and which word told you?
At Grade: Mark the address in both openings, name three assumptions the book makes about its reader, and quote the words that carry each.
Extension: The cell phone opening assumes the reader owns a phone that somebody else pays for. Say who that assumption leaves out, and say whether the section still works for a reader it does not describe.

English learners

Second-person address is not the neutral choice in every written tradition and can read as intrusive rather than friendly. Say plainly that English popular non-fiction for young readers does this deliberately, to make the reader a character. Rehearse the naming frame aloud: The book assumes I ___. I know because it says ___.

Materials

Both printed section openings
Pencil
Notebook
Printed cell phone opening
Printed book opening
Printed turn-the-page line
Word cards: address, assume, rewrite, switch

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

12. Where the book stops to explain Text features · Recognising how an informational text defines a term as it goes

This book never sends a reader to a glossary; it defines each term in the sentence where the term is first needed, and it marks the term four different ways — quotation marks, brackets, a plain is sentence, and a whole two-sentence aside on where a phrase came from. Students take the definitions apart, compare the markings, and then write one in the book's own pattern.

Full lesson — 20 minutes

1. Find the two things a definition sentence does (5 min)
Read these two definitions aloud. Each does the same two jobs: it names the term and it says what the term means. Underline the term in each and bracket the part that supplies the meaning. Say aloud which comes first in each sentence.
Word preview: definition
Anything left over after paying all the costs of that product or service is called “profit.”
The minimum wage is set by the government, and is the lowest amount an employer can legally pay someone for work.
2. Compare three ways of marking a term (5 min)
These three definitions mark the term differently: one puts it in quotation marks, one tucks the meaning inside brackets, one just states it. Read each aloud and say how the term is marked. Then say which marking makes the definition easiest to spot while reading fast.
Word preview: marked
Sometimes stores sell something too cheap on purpose. This is called a “loss leader.”
Possible pecuniary penalties! (Pecuniary means “relating to money,” by the way.)
Indentured workers are people who work for a specific number of years in exchange for food, clothing, transportation, and shelter—but no cash. After those years, they are free to go.
3. Read a definition that explains where a phrase came from (5 min)
This one does something extra: it says not just what the phrase means but where it came from. Read it aloud, then say which sentence gives the meaning and which gives the origin. Say why a reader might want both.
Word preview: origin
We use the phrase “the bottom line” a lot, but what the heck does it mean? It comes from the world of math. When you add, subtract, or multiply a stack of numbers, the result is at the bottom of the stack.
4. Write the definition this passage is missing (5 min)
This passage uses a term without stopping to define it. Read it and pick the word a reader might not know. Then write a one-sentence definition for it in the pattern the book uses, marking your term the way one of the book's definitions marks its own.
Word preview: pattern
A tip is an optional way of saying “thank you.” Many people who work serving food are paid minimum wage, so a tip tops up the worker’s pay to a better level.
The minimum wage is set by the government, and is the lowest amount an employer can legally pay someone for work.

Short version — 9 minutes

1. Find the two things a definition sentence does (5 min)
Read these two definitions aloud. Underline the term in each and bracket the part supplying the meaning. Say which comes first in each.
Word preview: definition
Anything left over after paying all the costs of that product or service is called “profit.”
The minimum wage is set by the government, and is the lowest amount an employer can legally pay someone for work.
2. Compare three ways of marking a term (4 min)
These three definitions mark the term differently. Say how each is marked, and say which marking is easiest to spot while reading fast.
Word preview: marked
Sometimes stores sell something too cheap on purpose. This is called a “loss leader.”
Possible pecuniary penalties! (Pecuniary means “relating to money,” by the way.)
Indentured workers are people who work for a specific number of years in exchange for food, clothing, transportation, and shelter—but no cash. After those years, they are free to go.

Three levels

Support: Use the profit definition and the minimum wage definition only. For each, the student points to the term and then reads aloud only the part that says what it means. Two pointings and two readings complete the task.
At Grade: Take apart all the printed definitions, name how each marks its term, and write one definition of your own in the book's pattern.
Extension: The bottom line entry spends two sentences on where the phrase came from before it ever says what it means today. Say what a reader gains from the detour, and say whether the entry would be clearer if the two sentences were swapped.

English learners

Definition sentences are the highest-value structure in this book for a student reading in a second language: once the pattern is visible, unknown terms stop being obstacles. Teach the signals explicitly — is called, means, is, quotation marks, brackets. Rehearse aloud: The term is ___. It means ___. Students may give the meaning in their strongest language first.

Materials

Both printed definitions
Pencil
All three printed definitions
Printed bottom line definition
Printed tip passage
Printed minimum wage definition
Notebook
Word cards: definition, marked, origin, pattern

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

13. One link in the chain Text structure · Following a numbered sequence and retelling it in order

The shoe section is the only place in this book that numbers its steps, and it supplies its own name for the structure: a chain, with each stage a link. Students read the first link and two late ones, name what each hands to the next, circle the sequence words that hold the order together, and retell the chain aloud in their own sentences. The reading work is order and hand-off, not arithmetic.

Full lesson — 20 minutes

1. Read the first link and say what it hands on (5 min)
Read this numbered step aloud. Say who is doing something, what they end up with, and who receives it. The last sentence names what the whole passage is part of; read that sentence again and say the word it uses for one part of it.
Word preview: link
1 Farmers raise cows for milk or meat. When the cows are slaughtered, the skins can be sold to a tannery for about $1 per skin. The tannery is one link in the chain from raw material to finished shoes.
2. Read two later links and name what repeats (5 min)
Read these two numbered steps aloud. Say what both of them do to the price, using the word each passage itself uses. Then say what is different about the second one, quoting the words that mark the difference.
Word preview: again
6 Viking then sells the shoes to a retailer—a shoe store or department store—for about $32 per pair. So Viking has doubled the price, adding another $16 on top of the cost of making and shipping the pair of shoes.
7 The retailer then doubles the price again, and adds a touch extra … selling the shoes at $65. So the retailer raises the price $33 per pair, but the retailer also has to pay their costs out of that.
3. Find the words that hold the chain in order (5 min)
Read all three numbered steps in front of you. Besides the numbers, the author uses words that put the steps in sequence: then, so, again. Circle every such word and say which of them could be removed without a reader losing the order.
Word preview: sequence
1 Farmers raise cows for milk or meat. When the cows are slaughtered, the skins can be sold to a tannery for about $1 per skin. The tannery is one link in the chain from raw material to finished shoes.
6 Viking then sells the shoes to a retailer—a shoe store or department store—for about $32 per pair. So Viking has doubled the price, adding another $16 on top of the cost of making and shipping the pair of shoes.
7 The retailer then doubles the price again, and adds a touch extra … selling the shoes at $65. So the retailer raises the price $33 per pair, but the retailer also has to pay their costs out of that.
4. Retell the chain in your own sentences (5 min)
Using only the printed steps in front of you, retell the chain aloud to a partner in three sentences, each beginning with First, Then or Finally. Name at each stage who has the shoes and who has just been paid. Your partner checks your order against the numbers on the page.
Word preview: retell
1 Farmers raise cows for milk or meat. When the cows are slaughtered, the skins can be sold to a tannery for about $1 per skin. The tannery is one link in the chain from raw material to finished shoes.
7 The retailer then doubles the price again, and adds a touch extra … selling the shoes at $65. So the retailer raises the price $33 per pair, but the retailer also has to pay their costs out of that.

Short version — 9 minutes

1. Read the first link and say what it hands on (4 min)
Read this numbered step aloud. Say who is doing something, what they end up with, and who receives it.
Word preview: link
1 Farmers raise cows for milk or meat. When the cows are slaughtered, the skins can be sold to a tannery for about $1 per skin. The tannery is one link in the chain from raw material to finished shoes.
2. Read two later links and name what repeats (5 min)
Read these two numbered steps aloud. Say what both do to the price, using each passage's own word, and say what is different about the second.
Word preview: again
6 Viking then sells the shoes to a retailer—a shoe store or department store—for about $32 per pair. So Viking has doubled the price, adding another $16 on top of the cost of making and shipping the pair of shoes.
7 The retailer then doubles the price again, and adds a touch extra … selling the shoes at $65. So the retailer raises the price $33 per pair, but the retailer also has to pay their costs out of that.

Three levels

Support: Use the first and last links only. Give the student two cards, one per link, and ask which comes first and how they know. Then have them say who has the shoes at the end.
At Grade: Read all three links, name what each hands on, circle the sequence words, and retell the chain in three ordered sentences.
Extension: The passage calls this a chain from raw material to finished shoes, but the printed steps skip from the first link to the sixth. Say what the reader is trusted to assume is in between, and say whether the word chain still fits a sequence with gaps in it.

English learners

Sequence markers carry the structure and are easy to read past: then, so, again, one link in the chain. Read those aloud on their own first. The word link has an everyday meaning and a chain-of-supply meaning, and the passage relies on both. Rehearse aloud: First ___. Then ___. Finally ___. A student may sequence the cards physically before speaking.

Materials

Printed first link
Both printed later links
All three printed links
Pencil
Printed first and last links
Word cards: link, again, sequence, retell

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

14. Where the book takes a side Author's craft · Separating what a text reports from what it argues

Most of this book reports; one section argues. In the chocolate pages the author asks a question that is really an accusation, chooses words like unfairly and controversial that another writer could have declined, and then closes by telling the reader that buying is itself a choice. Students separate the checkable from the judged, hold a neutral definition against a loaded sentence, and decide whether they were persuaded.

Full lesson — 20 minutes

1. Read the question the section puts to you (5 min)
Read this aloud. It opens with a question and then answers it with a second question that is not really asking anything. Say what the second question is actually claiming. Then say what the author wants the reader to feel about the answer.
Word preview: claiming
What would you do for a fancy chocolate bar? How about saying “okay” to a whole family working every single day for one year, and only earning a total of $1,000 to $2,000?
2. Separate the fact from the judgement (5 min)
Read this sentence aloud twice. Mark the parts that state something that could be checked, and mark the parts that give the author's opinion. Say aloud which words are the opinion words — the ones another writer could have chosen differently.
Word preview: judgement
Chocolate is one of the most controversial products on the market because most cocoa beans are grown in faraway countries at unfairly low wages and under difficult working conditions, yet the markup can be really steep.
3. Read a neutral definition beside a loaded one (5 min)
Here is the same section's plain definition of a term. Read it aloud. Say whether it takes a side the way the earlier sentence did, and quote the words that settle it. Then say why an author might write one sentence with an opinion and the next without.
Word preview: neutral
Fair trade means the companies that buy the cocoa beans pay higher prices for them, and those costs get passed on to you and me.
4. Name what the section asks the reader to do (5 min)
Read the closing lines of this section aloud. Say what the author says a reader is doing whenever they buy a chocolate bar. Then write one sentence saying whether you were persuaded, quoting the words that did or did not persuade you.
Word preview: persuade
Whichever bar you choose, you are making a choice not only about the price you pay, but also about the way of life for people in other countries.
There’s a lot of history in that cup.

Short version — 9 minutes

1. Read the question the section puts to you (4 min)
Read this aloud. Say what the second question is actually claiming and what the author wants a reader to feel about it.
Word preview: claiming
What would you do for a fancy chocolate bar? How about saying “okay” to a whole family working every single day for one year, and only earning a total of $1,000 to $2,000?
2. Separate the fact from the judgement (5 min)
Read this sentence aloud twice. Mark what could be checked and mark the author's opinion. Say which words are the opinion words.
Word preview: judgement
Chocolate is one of the most controversial products on the market because most cocoa beans are grown in faraway countries at unfairly low wages and under difficult working conditions, yet the markup can be really steep.

Three levels

Support: Work with the controversy sentence alone. Read it aloud and ask the student to find the one word that tells you what the author thinks rather than what happened. Unfairly is the answer; saying why is the task.
At Grade: Mark fact and judgement across the printed sentences, and say whether the fair trade definition takes a side.
Extension: The section's closing sentence claims a reader is making a choice about other people's lives whenever they buy a bar. Say what would have to be true for that claim to hold, and say whether anything printed here establishes it.

English learners

Judgement is carried by single words here — unfairly, controversial, steep — and a reader working hard on the sentence's shape will read straight past them. Pull those three words out and discuss them before the passage. Rehearse aloud: This part could be checked. This part is what the author thinks. Students may mark the two kinds in different colours before speaking.

Materials

Printed chocolate question
Printed controversy sentence
Pencil
Printed fair trade definition
Printed closing lines
Notebook
Word cards: claiming, judgement, neutral, persuade

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.

15. Three kinds of question Text structure · Explaining what a question is doing in an informational text

This book asks far more questions than it answers, and it uses them for at least three different jobs: hooking a reader into a section, turning a corner mid-explanation, and handing the reader something to work out for themselves. Students find the questions, notice which get answered, and sort them by the job each is doing. Nothing here requires working with the prices the questions surround.

Full lesson — 20 minutes

1. Count the questions and say who answers them (5 min)
Read this passage aloud. It asks three questions in a row and answers only the last. Say the three questions aloud in order, then say the answer the author supplies and which question it belongs to.
Word preview: question
Have you ever paid $20 for something and then gone back to the same store a week later to find it now selling for $15? Does that make you mad? Were you ripped off? Maybe, but probably not.
2. Watch a question move the story forward (5 min)
Read these two passages in order. The second uses a two-word question to turn a corner. Find that question, say it aloud, and say what the author does immediately after asking it. Say why the passage does not simply continue without it.
Word preview: turn
Sale! A store buys a shirt for $10 and agrees to pay the supplier later. The store has 90 days to sell the shirt so it can pay back the supplier the $10. The store plans to sell the shirt for $15.
The store offers the shirt to its customers for $15, but no one buys it. Now what? You guessed it: the store puts the shirt on sale.
3. Read a question the author answers with a hint (5 min)
Read these two lines aloud. The author asks where the money goes and then refuses to answer plainly, giving a hint instead. Say what the hint is pointing at, and say why the author chose a hint over a list.
Word preview: hint
So where does that tax money go? What does the government do with it?
Hint: you’re walking on it, driving on it, seeing it overhead, and using it every time you flush.
4. Sort the questions by what each one is for (5 min)
Look at the questions printed here. Sort them into three jobs: one that hooks a reader at the start of a section, one that turns a corner in the middle of an explanation, and one that hands the reader something to work out. Say your sorting aloud and defend one placement using the words of the question itself.
Word preview: sort
That thing on your head says a lot about you. Does your baseball cap reveal your favorite team? Or which movie or band you like the best?
The store offers the shirt to its customers for $15, but no one buys it. Now what? You guessed it: the store puts the shirt on sale.
So where does that tax money go? What does the government do with it?

Short version — 9 minutes

1. Count the questions and say who answers them (4 min)
Read this aloud. It asks three questions and answers only the last. Say the three questions in order, then say the answer and which question it belongs to.
Word preview: question
Have you ever paid $20 for something and then gone back to the same store a week later to find it now selling for $15? Does that make you mad? Were you ripped off? Maybe, but probably not.
2. Watch a question move the story forward (5 min)
Read these two passages in order. Find the two-word question that turns a corner, say it aloud, and say what the author does immediately after asking it.
Word preview: turn
Sale! A store buys a shirt for $10 and agrees to pay the supplier later. The store has 90 days to sell the shirt so it can pay back the supplier the $10. The store plans to sell the shirt for $15.
The store offers the shirt to its customers for $15, but no one buys it. Now what? You guessed it: the store puts the shirt on sale.

Three levels

Support: Work with the sale opening only. Have the student read it aloud and raise a hand at each question mark. Then ask one thing: which question does the author actually answer?
At Grade: Find the questions across the printed passages, say which are answered, and sort at least three by the job each is doing.
Extension: The tax lines ask a question and answer it with a hint rather than a list. Say what the author is assuming about the reader by doing that, and say whether a reader who missed the hint could recover the answer from anything else printed here.

English learners

Rhetorical questions are questions that do not want an answer, and a student may reasonably try to answer every one aloud. Name the difference before reading and let students mark real questions and rhetorical ones with two different symbols. Rehearse aloud: This question is here to ___. It is answered / not answered.

Materials

Printed sale opening
Both printed sale passages
Both printed tax lines
All three printed question passages
Three sorting labels: hook, turn, work it out
Word cards: question, turn, hint, sort

Standards & curriculum

Choose your curriculum above to see the standards for this lesson.