Manga Math Mysteries #5: The Ancient Formula

$Manga Math Mysteries #5: The Ancient Formula book cover$

Grade 3
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.

1Four fourths make a cup: finding the rest of the mix
2Two eighths, one fourth: the same wedge under two names
3The two blank wedges: how much of the formula is not there
4Six wedges against two: saying the comparison both ways
5One eighth of what? Sharing four cups, one cup and eight cups

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 rest is a number: reading a recipe that hides one amount in words
7Cut, shared, sold, found, joined: retelling the disk in the order the fractions allow
8What the two blank wedges are worth
9Was a fourth each a good plan? Writing the case into the journal
10Three times as much, one third as much: two true sentences about the same two piles

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.

11Which Means: How This Book Teaches You Its Words
12Caption, Speaker, Bracket: Reading a Comic in Print
13A Secret Everyone Knows: Following an Idea to the End
14This Sentence Is Broken: Reading a Damaged Page
15Was Miranda a Thief? Weighing What the Book Tells You

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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. Four fourths make a cup: finding the rest of the mix Concept · Subtracting a unit fraction from one whole with like denominators

The book gives students a recipe that names one part and hides the other: a whole cup of mix, one fourth of it blue, and the red left only as the rest. Students build the whole out of four one-fourth measures so that 4/4 and 1 whole are the same amount of rice in front of them, then remove the blue fourth and count what remains. The rest is a subtraction with a like denominator, and 4/4 can stand in for 1 so the subtraction has something to take from. The recipe card is drawn three times in the book's own panels; students build the recipe once, because it is one cup of mix, not three.

Full lesson — 20 minutes

1. Build the whole from four fourths (5 min)
Each pair snaps four one-fourth cup measures into a line and pours dry rice from all four into one whole cup, filling it exactly to the rim. Say what you did as a count of fourths: one fourth, two fourths, three fourths, four fourths. Write 4/4 on the card beside the full cup and write 1 whole underneath it.
Word preview: fourth, whole
It takes 4 one-fourth cups to make 4/4, or 1 whole cup.
2. Take the blue fourth away (5 min)
Set one of the four fourths aside and label it blue powder. Count what is left by fourths, touching each measure as you say it, and write 3/4 on the card. Under it write the sentence 4/4 minus 1/4 equals 3/4 using the numbers, not the words.
Word preview: subtract, rest
The rest is red, so we just subtract 1/4 from 4/4.
4/4 minus 1/4 equals 3/4.
3. Measure the red three times (5 min)
Fill the one-fourth cup with rice and tip it into the empty pitcher, three separate times, saying the running total aloud after each tip: one fourth, two fourths, three fourths. Stop when the card says stop. Check the pitcher against a partner's 3/4 cup measure and say whether the two agree.
Word preview: measure
SO WE NEED TO MEASURE OUT 1/4 CUP THREE TIMES.
We need 3/4 cup red powder.
4. Write it down so nobody repeats the work (5 min)
Copy the finished recipe onto your own card: one cup of mix total, one fourth blue, three fourths red. Trade cards with another pair and make their recipe from your card alone, without speaking. If you cannot make it, tell them which number was missing from the card.
Word preview: total
NOW WE WON'T HAVE TO DO THE MATH AGAIN NEXT TIME.
I DIDN'T THINK TO WRITE IT DOWN, THOUGH. I HAD TO DO THE MATH TWICE.

Short version — 9 minutes

1. Build the whole from four fourths (5 min)
Snap four one-fourth cup measures into a line and pour dry rice from all four into one whole cup. Count aloud as you pour: one fourth, two fourths, three fourths, four fourths. Write 4/4 beside the full cup and 1 whole underneath.
Word preview: fourth, whole
It takes 4 one-fourth cups to make 4/4, or 1 whole cup.
2. Take the blue fourth away (4 min)
Set one fourth aside and call it the blue powder. Count what is left by fourths, touching each measure, and write 3/4 on the card. Write 4/4 minus 1/4 equals 3/4 underneath in numbers.
Word preview: subtract, rest
4/4 minus 1/4 equals 3/4.

Three levels

Support: Stay with the four snapped measures and do not write the number sentence. Set the blue fourth aside and answer only how many fourths are left, counting them by touch. The answer is three fourths said aloud, and the writing can wait for the next lesson.
At Grade: Build the whole, remove the blue fourth, write 4/4 minus 1/4 equals 3/4, and then measure the red out in three separate tips of the quarter cup so the written 3/4 and the poured 3/4 are checked against each other.
Extension: Change the recipe so the blue is two fourths instead of one and write the new number sentence before touching any rice, then pour to test it. Say what stays the same in both recipes and what changes, naming the whole as the thing that did not move.

English learners

The word fourth does two jobs in this lesson that many languages separate: it names a position in order and it names one of four equal parts. Here it is always the part. The frame to rehearse is: the whole is ___ , one fourth is blue, so the rest is ___ fourths. Spanish cuarto, Mandarin si fen zhi yi and Arabic rub' all name the part cleanly, so invite students to say the recipe first in their strongest language and then in English, keeping the same two numbers in the same two places.

Materials

Four one-fourth cup measures per pair
A one-cup measure per pair
Dry rice
A recipe card per pair
A blue label card
A red label card
A small pitcher per pair
A three-fourths cup measure for checking
A blank recipe card per student
A pencil
Word cards: fourth, whole, the rest

Standards & curriculum

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

2. Two eighths, one fourth: the same wedge under two names Representation · Recognising equivalent fractions with a folded circle model

The book states three equivalences and proves none of them: 2/8 is the same as 1/4, six pieces make 6/8 or 3/4, and the disk splits eight ways. Students cut the disk themselves so the eight parts are equal because they folded them equal, then test each stated equivalence by covering one shape with another. What makes this a representation lesson rather than a naming exercise is that the equals sign is earned by paper lying flat on paper, and a student who writes 2/8 = 1/4 can point at the covering that made it true.

Full lesson — 20 minutes

1. Cut one disk into eight equal parts (5 min)
Fold a paper disk in half, in half again, and in half once more, then open it and cut on the folds to make eight wedges. Check the wedges against each other by stacking them; if any two do not match, fold a fresh disk. Write 1/8 on the back of every wedge.
Word preview: eighth, equal
He cut the disk into 8 pieces.
1 disk divided into 8 pieces. Each piece is 1/8 of a disk.
2. Deal two wedges to each disciple (5 min)
Deal your eight wedges out to four disciple cards, two to each card, and stop when the wedges run out. Write under one card how much of the disk that disciple holds, using eighths. Then lay the two wedges from one card over a fourth-circle template and write the second name for the same amount.
Word preview: disciple
EACH DISCIPLE GOT TWO OF THE EIGHT PIECES-- SO EACH HAD 1/4 OF THE FORMULA.
3. Show that two eighths and one fourth cover each other (5 min)
Place two eighth wedges on top of one fourth wedge so no paper shows at any edge. Say the sentence the covering proves: two eighths is the same as one fourth. Write 2/8 = 1/4 on your record strip and draw around the shape you covered.
Word preview: same as
--AND 2/8 IS THE SAME AS 1/4.
MIRANDA HAS 2/8, OR 1/4, OF A DISK!
4. Name six wedges two ways (5 min)
Put six of your eighth wedges together and write how much of the disk they make in eighths. Then group them into pairs, count the pairs against the fourth template, and write the same amount a second way. Both names go on the same line of the strip with an equals sign between them.
Word preview: equivalent
The Kung Fu Journal has 6 pieces. That makes 6/8, or 3/4, of a disk.

Short version — 9 minutes

1. Cut one disk into eight equal parts (5 min)
Fold a paper disk in half three times, open it, and cut on the folds to make eight wedges. Stack the wedges to check they match. Write 1/8 on the back of each one.
Word preview: eighth, equal
1 disk divided into 8 pieces. Each piece is 1/8 of a disk.
2. Show that two eighths and one fourth cover each other (4 min)
Lay two eighth wedges on one fourth wedge so no paper shows at the edges. Say what the covering proves: two eighths is the same as one fourth. Write 2/8 = 1/4 on your strip.
Word preview: same as
--AND 2/8 IS THE SAME AS 1/4.

Three levels

Support: Work with the eight wedges and the one fourth template only. Cover the fourth with two eighths, say two eighths is the same as one fourth, and stop there. Leave 6/8 and 3/4 for another day; one covering proved by hand is the whole job.
At Grade: Cut the eight wedges, deal two to each of four disciples, cover a fourth with two eighths and then name six wedges as both 6/8 and 3/4, writing each pair of names with an equals sign between them.
Extension: Fold a second disk into sixteenths and find every wedge in your sixteenths that covers exactly one of your eighths. Write the pairs you find and say what happens to the top number and the bottom number each time, without using the word rule.

English learners

Eighth and fourth are ordinal words doing part work again, and English makes it worse by reusing them for dates and floors. Anchor them to the paper: this is one of eight equal pieces. The frame to rehearse is: two ___ cover one ___ , so they are the same. Many students will have a language that names the part by its count first, which is exactly the order the fraction is written in; invite them to say 2/8 in that language and then place the wedges, so the saying and the covering happen together.

Materials

A paper disk per student
Scissors
A pencil
Four disciple cards per student
A fourth-circle template
A fourth wedge per student
A record strip
Word cards: eighth, equal parts, the same as

Standards & curriculum

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

3. The two blank wedges: how much of the formula is not there Reasoning · Finding the missing part of a whole from a stated count and a stated total

The book asks its own question twice and never answers it in words: what do the two blank wedges mean. Everything needed to answer it is on the page but never brought together, because the count of pictures is on one page and the size of the whole is on another. Students put the two facts side by side and derive a fraction the book does not print as a fraction of absence. The reasoning demand is the derivation, not the arithmetic: students must notice that a count is not yet a fraction and say what the count was missing.

Full lesson — 20 minutes

1. Read the journal disk and count what is there (4 min)
Look at the journal disk card and count the wedges that carry a herb picture. Write that count in the first box of your evidence strip. Do not write a fraction yet; write only how many pictures you can see.
Word preview: wedge, blank
Maybe you're supposed to copy the pictures onto the blank disk?
But what do the two blank wedges mean?
2. Find how many parts a whole formula needs (4 min)
Find the sentence on the evidence sheet that says how many equal parts the whole formula is split into and write that number in the second box. Say why the count in box one is not yet a fraction: a fraction needs the whole as well as the part.
Word preview: whole, part
THE FORMULA IS SPLIT INTO 8 EQUAL PARTS-- SO EACH PIECE OF THE DISK REPRESENTS 1/8 OF THE TOTAL FORMULA.
3. Work out how much of the formula is missing (7 min)
Using only your two boxes, write the fraction of the formula the journal holds and then the fraction it is missing. Build the missing amount out of blank wedges on your disk card so you can see it as well as write it. Write one sentence saying how you knew the missing amount without being told it.
Word preview: missing
Why are there two blank wedges in the disk? You can't make the jow if you don't have the whole formula.
4. Check your answer against the buyer's pieces (5 min)
Read the two sentences on the check card, which say what the journal holds and what Miranda holds. Lay your missing wedges beside Miranda's pieces and say whether they match. Then write the addition that makes the whole disk, using both fractions.
Word preview: altogether
The Kung Fu Journal has 6 pieces. That makes 6/8, or 3/4, of a disk.
6/8 + 2/8 is 1 whole disk.

Short version — 9 minutes

1. Read the journal disk and count what is there (4 min)
Count the wedges on the journal disk card that carry a herb picture and write that number in the first box of your strip. Write only the count, not a fraction.
Word preview: wedge, blank
But what do the two blank wedges mean?
2. Work out how much of the formula is missing (5 min)
The whole formula is eight equal parts. Using your count and that eight, write the fraction the journal holds and the fraction it is missing. Build the missing amount from blank wedges so you can see it.
Word preview: missing
Why are there two blank wedges in the disk? You can't make the jow if you don't have the whole formula.

Three levels

Support: Work with the disk card cut into its eight wedges rather than drawn. Take out the wedges that carry pictures and hold what is left in your hand. Say how many are in your hand and how many the whole disk had, and let those two numbers be the answer before any fraction is written.
At Grade: Count the pictured wedges, find the eight from the evidence sheet, write both the fraction held and the fraction missing, and then check the missing amount against Miranda's two pieces before writing the addition that closes the disk.
Extension: Once you have the missing fraction, work out what fraction of the entire formula the journal holds when there are two disks, not one. Say which whole each of your two answers is measured against, and why the same six wedges can honestly be called by two different fractions.

English learners

This lesson turns on the difference between how many and how much of, which many languages mark with a classifier or a separate construction and English marks only by the fraction bar. Rehearse the pair: there are ___ wedges; that is ___ of the disk. The word missing is also worth pre-teaching against absent and lost, since only missing carries the sense of a gap in something otherwise complete, which is exactly what the two blank wedges are.

Materials

A journal disk card per pair
An evidence strip per pair
An evidence sheet per pair
Blank paper wedges
A pencil
A check card per pair
Word cards: missing, whole, part of

Standards & curriculum

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

4. Six wedges against two: saying the comparison both ways Application · Comparing two fractions of the same whole by matching equal groups

The book quantifies both sides of this comparison and supplies no comparing word for it at all: it prints 6/8 and it prints 2/8 and it never says which is bigger or by how much. Students reach the relation by matching rows rather than by dividing, then say it forward and backward, which is the work the book leaves undone. The application is that a comparison has two true sentences and the numbers in them are different, so choosing which to say is part of saying it correctly.

Full lesson — 20 minutes

1. Lay the two shares side by side (5 min)
Build the journal's share out of six eighth wedges and Miranda's share out of two, and lay the two groups in two rows on your mat. Do not count yet. Write under each row how much of a disk it is, in eighths.
Word preview: share
There are 6 wedges--
THE SIFU I MET HAD THESE TWO PIECES.
2. Match the rows to find how many times bigger (5 min)
Break the journal's six wedges into groups the size of Miranda's two. Count how many groups you made. Say the comparison out loud using that number: the journal has ___ times as much of the disk as Miranda.
Word preview: times as much
6/8 of a disk-- in the kung fu journal.
3. Turn the sentence around (5 min)
Write the same comparison the other way, starting with Miranda. You may not use the words the journal has; begin with Miranda has. Say what number had to change when you turned the sentence around and what stayed the same.
Word preview: one third of
MIRANDA HAS 2/8, OR 1/4, OF A DISK!
4. Close the disk and check both sentences (5 min)
Push the two rows together into one circle and write the addition that says what they make. Then read both of your comparison sentences aloud with the closed disk in front of you and say whether each one is still true now that the pieces are joined.
Word preview: whole
6/8 plus the 2/8 she bought from the kung fu master make 1 whole disk.

Short version — 9 minutes

1. Lay the two shares side by side (5 min)
Build the journal's share from six eighth wedges and Miranda's from two, and lay them in two rows. Write under each row how much of a disk it is, in eighths.
Word preview: share
There are 6 wedges--
2. Match the rows to find how many times bigger (4 min)
Break the six journal wedges into groups the size of Miranda's two and count the groups. Say the comparison aloud: the journal has ___ times as much of the disk as Miranda.
Word preview: times as much
6/8 of a disk-- in the kung fu journal.

Three levels

Support: Use the two rows and answer only which row has more of the disk and how many wedges more. Point along the extra wedges as you count them. The multiplying comparison can wait; more than, said with the rows in front of you, is a true comparison.
At Grade: Lay both shares out, match the journal's six into groups of two to find the factor, then write the comparison forward and reversed and close the disk to check that the addition still holds.
Extension: Write a third true comparison of the same two shares that uses neither times as much nor one third of, and say what your sentence measures that the other two do not. Then decide which of your three sentences would be most useful to someone trying to complete the formula.

English learners

Reversing a comparison is a grammatical operation as much as a mathematical one, and languages differ in whether the thing being compared or the yardstick it is measured against comes first, so a student may reverse the words correctly and still keep the wrong number. Rehearse both frames as a pair: the journal has three times as much as Miranda; Miranda has one third as much as the journal. Ask for both in the strongest language first, then in English, and check that the number moved with the meaning.

Materials

Eight eighth wedges per pair
A two-row comparison mat
A comparison sentence strip
A pencil
A record sheet per pair
Word cards: times as much, one third of, share

Standards & curriculum

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

5. One eighth of what? Sharing four cups, one cup and eight cups Fluency · Dividing a quantity into equal shares and naming the share as a fraction of the whole

The book uses the same wedge to mean an eighth of a cup on one page and a whole cup on another, and says so plainly, but never puts the two side by side for comparison. Students perform three sharings in a row so that the eighth changes size in their hands while the number of sharers does not. They deal out equal shares quickly and correctly and read off what one share is; the point that lands is that one eighth is always one eighth of something, and the something has to be named.

Full lesson — 20 minutes

1. Share four cups among four people (5 min)
Pour four cups of water one at a time into four labelled cups on the tray, going round the four in turn until the pitcher is empty. Count how many whole cups each person ended with. Write the division that says what you did, using the number of cups and the number of people.
Word preview: divide, equally
SO WE'RE DIVIDING 4 CUPS OF LIQUID INTO FOURTHS. EVERYONE WILL GET 1 CUP.
2. Share one cup among eight (5 min)
Now share a single cup of water equally into eight small pots, going round until the cup is empty. Write what fraction of a cup each pot holds. Say what changed between this sharing and the last one, naming both the number shared and the number of sharers.
Word preview: eighth
SUPPOSE YOU WANTED 1 CUP OF JOW. THEN EACH PIE WEDGE WOULD REPRESENT 1/8 CUP.
3. Share eight cups among eight (5 min)
Share eight cups of water into the same eight pots, one round at a time. Write what each pot holds now. Put your three answers in a row and read them aloud in order, saying each time how many cups were shared and among how many.
Word preview: each
If you wanted 8 cups of jow, then each picture would represent 1 cup--1/8 of 8.
4. Say what the eighth was an eighth of (5 min)
For each of your three sharings, write the sentence one eighth of ___ is ___ , or say why that sentence does not fit. Then explain to another group why a wedge meant a fraction of a cup in one sharing and a whole cup in another, when the wedge never changed.
Word preview: of
IF THERE WAS JUST ONE PIECE WITH A CERTAIN PICTURE, THEN YOU WOULD PUT 1/8 CUP OF THAT HERB INTO THE JOW.

Short version — 9 minutes

1. Share four cups among four people (5 min)
Pour four cups of water one at a time into four labelled cups, going round in turn until the pitcher is empty. Count what each person got and write the division that says what you did.
Word preview: divide, equally
SO WE'RE DIVIDING 4 CUPS OF LIQUID INTO FOURTHS. EVERYONE WILL GET 1 CUP.
2. Share one cup among eight (4 min)
Share a single cup of water equally into eight small pots, going round until the cup is empty. Write what fraction of a cup each pot holds, and say what changed from the sharing before.
Word preview: eighth
SUPPOSE YOU WANTED 1 CUP OF JOW. THEN EACH PIE WEDGE WOULD REPRESENT 1/8 CUP.

Three levels

Support: Do the first two sharings only, and use dry rice rather than water so a spill costs nothing. Answer what one person got each time, in cups for the first and as a fraction of a cup for the second. The third sharing and the comparison can wait.
At Grade: Perform all three sharings, record what one share was each time, and then write the one eighth of ___ is ___ sentence for the sharings where it fits, saying why it does not fit the first.
Extension: Work out how many cups would have to be shared among eight for one share to be exactly two cups, and say how you knew before you poured. Then describe what happens to one share every time the amount shared doubles and the number of sharers stays at eight.

English learners

The little word of is doing the heaviest lifting in this lesson and is often the last thing a new English speaker gets right, because many languages attach the part to the whole with a case ending or a different particle rather than a separate word. Rehearse the full frame every time rather than the fragment: one eighth of eight cups is one cup. Encourage students to say the whole sentence in their strongest language first; if the of-phrase is a single word there, the frame still holds and the two numbers still occupy the same two slots.

Materials

A pitcher of four cups of water per group
Four labelled cups per group
A tray
Eight small pots per group
A one-cup measure
A record row per group
A sentence frame card per group
Word cards: divide, equal share, one eighth of

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 rest is a number: reading a recipe that hides one amount in words Integrated · Students find the unstated amount of red powder by reading the two words that carry it, then test what happens to the recipe when those words are changed.

Students find the unstated amount of red powder by reading the two words that carry it, then test what happens to the recipe when those words are changed.

Full lesson — 20 minutes

1. Read the card and find what is missing (4 min)
Students read the recipe card and list what it tells them and what it does not. They mark the blue amount as given and the red amount as missing, and say which words on the card are doing the work for red.
2. Work out the rest (6 min)
Students build one whole cup from four quarter-cup measures, set aside the blue fourth, and count and write what remains as a fraction. They measure the red out in three tips of the quarter cup.
3. Break the card on purpose (6 min)
Students rewrite the card replacing the rest with some, and try to make the drink from their new card. They write the sentence saying what the new card fails to fix, using the words total and the rest correctly.
4. Say the recipe so a stranger could make it (4 min)
Each pair reads their corrected card to another pair, who must make it without asking a question. Any question asked marks a place where the language did not carry the quantity.

Short version — 9 minutes

1. Work out the rest (6 min)
Students build one whole cup from four quarter-cup measures, set aside the blue fourth, and count and write what remains as a fraction. They measure the red out in three tips of the quarter cup.
2. Break the card on purpose (6 min)
Students rewrite the card replacing the rest with some, and try to make the drink from their new card. They write the sentence saying what the new card fails to fix, using the words total and the rest correctly.

Three levels

Support: Keep the four quarter-cup measures in front of the student throughout and let the missing amount be found by lifting the blue one away rather than by writing. The student says the rest is three of these before any fraction is written.
At grade: Students find three fourths by building and removing, write the number sentence, then perform the swap and write one sentence naming what the vaguer card no longer determines.
Extension: Students write a third version of the card that fixes the red amount without using the word rest and without stating a fraction, then test whether another pair can make it. They say which of the three cards they would put in a journal and why.

English learners

The complement sense of the rest is the pinch point: many students meet rest first as remainder in the sense of leftovers, which suggests something small or discarded rather than the larger part, and here the rest is three times the named part. Rehearse the frame one fourth is blue, so the rest, three fourths, is red, and let students say it in their strongest language first. Where a language marks the complement with a single word, invite that word onto the card beside the English so the two can be compared as equals.

Materials

A recipe card per pair
Four quarter-cup measures
A one-cup measure
Dry rice
A blank card for the rewrite
The recipe card enlarged
A word bank showing total, the rest, equal

Standards & curriculum

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

7. Cut, shared, sold, found, joined: retelling the disk in the order the fractions allow Integrated · Students rebuild the disk's five-event history in order and show that two of the events cannot be swapped without the fractions ceasing to make sense.

Students rebuild the disk's five-event history in order and show that two of the events cannot be swapped without the fractions ceasing to make sense.

Full lesson — 20 minutes

1. Lay the five events on the line (5 min)
Students take five event cards, read them, and place them in order on the event line. They move paper wedges onto each station to show how much of the disk is where after that event.
2. Say the amount at every step (5 min)
Students retell the chain aloud with a partner, saying the fraction each holder has after each event. The partner stops the retelling at any sentence with no fraction in it.
3. Swap two events and find the break (6 min)
Students exchange the last two events and retell again. They find the sentence that can no longer be said and write down which fraction it needed that was not yet there.
4. Close the disk (4 min)
Students bring the two holdings together, write the addition, and say the final sentence of the true order with the completed disk in front of them.

Short version — 9 minutes

1. Lay the five events on the line (5 min)
Students take five event cards, read them, and place them in order on the event line. They move paper wedges onto each station to show how much of the disk is where after that event.
2. Swap two events and find the break (6 min)
Students exchange the last two events and retell again. They find the sentence that can no longer be said and write down which fraction it needed that was not yet there.

Three levels

Support: Work with three events rather than five: the cut, the sale and the joining. The student places the wedges and retells with the three sentence starters supplied on cards. The pivot argument is not asked for; finding that the joining must come last is enough.
At grade: Students order all five events, retell with a fraction in every sentence, perform the swap, and name the fraction the broken retelling was missing.
Extension: Students write the version of the chain that the other story in the book tells, where the disk stays in the clock, and say which events the two versions share and which they cannot both have. They then explain why sixteen parts rather than eight makes both tellings true at once.

English learners

The chain needs sequence connectives and fraction language in the same sentence, which is a heavy load. Supply the connectives on cards so the effort goes into the quantity: first the disk was cut into eight, so each piece was one eighth. Let students rehearse the sequence in their strongest language and then place only the fraction into English, since the fraction is the part being assessed. Watch for got and had reading as the same event; the sale changes who holds two eighths without changing the amount, and that distinction is carried by the verb.

Materials

Five event cards per pair
Eight paper wedges per pair
An event line mat
Sentence starter cards
The event line enlarged
A whole disk divided into eighths

Standards & curriculum

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

8. What the two blank wedges are worth Integrated · Students answer the question the book asks twice and never answers, deriving the missing fraction of the formula from three sentences on three different pages.

Students answer the question the book asks twice and never answers, deriving the missing fraction of the formula from three sentences on three different pages.

Full lesson — 20 minutes

1. Count what is on the disk (4 min)
Students examine the journal disk card and count the wedges carrying a picture and the wedges left blank. They write both counts and are told not to write a fraction yet.
2. Find the whole (5 min)
Students hunt the evidence sheet for the sentence that says how many equal parts the whole formula has. They write it, and say aloud why the counts from segment one were not yet fractions.
3. Name the missing amount (6 min)
Students write the fraction the journal holds and the fraction it lacks, build the lacking amount from blank wedges, and rename it in fourths by pairing.
4. Write how you knew (5 min)
Each student writes one sentence for the kung fu journal explaining how the missing fraction was found, naming the three sentences it rests on.

Short version — 9 minutes

1. Count what is on the disk (4 min)
Students examine the journal disk card and count the wedges carrying a picture and the wedges left blank. They write both counts and are told not to write a fraction yet.
2. Name the missing amount (6 min)
Students write the fraction the journal holds and the fraction it lacks, build the lacking amount from blank wedges, and rename it in fourths by pairing.

Three levels

Support: Give the student the disk already cut into eight wedges rather than drawn. The student lifts out the pictured wedges and holds what is left. The counts two and eight are the answer at this level, and the fraction is written for them to read back.
At grade: Students derive two eighths from the three sentences, rename it as one fourth, and write the explaining sentence naming their evidence.
Extension: Students work out what fraction of the entire formula the journal holds once the second disk is known to exist, and explain how the same six wedges can honestly be six eighths and six sixteenths at the same time by naming which whole each answer measures.

English learners

The construction a fraction of is the load here, and the trap is answering two when the question asks how much rather than how many. Rehearse the pair explicitly: there are two blank wedges; that is two eighths of the formula. Because the written sentence is the assessed evidence, let students compose it orally in their strongest language first and then write the English, and supply the sentence frame I knew the journal was missing ___ because ___ so that the reasoning rather than the syntax is what costs them effort.

Materials

A journal disk card per pair
An evidence sheet per pair
Blank paper wedges
An evidence strip
A sentence frame card
The journal disk enlarged
The three evidence sentences displayed together

Standards & curriculum

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

9. Was a fourth each a good plan? Writing the case into the journal Integrated · Students take a position on whether Sifu Leung's split could have kept his disciples together, and defend it in a journal entry that must carry the fractions it rests on.

Students take a position on whether Sifu Leung's split could have kept his disciples together, and defend it in a journal entry that must carry the fractions it rests on.

Full lesson — 20 minutes

1. Hear the plan and the outcome (4 min)
Students read the three sentences that set out the split and its failure, and build one disciple's share from wedges so the fourth is in their hands before they judge it.
2. Test each position with the wedges (7 min)
Students test all three positions physically: four fourths closing the disk, two fourths making a half, and the two-disk set showing a share as one sixteenth. They mark on a card which test surprised them.
3. Choose and fund a position (4 min)
Students choose the position they will defend and write the two fractions that fund it at the top of the journal page, before writing any prose.
4. Write the journal entry (5 min)
Each student writes the entry for the next student to receive a journal, stating the position and using both fractions to say what is possible or impossible.

Short version — 9 minutes

1. Test each position with the wedges (7 min)
Students test all three positions physically: four fourths closing the disk, two fourths making a half, and the two-disk set showing a share as one sixteenth. They mark on a card which test surprised them.
2. Write the journal entry (5 min)
Each student writes the entry for the next student to receive a journal, stating the position and using both fractions to say what is possible or impossible.

Three levels

Support: Offer the first two positions only and supply both fractions already written on the page. The student tests them with the wedges, chooses one, and completes a two-sentence frame rather than composing the entry from scratch. The sixteenths position is not raised at this tier.
At grade: Students test all three positions, choose one, name its two funding fractions and write the journal entry to the named reader.
Extension: Students write the entry for the position they did not choose and then say which of the two cases is stronger and what quantity would have to change to reverse their judgement. They may propose a different number of pieces per disciple that would fix the plan, and must show what it does to the coalition of two.

English learners

The mathematical work of justification is carried by because and so, and by the modal verbs can and could not, which is exactly where a case in writing is hardest for a new English speaker. Supply the frame I think the plan was ___ because ___ of the formula is not enough to ___ . Because the assessed artifact is written, let students build the case orally in their strongest language and with the wedges first, and treat the fractions as the non-negotiable content while the surrounding sentence may be supported. A student who writes two correct fractions in a shaky sentence has done the mathematics of this lesson.

Materials

Eight wedges per pair
A second eight-wedge set
A position card
A journal page per student
A sentence frame card
The three positions displayed
A two-disk diagram of sixteen parts

Standards & curriculum

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

10. Three times as much, one third as much: two true sentences about the same two piles Integrated · Students compare the journal's six eighths against Miranda's two eighths by matching groups, then say the comparison in both directions and account for why the numbers differ.

Students compare the journal's six eighths against Miranda's two eighths by matching groups, then say the comparison in both directions and account for why the numbers differ.

Full lesson — 20 minutes

1. Build both piles (4 min)
Students build the journal's six wedges and Miranda's two in two rows on the mat and write the fraction under each row. No comparison is made yet.
2. Match the rows into groups (6 min)
Students break the six into groups the size of the two and count the groups, then say the forward comparison aloud with that number in it.
3. Turn the sentence around (6 min)
Students write the comparison starting with Miranda, forbidden from beginning with the journal. They mark which number changed and which stayed, and say why the piles did not move.
4. Join the piles and test both sentences (4 min)
Students push the rows together into one disk, write the addition, and decide whether each of their two sentences is still true of the joined pieces.

Short version — 9 minutes

1. Match the rows into groups (6 min)
Students break the six into groups the size of the two and count the groups, then say the forward comparison aloud with that number in it.
2. Turn the sentence around (6 min)
Students write the comparison starting with Miranda, forbidden from beginning with the journal. They mark which number changed and which stayed, and say why the piles did not move.

Three levels

Support: Stay with more than and fewer than, and count the extra wedges by pointing along them. The student answers which pile has more of the disk and by how many wedges, and says one sentence. The reversal into thirds is not asked for at this tier.
At grade: Students match the rows to find the factor, say the forward comparison, write the reversed one and name the number that changed.
Extension: Students write a third true comparison of the same two piles that uses neither three times nor one third, then say what their sentence measures that the other two do not, and which sentence a person trying to complete the formula would most want to hear.

English learners

Reversing a comparison requires moving the number as well as the nouns, and this is where languages that place the yardstick of a comparison before the thing being compared will trip a student who has reversed correctly in their own grammar. Rehearse the two frames as a pair, always together, never one alone: the journal has three times as much as Miranda; Miranda has one third as much as the journal. Invite the pair in the strongest language first and check the numbers moved with the nouns. Note also that the book's own word or, as in 6/8 or 3/4, means the same amount renamed and not a choice between two amounts.

Materials

Eight paper wedges per pair
A two-row comparison mat
A comparison sentence strip
A pencil
A two-row comparison enlarged
Both sentence frames displayed together

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. Which Means: How This Book Teaches You Its Words Language · Using a Sentence's Own Explanation to Learn a New Word

This book teaches its own vocabulary inside the sentence, using the phrase which means and a pair of dashes to slip a definition in without stopping the story. Students find three words defined that way, work out the family relationship each one names, then use the same pattern to explain a word of their own. The skill is using in-text definitions and appositives; the relationships are named, never counted or placed on a chart.

Full lesson — 20 minutes

1. Find the words that explain a word (6 min)
The teacher reads the passage below aloud. Three times the writer stops to tell you what a word means. Read it again and underline the phrase which means each time you meet it. Say aloud what sifu means and what sigung means, using only what the passage tells you.
Word preview: means
[Caption] So we call you "sifu"--which means "mother" or "father"--because you're our teacher. [Caption] We call sigung "sigung"--which means "grandfather"--because he's your teacher. [Caption] ... and we call your grandfather Si Tai Gung--which means "great-grandfather"--because he was sigung's teacher. [Caption] What would we call Leung Jan? [Caption] You would call him sifu Leung--
2. Notice the punctuation doing the work (6 min)
Look at the same passage, printed below. Each explanation sits between two dashes. With a partner, read one sentence aloud skipping everything between the dashes, then read it again including it. Say what the sentence still tells you without the explanation and what it gains with it.
Word preview: dashes
[Caption] So we call you "sifu"--which means "mother" or "father"--because you're our teacher. [Caption] We call sigung "sigung"--which means "grandfather"--because he's your teacher. [Caption] ... and we call your grandfather Si Tai Gung--which means "great-grandfather"--because he was sigung's teacher. [Caption] What would we call Leung Jan? [Caption] You would call him sifu Leung--
3. Meet a word explained a different way (4 min)
Read the passage below. Here a student works out a word's meaning by taking it apart rather than being told. Point to the part of the passage that gives the meaning of quad. Say aloud how this is different from the way sifu was explained.
Word preview: quad
[Caption] To help you remember a move, you can think about dividing your body into quadrants. [Caption] Quad means "four," so that means you’re dividing your body into four parts?
4. Explain a word the same way (4 min)
Look again at the passage printed below and reread one of its which means explanations. Now choose a word you know that somebody younger might not. Say a sentence that explains it the same way, slipping the meaning in between two dashes. Your partner says whether the sentence would still make sense with the explanation taken out.
Word preview: explain
[Caption] So we call you "sifu"--which means "mother" or "father"--because you're our teacher. [Caption] We call sigung "sigung"--which means "grandfather"--because he's your teacher. [Caption] ... and we call your grandfather Si Tai Gung--which means "great-grandfather"--because he was sigung's teacher. [Caption] What would we call Leung Jan? [Caption] You would call him sifu Leung--

Short version — 9 minutes

1. Find the words that explain a word (5 min)
The teacher reads the passage below. Underline which means each time it appears, then say what sifu and sigung mean using only what the passage tells you.
Word preview: means
[Caption] So we call you "sifu"--which means "mother" or "father"--because you're our teacher. [Caption] We call sigung "sigung"--which means "grandfather"--because he's your teacher. [Caption] ... and we call your grandfather Si Tai Gung--which means "great-grandfather"--because he was sigung's teacher. [Caption] What would we call Leung Jan? [Caption] You would call him sifu Leung--
2. Meet a word explained a different way (4 min)
Read the passage below. Point to the part that gives the meaning of quad, and say how this differs from the way sifu was explained.
Word preview: quad
[Caption] To help you remember a move, you can think about dividing your body into quadrants. [Caption] Quad means "four," so that means you’re dividing your body into four parts?

Three levels

Support: Use the passage in step 1. The teacher reads the sifu sentence only. Find which means. Say the two words that follow it. Then say: sifu means teacher.
At Grade: Explain sifu, sigung and Si Tai Gung from the passage, and say how the dashes tell a reader that an explanation is coming.
Extension: The book explains sifu with which means but explains quad by putting the meaning in quotation marks. Say two sentences about why a writer might choose one method over the other, and which helped you more.

English learners

This passage is unusually friendly to multilingual readers because it does openly what readers are normally expected to infer: it states meanings. Name that aloud. The relationship words themselves, teacher of my teacher, may map onto terms students already have, so invite them to give the equivalent chain in their strongest language before working in English. Rehearsable frame: ___ means ___, so ___.

Materials

Manga Math Mysteries #5: The Ancient Formula, the passage printed in this step
definition mapping sheet
Word cards: means, dashes, quad, explain

Standards & curriculum

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

12. Caption, Speaker, Bracket: Reading a Comic in Print Language · Reading How a Graphic Novel Marks Who Is Speaking

This book is a comic that has been typed out, so its pictures arrive as bracketed notes and its speech arrives labelled Caption or Speaker. Students learn to read those labels, sort what is shown from what is said, and then meet a page where the person typing could not tell who was speaking and marked it with a question mark. The skill is reading text features and judging how reliable a label is.

Full lesson — 20 minutes

1. Sort what is shown from what is said (6 min)
The teacher reads the passage below aloud, saying the bracketed parts in a different voice. Read it again together. Put one finger on something a reader would see in a picture and another on something a person says out loud. Say aloud how the labels told you which was which.
Word preview: caption
[Caption] Each kung fu move has three parts. There's how you start. [They demonstrate with swords.] [Caption] There's how you finish. [They clash blades.] [Caption] And there's how you get from one to the other. [Caption] If you only learn the starting and stopping positions, you're missing 1/3 of the move.
2. Read a page where the pictures carry the action (6 min)
Read the passage below with a partner. Much of what happens here is inside the square brackets rather than in anybody's speech. Say aloud what happens in this scene, using the bracketed notes. Then say what you would not know if the brackets were removed.
Word preview: brackets
[Caption] --BUT SIGUNG WAS ANGRY, AND HE ACCUSED MIRANDA WHERE YOU COULD HEAR HIM. [They stand together and talk quietly.] [Caption] YEAH. [Caption] ADULTS-- EVEN KUNG FU MASTERS-- AREN'T ALWAYS PERFECT.
3. Meet a label the typist was not sure about (4 min)
Read the passage below exactly as it is printed. Notice JOY?: and YES, JOY?: with question marks in them. Those question marks were put there by the person typing the book up, because they could not tell who was speaking from the picture. We are leaving them as they are. Say aloud what a reader can and cannot be sure of on this page.
Word preview: unsure
Page 21 [Caption] We'll work on the form until Faiza gets back. [They practice with swords in a studio.] [The student looks pensive.] [Clock faces are shown.] JOY?: Sigung? YES, JOY?: [The woman says she is doing the move wrong.]
4. Say what a page with no words can still do (4 min)
Two passages are printed below. The second is a whole page of this book that has no words on it at all, and the note is all that was typed. Read both. Say aloud what a reader misses on a page like that, and how they might work out what happened from the pages around it.
Word preview: missing
Page 21 [Caption] We'll work on the form until Faiza gets back. [They practice with swords in a studio.] [The student looks pensive.] [Clock faces are shown.] JOY?: Sigung? YES, JOY?: [The woman says she is doing the move wrong.]
Page 17 [No visible text on the page.]

Short version — 9 minutes

1. Sort what is shown from what is said (5 min)
The teacher reads the passage below, using a different voice for bracketed parts. Point to something seen in a picture and something said aloud, and say how you knew.
Word preview: caption
[Caption] Each kung fu move has three parts. There's how you start. [They demonstrate with swords.] [Caption] There's how you finish. [They clash blades.] [Caption] And there's how you get from one to the other. [Caption] If you only learn the starting and stopping positions, you're missing 1/3 of the move.
2. Meet a label the typist was not sure about (4 min)
Read the passage below as printed. Notice the question marks inside the speaker labels and say what a reader can and cannot be sure of here.
Word preview: unsure
Page 21 [Caption] We'll work on the form until Faiza gets back. [They practice with swords in a studio.] [The student looks pensive.] [Clock faces are shown.] JOY?: Sigung? YES, JOY?: [The woman says she is doing the move wrong.]

Three levels

Support: Use the passage in step 1. The teacher reads one bracketed note and one spoken line. Say which one you would see in a picture. Point to the square brackets.
At Grade: Sort the spoken lines from the bracketed picture notes in two passages, and explain what the question mark in JOY?: is telling a reader.
Extension: The transcriber wrote JOY?: rather than JOY:. Say two sentences about why marking uncertainty is more honest than guessing, and what a reader should do with a line labelled that way.

English learners

The conventions here are visual rather than linguistic: square brackets mean nobody said this, a colon after a name means this person speaks, a question mark inside a label means we are not sure. None of that is guessable from vocabulary. Teach the three marks as a key, written up where students can see it, before reading. Rehearsable frame: The brackets show ___. The label says ___ is speaking.

Materials

Manga Math Mysteries #5: The Ancient Formula, the passage printed in this step
label sorting cards
Word cards: caption, brackets, unsure, missing

Standards & curriculum

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

13. A Secret Everyone Knows: Following an Idea to the End Language · Tracing a Book's Message Through What Characters Say

One idea runs the length of this book: whether knowledge should be hidden or shared. Students follow it through four moments, from a teacher saying everyone needs help, to masters keeping secrets, to the closing line about a secret everyone knows. They state the message in their own words and support it with a quoted line. The skill is identifying a theme and citing evidence for it; the fractions the plot turns on are never worked.

Full lesson — 20 minutes

1. Start with a teacher answering a worry (6 min)
The teacher reads the passage below aloud. A student says she feels she should solve things alone, and her teacher answers. Read it again together. Say aloud what the student is worried about and what her teacher tells her. Underline the sentence you would quote to prove what the teacher believes.
Word preview: help
[Caption] A lot of the puzzles don't make sense--like this one. [Caption] I think I need help, but I also feel like I should answer these puzzles on my own. [They exchange the book.] [Caption] Everyone needs help sometimes. Even kung fu masters, like Sigung and me, ask others for help when we're learning something new.
2. Find the opposite view earlier in the book (6 min)
Read the passage below with a partner. It explains why the old masters kept things back. Say aloud their reason. Then say whether that reason sounds fair to you, and put it on your chart opposite what the teacher said in step 1.
Word preview: secret
[Caption] WHEN KUNG FU WAS FIRST INVENTED, LEARNING MARTIAL ARTS WAS LIKE HAVING SUPERPOWERS. [Caption] NO MASTER WANTED TO TEACH A BULLY. [Caption] MASTERS WANTED TO KNOW STUDENTS VERY WELL BEFORE TEACHING THEM THEIR BEST SECRETS.
3. Read where the book lands (4 min)
Read the passage below. This is the end of the argument, and the last line is the answer the book gives. Say that line aloud. Then say in your own words what the book has decided about keeping knowledge secret.
Word preview: message
SPEAKER: NOW ALL OF YOU HAVE YOUR OWN KUNG FU JOURNALS. SPEAKER: AND NO ONE WILL BE ABLE TO STEAL LEUNG JAN'S FORMULA. SPEAKER: YOU CAN'T STEAL A SECRET THAT EVERYONE KNOWS.
4. State the message and back it up (4 min)
Two passages are printed below, one from the middle of the book and one from its end. Read them again. Write or say one sentence giving the book's message about secrets. Then read out the exact words from one of these passages that support it, and say why that line is the best proof.
Word preview: proof
[Caption] WHEN KUNG FU WAS FIRST INVENTED, LEARNING MARTIAL ARTS WAS LIKE HAVING SUPERPOWERS. [Caption] NO MASTER WANTED TO TEACH A BULLY. [Caption] MASTERS WANTED TO KNOW STUDENTS VERY WELL BEFORE TEACHING THEM THEIR BEST SECRETS.
SPEAKER: NOW ALL OF YOU HAVE YOUR OWN KUNG FU JOURNALS. SPEAKER: AND NO ONE WILL BE ABLE TO STEAL LEUNG JAN'S FORMULA. SPEAKER: YOU CAN'T STEAL A SECRET THAT EVERYONE KNOWS.

Short version — 9 minutes

1. Start with a teacher answering a worry (5 min)
The teacher reads the passage below. Say what the student is worried about and what her teacher tells her, then underline the sentence proving what the teacher believes.
Word preview: help
[Caption] A lot of the puzzles don't make sense--like this one. [Caption] I think I need help, but I also feel like I should answer these puzzles on my own. [They exchange the book.] [Caption] Everyone needs help sometimes. Even kung fu masters, like Sigung and me, ask others for help when we're learning something new.
2. Read where the book lands (4 min)
Read the passage below and say its last line aloud. Say in your own words what the book has decided about keeping knowledge secret.
Word preview: message
SPEAKER: NOW ALL OF YOU HAVE YOUR OWN KUNG FU JOURNALS. SPEAKER: AND NO ONE WILL BE ABLE TO STEAL LEUNG JAN'S FORMULA. SPEAKER: YOU CAN'T STEAL A SECRET THAT EVERYONE KNOWS.

Three levels

Support: Use the passage in step 1. The teacher reads the reply. Say the words everyone needs help sometimes. Say whether the teacher thinks asking for help is good or bad.
At Grade: Put the case for keeping secrets and the book's final answer side by side, and state the message in one sentence with a quoted line supporting it.
Extension: The book ends on the line about a secret everyone knows. Say two sentences about whether that line answers the masters' worry about teaching a bully, or simply sets it aside.

English learners

The book's message arrives as a paradox, a secret everyone knows, which is a rhetorical shape rather than a literal claim and can read as a contradiction. Unpack it slowly: if everyone knows it, it is not a secret, so it cannot be stolen. Invite students to offer a saying from their strongest language that works by turning an idea around. Rehearsable frame: The book says ___ because ___.

Materials

Manga Math Mysteries #5: The Ancient Formula, the passage printed in this step
idea tracking chart
Word cards: help, secret, message, proof

Standards & curriculum

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

14. This Sentence Is Broken: Reading a Damaged Page Language · Recognising When a Printed Sentence Has Been Garbled

The last page of this book came out of the scanner tangled: two sentences are interleaved into one, and a fragment of a third is left stranded. The page is printed here exactly as it stands and is not repaired. Students read a clean page first, then the tangled one, work out which phrases got mixed into one another, and say what a careful reader should do. The skill is monitoring your own comprehension and noticing when a text, not the reader, has failed.

Full lesson — 20 minutes

1. Read a page that works (6 min)
The teacher reads the passage below aloud. Every sentence here is whole and does what it should. Read it again together. Say aloud what each sentence tells you about Sifu Leung Jan, and notice how easily you could follow it.
Word preview: whole
[Caption] Sifu Leung Jan was a great kung fu master. --BUT YOU WOULD BOW VERY DEEPLY WHEN YOU SAY IT. [Caption] He was also a doctor. [Caption] He invented a special kind of JOW--Chinese medicine for kung fu students.
2. Read the page that came out tangled (6 min)
Read the passage below exactly as printed. Something has gone wrong: the first sentence has two different sentences mixed into each other, and the next one is only a piece of a sentence. This is how the book was typed up, and we are not fixing it. Read it aloud and say honestly which parts you could not follow.
Word preview: tangled
Page 46 [Caption] Sifu Leung Jan worked so hard to keep teach it to the formula a secret. [Caption] Isn’t it so many of us? JOY: I don’t think so, Joy.
3. Say what the tangle hides (4 min)
The tangled passage is printed again below. With a partner, find the words that seem to belong to one sentence and the words that seem to belong to another. Say aloud one thing the page was probably trying to tell you. Then say how sure you are, and why you cannot be certain.
Word preview: certain
Page 46 [Caption] Sifu Leung Jan worked so hard to keep teach it to the formula a secret. [Caption] Isn’t it so many of us? JOY: I don’t think so, Joy.
4. Say what a good reader does about it (4 min)
Both passages are printed below, the clean one and the tangled one. Read them one after the other. Say two sentences to a partner about what a reader should do when a page stops making sense: how to tell whether the fault is yours or the book's, and why you should not quietly change the words.
Word preview: judge
[Caption] Sifu Leung Jan was a great kung fu master. --BUT YOU WOULD BOW VERY DEEPLY WHEN YOU SAY IT. [Caption] He was also a doctor. [Caption] He invented a special kind of JOW--Chinese medicine for kung fu students.
Page 46 [Caption] Sifu Leung Jan worked so hard to keep teach it to the formula a secret. [Caption] Isn’t it so many of us? JOY: I don’t think so, Joy.

Short version — 9 minutes

1. Read a page that works (5 min)
The teacher reads the passage below. Say what each whole sentence tells you about Sifu Leung Jan and notice how easily you followed it.
Word preview: whole
[Caption] Sifu Leung Jan was a great kung fu master. --BUT YOU WOULD BOW VERY DEEPLY WHEN YOU SAY IT. [Caption] He was also a doctor. [Caption] He invented a special kind of JOW--Chinese medicine for kung fu students.
2. Read the page that came out tangled (4 min)
Read the passage below exactly as printed. Read it aloud and say honestly which parts you could not follow.
Word preview: tangled
Page 46 [Caption] Sifu Leung Jan worked so hard to keep teach it to the formula a secret. [Caption] Isn’t it so many of us? JOY: I don’t think so, Joy.

Three levels

Support: Use the two passages. The teacher reads the clean one, then the tangled one. Say which one made sense. Say the word tangled. You do not have to fix it.
At Grade: Read both passages and say which sentences in the tangled one cannot be followed, and what makes them impossible to read straight through.
Extension: The tangled line mixes worked so hard to keep with teach it to. Say two sentences about what each of the two original sentences might have been, and explain why your answer is a guess rather than a reading.

English learners

Students still building English will assume a confusing sentence is their own failure, and this page would confirm that wrongly. Say clearly and first that this page is broken and that no reader can understand it. Read the clean passage immediately afterwards so the lesson ends on success rather than confusion. Rehearsable frame: I could not follow ___ because the book is ___.

Materials

Manga Math Mysteries #5: The Ancient Formula, the passage printed in this step
sentence untangling strips
Word cards: whole, tangled, certain, judge

Standards & curriculum

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

15. Was Miranda a Thief? Weighing What the Book Tells You Language · Judging a Character Fairly Using What the Text Says

Miranda arrives looking like a thief, is accused in front of the children, and turns out to have a harder story than that. Students gather what the book actually states about her, separate what a character believes from what the book confirms, and give a fair account of her. They also read the line where a student notices that adults can be wrong. The skill is evaluating a character against textual evidence.

Full lesson — 20 minutes

1. Read the accusation and the reaction (6 min)
The teacher reads the passage below aloud. An adult has accused somebody where the children could hear. Read it again together. Say aloud what the children conclude at the end of this passage, and underline the sentence that says it.
Word preview: accused
[Caption] --BUT SIGUNG WAS ANGRY, AND HE ACCUSED MIRANDA WHERE YOU COULD HEAR HIM. [They stand together and talk quietly.] [Caption] YEAH. [Caption] ADULTS-- EVEN KUNG FU MASTERS-- AREN'T ALWAYS PERFECT.
2. Gather what the book actually says about her (6 min)
Read the passage below with a partner. This is the teacher explaining Miranda's past. Write in your evidence column only things the book states plainly. Say aloud one thing you now know about why she left, and one thing the book still has not told you.
Word preview: evidence
[Caption] My grandfather asked Miranda to leave because she was a bully. [Caption] Miranda saw that I was not only strong, but I had sigung and you kids with me. She wouldn't fight me-- [Caption] Not even for something she'd wanted for so long.
3. Separate a belief from a fact (4 min)
Both passages are printed below. Read them again. One of them contains what a character believes about Miranda, and one contains what the book tells you directly. Sort two statements into your columns and say aloud how a reader can tell the difference.
Word preview: opinion
[Caption] --BUT SIGUNG WAS ANGRY, AND HE ACCUSED MIRANDA WHERE YOU COULD HEAR HIM. [They stand together and talk quietly.] [Caption] YEAH. [Caption] ADULTS-- EVEN KUNG FU MASTERS-- AREN'T ALWAYS PERFECT.
[Caption] My grandfather asked Miranda to leave because she was a bully. [Caption] Miranda saw that I was not only strong, but I had sigung and you kids with me. She wouldn't fight me-- [Caption] Not even for something she'd wanted for so long.
4. Give a fair account of her (4 min)
Read the passage printed below one more time. Now say three sentences about Miranda to a partner that you could defend from the book: what she did, why she was asked to leave, and one thing that is still uncertain. Your partner checks that you did not state a guess as a fact.
Word preview: fair
[Caption] My grandfather asked Miranda to leave because she was a bully. [Caption] Miranda saw that I was not only strong, but I had sigung and you kids with me. She wouldn't fight me-- [Caption] Not even for something she'd wanted for so long.

Short version — 9 minutes

1. Read the accusation and the reaction (5 min)
The teacher reads the passage below. Say what the children conclude at the end, and underline the sentence that says it.
Word preview: accused
[Caption] --BUT SIGUNG WAS ANGRY, AND HE ACCUSED MIRANDA WHERE YOU COULD HEAR HIM. [They stand together and talk quietly.] [Caption] YEAH. [Caption] ADULTS-- EVEN KUNG FU MASTERS-- AREN'T ALWAYS PERFECT.
2. Gather what the book actually says about her (4 min)
Read the passage below with a partner. Say one thing you now know about why Miranda left, and one thing the book still has not told you.
Word preview: evidence
[Caption] My grandfather asked Miranda to leave because she was a bully. [Caption] Miranda saw that I was not only strong, but I had sigung and you kids with me. She wouldn't fight me-- [Caption] Not even for something she'd wanted for so long.

Three levels

Support: Use the passage in step 1. The teacher reads the last line. Echo the words aren't always perfect. Say who the children are talking about. Say whether they still respect him.
At Grade: List what the book states plainly about Miranda, and say which claims about her are a character's belief rather than something the book confirms.
Extension: Sigung accuses Miranda, and the book later says she was asked to leave for bullying rather than for stealing. Say two sentences about whether his anger was fair, using only what the book states.

English learners

The distinction this lesson rests on is grammatical as much as moral: he accused her reports somebody's claim, while she was asked to leave states what happened. Both are past tense and look alike. Read a pair of sentences aloud and sort them into said and happened before applying the idea to Miranda. Rehearsable frame: The book says ___. A character thinks ___.

Materials

Manga Math Mysteries #5: The Ancient Formula, the passage printed in this step
evidence and opinion columns
Word cards: accused, evidence, opinion, fair

Standards & curriculum

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