Pythagoras and the Ratios

$Pythagoras and the Ratios book cover$

Grade 4
5 skill lessons · 3 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.

1Exactly Twice as Long
2Stand in a Line According to Height
3Exactly Twice, or More Than Twice
4The Biggest Number That Goes Into Both
5Cut, Not Stretched

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 Decides What You Measure
7Were the Rocks a Good Fix?
8Twenty-Four and Twelve, Said 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.

9The claim the first sentence makes
10Said, cried, quarreled, complained
11What the back matter takes back
12Five names, one word
13Starting on the wrong note

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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. Exactly Twice as Long Concept · Doubling a measured length and checking the double by laying the shorter one along it

Pythagoras will not tune Octavius's pipes by ear. He gives one instruction with a multiplier in it, that each pipe be cut so it is exactly twice as long as his own, and the word exactly is what makes it a measuring job rather than a guess. Students take a short strip as the given pipe, build a strip exactly twice as long, and prove the double by laying the short strip along the long one twice with no gap and no overhang. The book supplies the instruction and the reason for it; the strips supply the check.

Full lesson — 20 minutes

1. Read the instruction and say what exactly rules out (5 min)
With a partner, read the line in which Pythagoras says how long to cut the pipes. Say back to your partner what would count as following it and what would not. Then find the word exactly in the line and say what would change if it were missing: agree on one cut that would still be allowed without the word and would not be allowed with it.
Let’s cut your pipes so that each one is exactly twice as long as mine.”
We can’t change the width of your pipes, but we can change the length.
2. Build the pipe that is exactly twice as long (6 min)
Take the short strip from the envelope. This is Pythagoras's pipe. Cut or fold a second strip from the long blank so that it is exactly twice as long as the short one. Do not use a ruler. Work by laying the short strip down, marking where it ends, and laying it down again from that mark.
Let’s cut your pipes so that each one is exactly twice as long as mine.”
3. Prove it by laying the short strip along it twice (5 min)
Lay the short strip along your new strip starting at one end, mark the end, then move it to the mark and lay it again. Check both things aloud with your partner: that the second laying finishes exactly at the far end, and that neither laying leaves a gap or hangs over. If it does not finish exactly, say by how much it misses, in strips or in part of a strip, and fix it.
Pythagoras cut Octavius’s pipes.
4. Say the sentence about your own strips (4 min)
Say one sentence to another pair that names both of your strips and uses the words exactly twice as long, and then have them check it by laying your short strip along your long one while you watch. Write that same sentence on the report card. The sentence has to say which strip is the long one; a sentence that could describe either strip does not pass.
“Now your pipes sound like mine,” Pythagoras said, “only yours still sound deep while mine sound lighter.

Short version — 9 minutes

1. Build the pipe that is exactly twice as long (5 min)
Your teacher reads Pythagoras's instruction aloud. Take the short strip from the envelope and make a second strip that is exactly twice as long, by laying the short one down, marking where it ends, and laying it down again from that mark. Do not use a ruler.
Let’s cut your pipes so that each one is exactly twice as long as mine.”
2. Prove it by laying the short strip along it twice (4 min)
Lay the short strip along your new strip starting at one end, mark the end, then move it to the mark and lay it again. Check both things aloud with your partner: that the second laying finishes exactly at the far end, and that neither laying leaves a gap or hangs over. If it does not finish exactly, say by how much it misses, in strips or in part of a strip, and fix it.
Pythagoras cut Octavius’s pipes.

Three levels

Support: Work with a long strip that already carries one mark at the halfway point, so the building is a single lay-and-check rather than a lay, mark and lay again. Everything else is unchanged: lay the short strip along the marked strip twice, say aloud whether it finishes exactly at the end, and say the sentence about your own two strips.
At Grade: Build the doubled strip from a blank with no marks on it, prove it by laying the short strip twice, say by how much it misses if it misses, and say and write the sentence naming which strip is the long one.
Extension: Once your doubled strip passes, make a third strip that is exactly twice as long as the doubled one, and then say how many times the first short strip lays along the third. Say whether you could have found that number without building the third strip, and how.

English learners

The action carries the meaning here and transfers whole: a student with little English can lay the short strip twice and see for themselves whether it finishes at the end. The English that gets in the way is the frame twice as long as, in which the comparison word sits before the adjective and the thing compared to arrives last, an order many languages do not use, and the adverb exactly, which children often hear as a filler rather than as a condition. Rehearse one frame all lesson: This strip is exactly twice as long as that one. Students may argue about whether a strip passed in their strongest language and give the report sentence in English while pointing along both strips. Nobody is asked to say anything about themselves.

Materials

The two lines of Pythagoras's instruction on a card, one per pair
An envelope per pair holding one short paper strip and one long blank strip
A pencil
The two strips from the previous step
A report card with one sentence line, one per student
A long strip pre-marked at its halfway point, for the Support
A second long blank strip, for the Extension
Word cards: exactly, twice as long, measure

Standards & curriculum

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

2. Stand in a Line According to Height Representation · Ordering five measured lengths and naming the position of each in the order

Amara wants the front and Reyna says she is shorter, and Pythagoras settles it not by choosing between them but by giving a rule that settles every case at once: stand in a line according to height. He then states the whole order by name. Students order five strips of different lengths without a ruler, by laying each against the others, and then say and write where each strip sits in the order and what makes it sit there.

Full lesson — 20 minutes

1. Read the rule and the order it produced (4 min)
With a partner, read the line in which Pythagoras gives the rule for standing, and the line in which he says the order it produces. Say back what the rule is about, in one sentence, and then say who is at each end of the line he names. Say whether the rule alone tells you the order or whether you would also have to know something the sentence does not say.
“Why don’t you stand in a line according to height,” Pythagoras said.
“It should be Reyna, Amara, Thanos, Ionius, Octavius.”
2. Order the five strips by laying them against each other (6 min)
Tip the five strips out of the envelope. Without a ruler, put them in order from shortest to longest by laying pairs of strips side by side with their ends level. Every time you decide that one strip goes before another, say aloud to your partner which two you compared and which was shorter.
“Why don’t you stand in a line according to height,” Pythagoras said.
3. Name the position of each strip (5 min)
Lay your ordered strips on the five numbered places. Point at each strip in turn and say its position out loud, first, second, third, fourth, fifth, together with one thing that is true of it, either that it is longer than the one before or shorter than the one after. The strip at each end gets only one of those two.
“You’re standing in the same order as when you were playing, and your heights have a similar relationship to the lengths of the pipes.
4. Check another pair's order without moving it (5 min)
Swap tables with another pair. Without moving any strip, decide whether their order is right, and say to them which two strips you would compare to settle it if you were allowed to lift them. Then say Reyna's line about being the right size and say what it means about her place in the line rather than about her height on its own.
“I’m not small now,” Reyna said happily.
“I’m the right size for our group.”

Short version — 9 minutes

1. Order the five strips by laying them against each other (5 min)
Your teacher reads the rule Pythagoras gives for standing in a line. Tip out the five strips and put them in order from shortest to longest by laying pairs side by side with their ends level, saying aloud each time which two you compared and which was shorter.
“Why don’t you stand in a line according to height,” Pythagoras said.
2. Name the position of each strip (4 min)
Lay your ordered strips on the five numbered places. Point at each strip in turn and say its position out loud, first, second, third, fourth, fifth, together with one thing that is true of it, either that it is longer than the one before or shorter than the one after. The strip at each end gets only one of those two.
“You’re standing in the same order as when you were playing, and your heights have a similar relationship to the lengths of the pipes.

Three levels

Support: Order four strips instead of five, and start from two that are already placed at the ends. Everything else is unchanged: lay pairs side by side to decide, say aloud which two you compared each time, and say the position of each strip when they are all down.
At Grade: Order all five strips from a loose pile, say aloud which two you compared for every decision, name every position with one true thing about the strip in it, and check another pair's order without lifting a strip.
Extension: After your five are in order, take one strip away and hand your partner a sixth strip they have not seen. Have them place it in the order using no more than three comparisons, and say beforehand which three they will make and why those three are enough.

English learners

Ordering by laying strips together is language-independent and a student can do the whole of it silently and correctly. Two pieces of English carry the load and both are worth rehearsing rather than assuming. The first is the ordinal series first, second, third, fourth, fifth, which is irregular in English at its start and is not built the same way in every language. The second is the pair shorter than and longer than, where the compared thing follows than, and where children often produce the correct comparison with the two objects the wrong way round. Rehearse two frames: This one is shorter than that one. and This one is third. A student may reason about the order in their strongest language and give the positions in English while pointing along the line.

Materials

A card carrying Pythagoras's rule and the order he states, one per pair
An envelope per pair holding five paper strips of different lengths
A strip of paper marked with five numbered places
The five ordered strips and the numbered places from the previous step
A check card with a place for two strip numbers, one per pair
A sixth paper strip of a length between two of the others, for the Extension
Word cards: order, shorter than, longer than, position

Standards & curriculum

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

3. Exactly Twice, or More Than Twice Reasoning · Deciding whether a comparison of two measured lengths may be called exact

Pythagoras compares the two sets of pipes in one sentence and uses two different comparisons in it: the widths are exactly twice, the lengths are more than twice. Both are comparisons of the same kind between the same two objects, and only one of them is allowed the word exactly. Students measure two widths and two lengths of their own with a strip and no ruler, and decide for each which of the two phrases the measurement earns.

Full lesson — 20 minutes

1. Find the two comparisons in one sentence (4 min)
Read the sentence in which Pythagoras compares the two sets of pipes. With a partner, find the two comparisons inside it and say which part of a pipe each one is about. Then say which comparison is allowed the word exactly and which is not, and say what that tells you about the two measurements.
“Each of your pipes is exactly twice as wide as mine,” he said, “but they are more than twice as long.
Pythagoras compared the two sets of pipes.
2. Measure the two widths with the narrow strip (5 min)
Take the two card pipes from the envelope. Lay the narrow strip across the width of the small pipe, mark that width on the strip, then lay the marked strip across the width of the large pipe twice, end to end. Say aloud to your partner whether the two layings finish exactly at the far edge, or fall short, or overhang.
Pythagoras measured the length and width of each pipe.
3. Measure the two lengths the same way (6 min)
Do the same for the lengths. Mark the length of the small pipe on a fresh strip, then lay that marked strip along the large pipe twice. Say aloud whether the second laying finishes exactly at the end, falls short, or goes past it, and say roughly how far past, in whole strips or part of a strip.
Pythagoras measured the length and width of each pipe.
Octavius used the stylus to scratch the measurements into the clay tablet.
4. Choose the phrase each measurement earns (5 min)
For the widths and again for the lengths, choose one of the two phrases from the book, exactly twice as wide or more than twice as long, and say it to another pair with your strips on the table as the evidence. The listening pair must not agree until they have laid your marked strip themselves. Write both chosen phrases on the record card and, beside each, write what you saw the strip do.
“Each of your pipes is exactly twice as wide as mine,” he said, “but they are more than twice as long.

Short version — 9 minutes

1. Measure the two lengths the same way (5 min)
Your teacher reads the comparison sentence aloud and says that only one half of it is allowed the word exactly. Mark the length of the small pipe on a strip, lay that strip along the large pipe twice, and say aloud whether the second laying finishes at the end, falls short, or goes past.
Pythagoras measured the length and width of each pipe.
Octavius used the stylus to scratch the measurements into the clay tablet.
2. Choose the phrase each measurement earns (4 min)
For the widths and again for the lengths, choose one of the two phrases from the book, exactly twice as wide or more than twice as long, and say it to another pair with your strips on the table as the evidence. The listening pair must not agree until they have laid your marked strip themselves. Write both chosen phrases on the record card and, beside each, write what you saw the strip do.
“Each of your pipes is exactly twice as wide as mine,” he said, “but they are more than twice as long.

Three levels

Support: Compare only the lengths, and leave the widths out. Everything else is unchanged: mark the small pipe on the strip, lay it twice along the large one, say what you saw the strip do, and choose which of the two phrases from the book that earns.
At Grade: Compare both the widths and the lengths, choose the phrase each one earns, and say beside each choice what the strip did that made you choose it rather than the other phrase.
Extension: Say what would have to be true of the large pipe's length for the sentence to have read exactly twice as long instead. Then, without measuring again, say whether a pair who had used a strip twice as wide as yours would have reached the same two verdicts, and why.

English learners

The measuring transfers whole and the verdict does not: a student can see the overhang and still not have the words for it. Two things in the English are hard here and neither is about vocabulary difficulty. The first is that more than twice as long is one comparison built out of two, and the more than has to attach to the whole of twice as long rather than to long. The second is that exactly and more than sit in the same slot in the sentence and do opposite work. Rehearse both frames side by side all lesson: This one is exactly twice as wide as that one. and This one is more than twice as long as that one. Students may work out the verdict in their strongest language and say the chosen phrase in English while pointing at the overhang.

Materials

The comparison sentence enlarged on a card, one per pair
An envelope per pair holding two card pipes, one small and one large
A narrow paper strip
A pencil
A second narrow paper strip
A record card with two lines and a space beside each, one per student
A wider paper strip, for the Extension
Word cards: exactly, more than, width, length

Standards & curriculum

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

4. The Biggest Number That Goes Into Both Fluency · Finding the largest number that divides two given numbers exactly

The book names the thing it is looking for twice, once in Pythagoras's own words as the greatest common factor and once in the narration in plain words as the biggest number that could go into the top and bottom numbers. It then works one pair all the way through: for 24 and 12 the number is 12. Students build both numbers of a pair out of counters, try equal-group sizes from the largest down, and keep the largest size that leaves nothing over in either number.

Full lesson — 20 minutes

1. Read the two names for the same thing (4 min)
With a partner, read Pythagoras's line naming what to divide by, and the narration line that says the same thing in ordinary words. Say back to your partner what is being looked for, in your own words, and say the two conditions it has to meet: it goes into both numbers, and no bigger number does.
“We can simplify these numbers,” Pythagoras said, “if we divide both the top and bottom numbers by the greatest common factor.
For each pair Pythagoras figured out the biggest number that could go into the top and bottom numbers.
2. Work the book's own pair with counters (6 min)
Count out 24 counters into one tray and 12 into the other. Try to split both trays into equal groups of the same size, starting at 12 and working down. For each size you try, say aloud whether it leaves nothing over in both trays. Stop at the first size that works for both and say why you do not need to try any smaller size.
For 24 over 12, I can divide both by 12.”
3. Find the number for two more pairs (6 min)
Take the pair cards. For each pair, build both numbers in the trays and find the biggest equal-group size that leaves nothing over in either tray, working down from the smaller of the two numbers. Write the size you found on the card. If two group sizes both work, keep the bigger one and cross out the smaller.
For each pair Pythagoras figured out the biggest number that could go into the top and bottom numbers.
4. Say the sentence about one of your pairs (4 min)
Choose one of your pairs and say a sentence to another pair that names both numbers and the size you found, and says that no bigger size works. Write that sentence on the record card. The listening pair checks it by building one of the two numbers and making the groups.
Octavius wrote 24 over 12, then 20 over 12, and so on, to compare the other five pipes to the shortest one.

Short version — 9 minutes

1. Work the book's own pair with counters (5 min)
Your teacher reads the line in which Pythagoras divides both numbers by 12. Count out 24 counters into one tray and 12 into the other, and try equal-group sizes from 12 downwards until you find one that leaves nothing over in both trays.
For 24 over 12, I can divide both by 12.”
2. Find the number for two more pairs (4 min)
Take the pair cards. For each pair, build both numbers in the trays and find the biggest equal-group size that leaves nothing over in either tray, working down from the smaller of the two numbers. Write the size you found on the card. If two group sizes both work, keep the bigger one and cross out the smaller.
For each pair Pythagoras figured out the biggest number that could go into the top and bottom numbers.

Three levels

Support: Work only the book's pair, 24 and 12, and one more pair whose numbers are both under 12. Everything else is unchanged: build both numbers in the trays, try group sizes from the smaller number downwards, and say aloud whether each size leaves nothing over in both trays.
At Grade: Work the book's pair and two more, in each case naming the size aloud as you find it, writing it on the card, and saying and writing one sentence that names both numbers, the size, and that no bigger size works.
Extension: Make a pair of your own, both numbers under 24, for which the biggest size that works is 1, and give it to another pair to check. Then say what is true about a pair whose biggest size turns out to be one of the two numbers itself.

English learners

Building the groups and seeing what is left over transfers whole, and a student can find the right size with no English by pushing counters. The English is where the difficulty sits, because the book gives the same idea two names of very different registers, greatest common factor and the biggest number that could go into the top and bottom numbers, and a student who knows one may not recognise the other. Treat them as two names for one thing from the first minute and use both aloud every time. Rehearse one frame: The biggest size that works for 24 and 12 is 12. Students may work out and argue the size in their strongest language and give the sentence in English while pointing at the equal groups.

Materials

A card carrying both sentences, one per pair
Two trays and 40 counters per pair
Two pair cards per pair, each carrying two numbers within 24
A record card with one sentence line, one per student
An extra pair card with two numbers under 12, for the Support
A blank pair card, for the Extension
Word cards: factor, goes into, greatest, equal groups

Standards & curriculum

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

5. Cut, Not Stretched Application · Halving a length by folding and checking the two halves against each other

The pipes get shorter, never longer. Pythagoras cannot change their width and will not add to their length, so the only move he has is to cut, and the strips students work with here are cut the same way. Students halve a strip by folding it end to end, check the two halves against each other by laying one on the other, and say which of the two pieces the book's own instruction would have kept.

Full lesson — 20 minutes

1. Find what Pythagoras is allowed to change (4 min)
With a partner, read the line about what can and cannot be changed about Octavius's pipes. Say back which one thing Pythagoras is allowed to change, and then say whether the change he makes to it makes the pipes longer or shorter, using the line about the cutting as your reason.
We can’t change the width of your pipes, but we can change the length.
Pythagoras cut Octavius’s pipes.
2. Fold the strip into two equal parts (5 min)
Take the long strip. Bring one end over to meet the other end exactly, slide the fold until the two ends sit level, and crease. Open it. Say aloud to your partner how many parts the crease has made and whether you expect them to be the same size.
Pythagoras cut Octavius’s pipes.
3. Check the two halves against each other (6 min)
Cut along the crease. Lay one piece exactly on top of the other with one pair of ends level and check the far ends. Say aloud whether they match, and if they do not, say which piece is longer and by about how much. Then lay one piece along the whole uncut strip your teacher displays, twice, and say what that shows.
Pythagoras cut Octavius’s pipes.
“Now your pipes sound like mine,” Pythagoras said, “only yours still sound deep while mine sound lighter.
4. Say which piece the instruction keeps (5 min)
Read the cutting instruction again with your partner. Say to another pair, in one sentence that names both pieces, which piece a pipe maker following that instruction would keep and why the other would be no use. Write that sentence on the record line. Your sentence has to say what the kept piece is half of.
Let’s cut your pipes so that each one is exactly twice as long as mine.”

Short version — 9 minutes

1. Fold the strip into two equal parts (4 min)
Your teacher reads the line about what may be changed about the pipes. Take the long strip, bring one end over to meet the other exactly, slide until the ends sit level, and crease. Open it and say aloud how many parts the crease made.
Pythagoras cut Octavius’s pipes.
2. Check the two halves against each other (5 min)
Cut along the crease. Lay one piece exactly on top of the other with one pair of ends level and check the far ends. Say aloud whether they match, and if they do not, say which piece is longer and by about how much. Then lay one piece along the whole uncut strip your teacher displays, twice, and say what that shows.
Pythagoras cut Octavius’s pipes.
“Now your pipes sound like mine,” Pythagoras said, “only yours still sound deep while mine sound lighter.

Three levels

Support: Work with a strip that already carries a light crease at the fold, so the whole time goes into checking rather than folding. Everything else is unchanged: cut along the crease, lay one piece on the other, say whether the far ends match, and say which piece the instruction would keep.
At Grade: Fold the strip yourself with no crease to follow, cut, check the two pieces against each other, say by about how much they miss if they miss, and say and write which piece the instruction keeps and what it is half of.
Extension: Fold one of your halves in half again and say how many of the new small pieces would lay along the whole strip you started with. Say the number before you check it, then check it, and say what you would expect after one more fold without folding.

English learners

Folding, cutting and laying one piece on another are physical and transfer completely, and a student can show a correct half with no English at all. The English that carries the demand is the word half used two ways in the same lesson, once as a name for a piece and once inside the frame half of, where what follows of is the thing the piece came from. Children frequently produce this is a half and stop, which leaves out exactly the part that makes it mathematics. Rehearse one frame all lesson: This piece is half of the whole strip. Students may compare their pieces in their strongest language and give the sentence in English while holding up both pieces.

Materials

A card carrying the two lines about what may be changed and what was cut, one per pair
A long paper strip per student
Scissors, shared per pair
A record line card, one per student
A long paper strip pre-creased at its midpoint, for the Support
Word cards: half, equal parts, fold

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 Decides What You Measure Integrated · Students measure two pairs of paper pipes with a strip and no ruler, and decide for each pair which of the book's two phrases the measurement earns, exactly twice as wide or more than twice as long, then say a sentence about their own result using the phrase they chose.

Students measure two pairs of paper pipes with a strip and no ruler, and decide for each pair which of the book's two phrases the measurement earns, exactly twice as wide or more than twice as long, then say a sentence about their own result using the phrase they chose.

Full lesson — 20 minutes

1. Find both comparisons in one sentence (4 min)
In pairs, students read the sentence in which Pythagoras compares the two sets of pipes, and find the two comparisons inside it. They say which part of the pipe each comparison is about and which one is allowed the word exactly, then say what the sentence would mean if exactly were dropped from it.
2. Measure the two widths (4 min)
Pairs mark the width of the small card pipe on a strip, then lay the marked strip across the width of the large pipe twice, end to end, and say aloud whether the second laying finishes level, falls short, or goes past.
3. Measure the two lengths (5 min)
Pairs mark the length of the small pipe on a fresh strip and lay it twice along the large pipe. One partner says at each laying what is happening at the far end while the other holds the strips; if the second laying goes past the end they say by roughly how much, as a part of a strip.
4. Choose the phrase and show what earned it (7 min)
For the widths and again for the lengths, pairs choose one of the book's two phrases and say it to another pair with the strips on the table as evidence. The listening pair may not agree until they have laid the strip themselves and said what they saw. Each student then writes both chosen phrases on the record card with a note beside each saying what the strip did.

Short version — 9 minutes

1. Measure the two lengths (5 min)
Pairs mark the length of the small pipe on a fresh strip and lay it twice along the large pipe. One partner says at each laying what is happening at the far end while the other holds the strips; if the second laying goes past the end they say by roughly how much, as a part of a strip.
2. Choose the phrase and show what earned it (7 min)
For the widths and again for the lengths, pairs choose one of the book's two phrases and say it to another pair with the strips on the table as evidence. The listening pair may not agree until they have laid the strip themselves and said what they saw. Each student then writes both chosen phrases on the record card with a note beside each saying what the strip did.

Three levels

Support: Measure the lengths only and leave the widths out, so the whole time goes into one careful iteration and the choice that follows it. The language demand is untouched: the same two phrases to choose between, the same requirement to say what the strip did, the same check by another pair before they may agree.
At grade: Measure both the widths and the lengths, choose the phrase each earns, say and write what the strip did that made you choose it rather than the other phrase, and check another pair's claim by laying their strip yourself.
Extension: Say what would have to be true of the large pipe's length for the sentence to have read exactly twice as long. Then take the pipe pair where the answer was more than twice and say whether it is more than three times as well, and say how you know without laying the strip a third time.

English learners

The measuring transfers whole and the verdict does not: a student can see the overhang perfectly and still lack the words to report it. Two things in the English carry the load and neither is a matter of word difficulty. The first is that more than twice as long is one comparison built out of two, and the more than has to attach to the whole of twice as long rather than to long alone. The second is that exactly and more than occupy the same slot in the sentence and do opposite work, so the sentence looks the same shape either way. Rehearse both frames side by side and keep them displayed: This one is exactly twice as wide as that one. and This one is more than twice as long as that one. Students may settle the verdict in their strongest language and say the chosen phrase in English while pointing at the far end of the strip.

Materials

An envelope per pair holding two card pipes, one small and one large
Two narrow paper strips per pair
A pencil
A record card with two lines and a space for evidence beside each, one per student
The comparison sentence enlarged, with the words exactly and more than boxed
One marked strip shown laid twice across a width, finishing level

Standards & curriculum

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

7. Were the Rocks a Good Fix? Integrated · Students hang rocks on a taut string frame and count how many plucks in ten stay clear of the swinging weight, then take a position on whether the rocks were a good fix and defend it to a partner with their own count in the sentence.

Students hang rocks on a taut string frame and count how many plucks in ten stay clear of the swinging weight, then take a position on whether the rocks were a good fix and defend it to a partner with their own count in the sentence.

Full lesson — 20 minutes

1. Hear both sides from the book (4 min)
In pairs, students read Amara's complaint and Reyna's reply, and Pythagoras's answer to Amara. They say which of the two girls Pythagoras's answer agrees with and which it does not, and say what he offers instead of a fix. Each student says which side they lean to before any plucking, and the teacher records the split.
2. Count ten plucks (5 min)
Pairs hang the weight on the string frame, pluck ten times, and tally on the bench card every pluck that finishes with the weight not touching the plucking hand. One partner plucks and the other tallies, then they swap and do ten more. They say their two counts aloud.
3. Take a position with your number in it (6 min)
Each student says to a partner whether the rocks were a good fix, in one sentence that contains their own count out of ten. The partner is instructed not to agree or disagree until the number has been said. Each then hears the other pair's count, and says which count is larger and by how many.
4. Hold it or change it, and say which number moved you (5 min)
After hearing the other count, each student writes one sentence saying whether they are holding their position or changing it, naming both counts and saying what about the other pair's number does or does not move them. A student who holds must say why the other count is not enough; a student who changes must name the number that changed their mind.

Short version — 9 minutes

1. Count ten plucks (5 min)
Pairs hang the weight on the string frame, pluck ten times, and tally on the bench card every pluck that finishes with the weight not touching the plucking hand. One partner plucks and the other tallies, then they swap and do ten more. They say their two counts aloud.
2. Take a position with your number in it (6 min)
Each student says to a partner whether the rocks were a good fix, in one sentence that contains their own count out of ten. The partner is instructed not to agree or disagree until the number has been said. Each then hears the other pair's count, and says which count is larger and by how many.

Three levels

Support: Use a position card carrying a frame that already holds the shape of the argument, reading I think the rocks were a good fix because I got out of ten plucks clear, and the other pair got. The counting and the comparison are unchanged, and so is the requirement to say whether the other pair's number moves you; only the sentence is supplied.
At grade: Count your own ten plucks, state your position in a sentence containing your count, compare with another pair's count and say which is larger and by how many, then hold or change your position in writing and say what about the other number decided it.
Extension: Argue the position you did not take as strongly as you can, using the same two counts and nothing new. Then say what count out of ten would be low enough to change your mind whatever else was true, and say whether the book's own closing note, that using weights this way does not work in practice, should count as evidence in this argument or not.

English learners

The plucking and the tallying transfer whole and give every student a number to bring to the argument regardless of their English, which is the point of putting the counting before the talking. The English that carries the load is the because clause, where a reason follows a claim in one sentence, and the frame out of ten, in which the smaller number comes first and the whole comes second, an order that is reversed in some languages and that children often produce inverted. Rehearse two frames all lesson and keep them displayed: I got seven out of ten clear. and I think it was a good fix because I got seven out of ten clear. A student may take their position and argue it in their strongest language first and give the final sentence in English while pointing at their tally. Nobody is asked to say anything about themselves or about music they play at home.

Materials

A simple string frame per pair, with one string stretched between two pegs
A small weight per pair, hung from the string on a short loop
A bench card ruled for two sets of ten tallies, one per pair
A position card with two writing lines, one per student
A pencil
Amara's complaint, Reyna's reply and Pythagoras's answer, enlarged and kept up through the lesson
A single class record of the opening split, showing how many students leaned each way before any plucking

Standards & curriculum

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

8. Twenty-Four and Twelve, Said Both Ways Integrated · Students build the longest and shortest pipe as two towers of 24 and 12 cubes, find the relation between them by matching the short tower against the long one, and produce both sentences about it, the one the book's own arrangement invites and the one it does not.

Students build the longest and shortest pipe as two towers of 24 and 12 cubes, find the relation between them by matching the short tower against the long one, and produce both sentences about it, the one the book's own arrangement invites and the one it does not.

Full lesson — 20 minutes

1. Find the two numbers and the direction (4 min)
In pairs, students read the instruction Pythagoras gives Octavius and the sentence saying what Octavius wrote. They say which number is the length of which pipe, and say which of the two the book puts first every time. They say aloud one sentence the book could have written instead and did not.
2. Build the two towers and match them (5 min)
Pairs build a tower of 24 cubes and a tower of 12, stand them side by side with their bases level, and find how many times the short tower fits along the long one by laying it against it and marking the top of each fit. They say the number of fits aloud.
3. Say it the other way round (6 min)
Pairs break the long tower into two equal parts and stand one part beside the short tower to check they match. They then say two sentences about their towers, one beginning with the long tower and one beginning with the short tower, and say what is the same about the two and what changed. Each pair says both to another pair, who must point at the cubes that make each sentence true.
4. Write both and pass one on (5 min)
Each student writes both sentences on the card, then covers one and passes the card to a partner, who must rebuild the arrangement from the visible sentence alone and say what the hidden sentence must have said. Pairs check the rebuild against their own towers.

Short version — 9 minutes

1. Build the two towers and match them (5 min)
Pairs build a tower of 24 cubes and a tower of 12, stand them side by side with their bases level, and find how many times the short tower fits along the long one by laying it against it and marking the top of each fit. They say the number of fits aloud.
2. Say it the other way round (6 min)
Pairs break the long tower into two equal parts and stand one part beside the short tower to check they match. They then say two sentences about their towers, one beginning with the long tower and one beginning with the short tower, and say what is the same about the two and what changed. Each pair says both to another pair, who must point at the cubes that make each sentence true.

Three levels

Support: Build towers of 12 and 6 instead of 24 and 12, so the matching and the breaking are quicker and the same two sentences are reached with fewer cubes to lose count of. The language demand is untouched: both sentences, in both orders, said aloud and written, and the same requirement that a partner point at the cubes.
At grade: Build 24 and 12, find the number of fits by matching, break the long tower to show the relation from the other side, and say and write both sentences with the towers as evidence for each.
Extension: Say a third true sentence about the same two towers that uses neither twice nor half, and show on the cubes what makes it true. Then say whether your third sentence can also be turned round, and if it can, say the reversed form; if it cannot, say what is different about it.

English learners

The building and the matching transfer whole, and a student can show a correct relation with no English by standing the short tower against the long one. The English is where nearly all the difficulty sits and it is structural rather than lexical. Both sentences use the same two nouns and the same relation, and everything that changes is order and one word, so a student cannot rely on new vocabulary to signal that something has changed. The frame half of is the harder of the two, because what follows of is the thing the part came from, and children very often produce this tower is half and stop, which leaves out the half of the sentence that carries the mathematics. Rehearse both frames side by side and keep them displayed: The long tower is twice the short tower. and The short tower is half of the long tower. Students may work out the relation in their strongest language and give both sentences in English while pointing at each tower as they name it.

Materials

Forty unit cubes per pair
A sentence card with two writing lines and a fold, one per student
A pencil
The instruction to write each length above the length of the shortest, and the sentence saying what Octavius wrote, enlarged
One tower of 24 cubes standing beside one of 12, with the short tower shown laid against the long one

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.

9. The claim the first sentence makes Comprehension · Supporting a stated character trait with evidence from later in the text

The book's opening sentence makes a two-part claim about Pythagoras and then spends the rest of the pages testing it. Students find the claim, gather passages that prove each half, weigh one passage that proves both at once, and finally ask whether the ending upholds or revises it. Every judgement is anchored to quoted words, and nothing on the page needs to be counted.

Full lesson — 20 minutes

1. Find the trait the opening states outright (5 min)
Read the opening aloud. The narrator names what Pythagoras is like in one word and then, in the same sentence, names the trouble it causes him. Underline the trait word and underline the consequence. Say both aloud as one claim.
Word preview: curious
Long ago in ancient Greece, there lived a curious boy named Pythagoras. He liked finding out how things worked, which sometimes caused him to forget to finish his chores. One day Pythagoras had just finished proving that rocks cannot float when he heard a deep and horrible howling sound.
2. Collect the evidence the story supplies later (5 min)
The opening makes a claim; these two passages test it. Read both and, for each, write in your notebook which half of the opening claim it proves — the curiosity or the forgotten chores. Quote the words that do the proving.
Word preview: evidence
“That sounded excellent, but we’ve come to warn you, Pythagoras. You’re in trouble,” his cousin Amara said. “What have I done now?” Pythagoras asked. “Nothing,” Reyna said. “That’s the trouble. You were supposed to help your father gather olives today.”
“Today the mason went home because the rocks were not moved out of his way,” his father said. “Your mother asked you to do that yesterday.”
3. Weigh a passage that proves both halves at once (5 min)
This passage does something the others do not: it shows the curiosity and the forgetting in the same breath. Read it aloud in two voices. Then say which of Pythagoras's own words prove the curiosity and which prove the forgetting.
Word preview: responsibilities
“Father,” Pythagoras gasped, “I’m sorry I forgot about the olives, but I made an amazing discovery. I know how to tune pipes!” “You need to tune in to your responsibilities,” his father replied sternly. “Now fill this pannier with olives and then come home.”
4. Decide whether the ending settles the claim (5 min)
Read the closing lines. Say whether they claim Pythagoras stopped being curious, stopped forgetting, or something else, and quote the exact words that decide it. Then write one sentence saying whether the story's opening claim still holds at the end.
Word preview: better
That summer Pythagoras was better at finishing his chores. His father even gave him a new set of pipes and let him play music with his cousins every day.

Short version — 9 minutes

1. Find the trait the opening states outright (4 min)
Read the opening aloud. Underline the word naming what Pythagoras is like and underline the trouble it causes him. Say both aloud as one claim.
Word preview: curious
Long ago in ancient Greece, there lived a curious boy named Pythagoras. He liked finding out how things worked, which sometimes caused him to forget to finish his chores. One day Pythagoras had just finished proving that rocks cannot float when he heard a deep and horrible howling sound.
2. Collect the evidence the story supplies later (5 min)
Read both passages. For each, say which half of the opening claim it proves — the curiosity or the forgotten chores — and quote the words that prove it.
Word preview: evidence
“That sounded excellent, but we’ve come to warn you, Pythagoras. You’re in trouble,” his cousin Amara said. “What have I done now?” Pythagoras asked. “Nothing,” Reyna said. “That’s the trouble. You were supposed to help your father gather olives today.”
“Today the mason went home because the rocks were not moved out of his way,” his father said. “Your mother asked you to do that yesterday.”

Three levels

Support: Work with the curiosity half of the claim only. Give the student the opening and the olive passage, and ask them to point to one thing Pythagoras did because he wanted to find something out. Pointing plus one spoken sentence is the whole task.
At Grade: Find both halves of the opening claim and match at least one quoted passage to each. Say which passage is the strongest proof and why.
Extension: The closing lines say Pythagoras was better at finishing his chores, not that he stopped being curious. Say what the story would have to end with for the opening claim to be fully overturned, and whether this ending comes close.

English learners

The trait word curious is easily confused with strange, and its English sense here is the wanting-to-know one — name that before reading. Rehearse the evidence frame aloud: The story says he is ___. I know because ___. Students may gather and mark evidence silently and give the reason in their strongest language before rendering it in English.

Materials

Printed opening
Pencil
Both printed evidence passages
Notebook
Printed olive passage
Printed closing lines
Word cards: curious, evidence, responsibilities, better

Standards & curriculum

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

10. Said, cried, quarreled, complained Language · Reading what a dialogue tag adds beyond the spoken words

This book almost never lets a line of speech stand bare: it attaches a verb that reports the feeling behind it, and once it reports a nod instead of a voice. Students strip a tag away and put it back, rank several tags by how much they carry, find the one that reports a body rather than a voice, and then swap one to see what the exchange loses. The whole lesson lives in verb choice.

Full lesson — 20 minutes

1. Read the line without the tag, then with it (5 min)
Read the quarrel aloud twice: first read only the words inside the quotation marks, then read the whole thing including the words that say who spoke and how. Say what the tag added that the spoken words alone did not carry.
Word preview: quarreled
“I want to stand in front,” Amara said. “But I’m shorter!” Reyna quarreled.
2. Rank three tags by how much they tell you (5 min)
Here are three exchanges. Circle every word that reports how someone spoke — said, cried, complained, and any others. Rank the three passages by how much their tags tell you about the speaker's feeling, and defend your top choice aloud.
Word preview: complained, cried
“Cut them!” Octavius cried. “What if they sound worse?” “Believe me,” Pythagoras said, “nothing could sound worse.”
“How can I play a lyre with rocks swinging back and forth, hitting me?” Amara complained.
“Octavius,” said Pythagoras to his cousin, “were you making that awful noise?” “Unfortunately, yes,” Octavius said, nodding.
3. Find the tag that reports a body, not a voice (5 min)
One of the tags you circled reports something the speaker did with his body rather than something he did with his voice. Find it, say it aloud, and say what it tells you that a voice word could not. Then say what it suggests about how willingly Octavius answered.
Word preview: nodding
“Octavius,” said Pythagoras to his cousin, “were you making that awful noise?” “Unfortunately, yes,” Octavius said, nodding.
4. Swap a tag and test what changes (5 min)
Take this exchange and read it aloud swapping one tag for a different one — replace complained with asked, or with laughed. Say what changes about the speaker in your version. Then write one sentence explaining why the author's choice fits the story better, or does not.
Word preview: swap
“How can I play a lyre with rocks swinging back and forth, hitting me?” Amara complained.

Short version — 9 minutes

1. Read the line without the tag, then with it (4 min)
Read the quarrel aloud twice: only the quoted words, then the whole thing. Say what the tag added that the spoken words alone did not carry.
Word preview: quarreled
“I want to stand in front,” Amara said. “But I’m shorter!” Reyna quarreled.
2. Rank three tags by how much they tell you (5 min)
Circle every word reporting how someone spoke. Rank the three passages by how much their tags tell you about the speaker's feeling, and defend your top choice aloud.
Word preview: complained, cried
“Cut them!” Octavius cried. “What if they sound worse?” “Believe me,” Pythagoras said, “nothing could sound worse.”
“How can I play a lyre with rocks swinging back and forth, hitting me?” Amara complained.
“Octavius,” said Pythagoras to his cousin, “were you making that awful noise?” “Unfortunately, yes,” Octavius said, nodding.

Three levels

Support: Use the quarrel passage alone. Read it once as said and once as quarreled and let the student say which sounds angrier. Naming the difference aloud is the whole task; no ranking is needed.
At Grade: Circle every tag across the three exchanges, rank them by how much feeling they carry, and defend the ranking with the words themselves.
Extension: Two of these tags — cried and complained — could each be replaced by said without changing a single spoken word. Say what the story would lose in each case, and say whether the loss is the same size in both.

English learners

The tag verbs are the load here and several are near-synonyms in dictionary terms while differing sharply in feeling: said, cried, complained, quarreled, exclaimed. Act each one out before reading rather than defining it. Rehearse the frame aloud: She said it ___, so she felt ___. A student may read the quoted speech in their strongest language and the tag verb in English.

Materials

Printed quarrel passage
All three printed exchanges
Pencil
Printed noise exchange
Printed lyre complaint
Notebook
Word cards: quarreled, complained, cried, nodding, swap

Standards & curriculum

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

11. What the back matter takes back Comprehension · Telling what a text asserts as fact from what it presents as a story

This book tells a scene and then, in its own back matter, tells the reader that the scene probably never happened — while still holding on to a narrower claim it can defend. Students read the scene, read the source it came from, locate the retraction, and finish by naming the word the book substitutes for a claim of fact. The skill is separating what a text asserts from what it stages.

Full lesson — 20 minutes

1. Read what the story shows Pythagoras doing (5 min)
Read this exchange from the story. Say aloud what Pythagoras does here with the rocks and the strings, in one sentence of your own. Keep that sentence; you will test it against the book's own back matter.
Word preview: lyre
“How can I play a lyre with rocks swinging back and forth, hitting me?” Amara complained.
2. Read what the back matter says was written down (5 min)
The book's back matter names where the story came from. Read it and say who wrote the account, roughly when, and what that account claimed Pythagoras did. Underline the phrase in which the book admits the story is borrowed.
Word preview: According
During the second century CE, Greek mathematician Nichomachus of Gerasa wrote of Pythagoras’s experiment with musical strings. According to Nichomachus’s story, Pythagoras hung weights from strings (similar to what young Pythagoras does in this book) and found a mathematical ratio for the harmonious sounds he created.
3. Find where the book takes its own story back (5 min)
Read this passage and find the sentence in which the book says the events probably did not happen. Say it aloud. Then say what the same passage still claims is true, and mark the word that separates the two claims.
Word preview: likely
Today’s scholars point out that while the ratios as Nichomachus described them do correspond with the tones described, using weights to attain this result does not work in practice. It’s likely that Pythagoras never performed this experiment, but interestingly enough, Pythagoras did successfully perform similar mathematical experiments on another stringed instrument called a monochord.
4. Say what the book claims for itself in the end (5 min)
Read this closing line of the back matter. It stops claiming the story happened and claims something else instead. Say what word it uses in place of a claim of fact, and write one sentence saying what a reader should now believe about the rocks on the lyres.
Word preview: celebrates
Like Nichomachus’s tale, our story celebrates Pythagoras’s discovery of the relationship between mathematics and music.

Short version — 9 minutes

1. Read what the back matter says was written down (5 min)
Read the back matter naming where the story came from. Say who wrote the account and what it claimed Pythagoras did. Underline the phrase admitting the story is borrowed.
Word preview: According
During the second century CE, Greek mathematician Nichomachus of Gerasa wrote of Pythagoras’s experiment with musical strings. According to Nichomachus’s story, Pythagoras hung weights from strings (similar to what young Pythagoras does in this book) and found a mathematical ratio for the harmonious sounds he created.
2. Find where the book takes its own story back (4 min)
Find the sentence saying the events probably did not happen and say it aloud. Then say what the passage still claims is true.
Word preview: likely
Today’s scholars point out that while the ratios as Nichomachus described them do correspond with the tones described, using weights to attain this result does not work in practice. It’s likely that Pythagoras never performed this experiment, but interestingly enough, Pythagoras did successfully perform similar mathematical experiments on another stringed instrument called a monochord.

Three levels

Support: Use the scholars passage alone. Read it aloud with the student and ask a single question: does this passage say the rock experiment really happened? Let them find the word likely and answer from it.
At Grade: Match the scene to the back matter, locate the retraction, and say in your own words what a reader should now believe about the rocks.
Extension: The scholars passage denies one thing and affirms another in a single sentence joined by but. Say precisely what is denied and what is affirmed, and say why the author might have wanted both halves in one sentence rather than two.

English learners

Hedging language does the work in this lesson and it is exactly what a reader in a second language skips: It's likely, According to, scholars point out, our story celebrates. Read those four phrases aloud on their own before the passages. Rehearse the frame: The book says ___ probably did not happen, but ___ is still true.

Materials

Printed lyre complaint
Notebook
Printed back matter on Nichomachus
Pencil
Printed scholars passage
Printed closing back-matter line
Word cards: lyre, According, likely, celebrates

Standards & curriculum

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

12. Five names, one word Vocabulary · Working out a word built from the first letters of other words

The book plants a list of five names in a fixed order and then, pages later, builds a word out of their first letters and has the character explain the trick in his own dialogue. A second joke rides on top of it in the closing line. Students reconstruct how the word was assembled, name what the joke buys the reader, and read one cousin's reply as a piece of characterisation rather than as wordplay.

Full lesson — 20 minutes

1. Read the line-up that sets the reveal up (5 min)
Read this passage aloud. Pythagoras names five cousins in a fixed order. Write the five names down that order in your notebook, exactly as he says them, because the order matters later.
Word preview: order
“Why don’t you stand in a line according to height,” Pythagoras said. “It should be Reyna, Amara, Thanos, Ionius, Octavius.”
2. Find how the word is made (5 min)
Read this passage aloud. Pythagoras coins a word here. Take the list of names you wrote down, mark the first letter of each, and say aloud how those letters make the word he coins. Then quote the words in which he explains the trick himself.
Word preview: coins
“This is funny,” Pythagoras said to his cousins. “You’re standing in the same order as when you were playing, and your heights have a similar relationship to the lengths of the pipes. So I was thinking, when we measure relationships, let’s call them RATIOs for the first letters of your names.”
“Why don’t you stand in a line according to height,” Pythagoras said. “It should be Reyna, Amara, Thanos, Ionius, Octavius.”
3. Say what the joke costs and what it buys (5 min)
The word Pythagoras coins is a real word he could not actually have invented this way. Say what a reader gets from the joke anyway. Then read this closing line, which extends the same joke into a second one, and say what two meanings the phrase rock group carries here.
Word preview: rock
Whenever they performed, they introduced themselves as Pythagoras and the Ratios—the first rock group.
4. Hear how one cousin reads herself into the word (5 min)
Reyna answers the coining with something about herself, not about the word. Read her line aloud. Say what she was unhappy about earlier and what the line-up changed for her. Then write one sentence saying why the author gave her the last word here rather than giving it to Pythagoras.
Word preview: size
“I’m not small now,” Reyna said happily. “I’m the right size for our group.”
“I want to stand in front,” Amara said. “But I’m shorter!” Reyna quarreled.

Short version — 9 minutes

1. Read the line-up that sets the reveal up (4 min)
Read this passage aloud. Write the five cousins' names in the order Pythagoras says them, exactly as he says them.
Word preview: order
“Why don’t you stand in a line according to height,” Pythagoras said. “It should be Reyna, Amara, Thanos, Ionius, Octavius.”
2. Find how the word is made (5 min)
Read this passage aloud. Mark the first letter of each name on your list and say how those letters make the word Pythagoras coins. Quote the words in which he explains the trick.
Word preview: coins
“This is funny,” Pythagoras said to his cousins. “You’re standing in the same order as when you were playing, and your heights have a similar relationship to the lengths of the pipes. So I was thinking, when we measure relationships, let’s call them RATIOs for the first letters of your names.”
“Why don’t you stand in a line according to height,” Pythagoras said. “It should be Reyna, Amara, Thanos, Ionius, Octavius.”

Three levels

Support: Write the five names in a column with the first letter of each in a different colour, and let the student read down the coloured column aloud. Hearing the word fall out of the letters is the whole task.
At Grade: Reconstruct the word from the ordered names, quote the line in which Pythagoras explains the trick, and say what the closing rock group line adds.
Extension: The trick only works because the cousins were lined up by height first. Say what would have happened to the word if Amara had got her way and stood in front, and say what that tells you about how carefully the author arranged the earlier scene.

English learners

A word built from initials is a device many writing systems do not use in the same way, so demonstrate it with a familiar English example before reading. The double meaning of rock — the stones on the lyres and a kind of music — needs naming outright; it cannot be inferred. Rehearse aloud: The first letters are ___, and together they spell ___.

Materials

Printed line-up passage
Notebook
Both printed passages
Pencil
Printed closing line
Both printed Reyna passages
Word cards: order, coins, rock, size

Standards & curriculum

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

13. Starting on the wrong note Comprehension · Tracing how a character changes and quoting what marks the change

Two brothers arrive to stop their sisters performing and, within a few lines, ask to join instead. The book marks the turn with an apology built out of a musical phrase used about behaviour. Students read both moments in voices, name what shifted, unpack the double-duty phrase, and finally write the change as one claim carrying a quotation from each end of it.

Full lesson — 20 minutes

1. Read what the brothers come to say (5 min)
Read this passage aloud in two voices. Say what Thanos and Ionius came to do, and quote the exact words that give their reason. Say who they are speaking about and who they are speaking to.
Word preview: embarrass
“We’ve come to tell you that our sisters won’t be joining you,” announced Thanos. “We don’t want them to embarrass the family by trying to play their lyres together,” Ionius added.
2. Read what they say a few lines later (5 min)
Read this second passage aloud in the same two voices. Say what has changed in what they want. Then find the one thing that happened between the two passages that could have changed their minds, and say it in a sentence of your own.
Word preview: apology
“That actually sounded good,” Ionius exclaimed. “I liked it, too,” Thanos added. “I’m sorry we started on the wrong note. Can we join your group?”
3. Read the phrase that carries two meanings at once (5 min)
One phrase in their apology comes from music and is being used about behaviour. Find it and say it aloud. Say what it means about how they behaved earlier, and say why this particular phrase fits this particular story better than a plain apology would.
Word preview: phrase
“That actually sounded good,” Ionius exclaimed. “I liked it, too,” Thanos added. “I’m sorry we started on the wrong note. Can we join your group?”
4. Put the change into one sentence with evidence (5 min)
Write one sentence that names how Thanos and Ionius changed, and attach a quotation from each of the two passages to support it. Read your sentence and both quotations aloud to a partner. Your partner checks that each quotation really says what you claim it says.
Word preview: changed
“We’ve come to tell you that our sisters won’t be joining you,” announced Thanos. “We don’t want them to embarrass the family by trying to play their lyres together,” Ionius added.
“That actually sounded good,” Ionius exclaimed. “I liked it, too,” Thanos added. “I’m sorry we started on the wrong note. Can we join your group?”

Short version — 9 minutes

1. Read what the brothers come to say (4 min)
Read this aloud in two voices. Say what Thanos and Ionius came to do and quote the exact words giving their reason.
Word preview: embarrass
“We’ve come to tell you that our sisters won’t be joining you,” announced Thanos. “We don’t want them to embarrass the family by trying to play their lyres together,” Ionius added.
2. Read what they say a few lines later (5 min)
Read this aloud in the same two voices. Say what has changed in what they want, and say what happened in between that could have changed their minds.
Word preview: apology
“That actually sounded good,” Ionius exclaimed. “I liked it, too,” Thanos added. “I’m sorry we started on the wrong note. Can we join your group?”

Three levels

Support: Read both passages aloud with the student and ask one question: at the start, did the brothers want the girls to play? At the end, did they? Two spoken answers, each pointing at a printed line, complete the task.
At Grade: Name what changed, say what caused it, and support the claim with one quotation from each passage.
Extension: The brothers never say they were wrong about their sisters — only that they started on the wrong note. Say what they have and have not admitted, and say whether their apology fully answers what they came in saying.

English learners

Started on the wrong note is an idiom whose literal reading is a music instruction, which is exactly why the author chose it here; give the figurative meaning outright before reading. Rehearse the change frame aloud: At first they wanted ___. Then they wanted ___. It changed when ___. A student may name the change in their strongest language before quoting the English.

Materials

Printed brothers passage
Printed change-of-mind passage
Both printed brothers passages
Notebook
Word cards: embarrass, apology, phrase, changed

Standards & curriculum

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