Mystery Math

$Mystery Math book cover$

Grade 4
4 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.

1Get the Mystery Number Alone
2Both Sides of the Equal Sign
3Weigh the Mystery Number
4Turn the Story into a Sentence

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.

5The Words That Move the Weight
6The Number the Book Never Prints
7Did He Tell Them or Not?

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.

8Four names for one thing
9Four headings, one shape
10Why is there a haunted house in this book?
11Egor, Igor, Eager
12The seesaw that never leaves

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Skill lessons

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

1. Get the Mystery Number Alone Application · Finding an unknown by undoing the operation on both sides

The book works four haunted-house problems and each one runs the same procedure: name the unknown with a letter, write the sentence, then do one thing to both sides to strip the number away from the letter. Students carry out that procedure on the book's own two additive cases with counters and a balance mat, undoing a minus 6 by adding six to both sides and a plus 12 by subtracting twelve from both sides. The fluency being built is not the arithmetic, which is small, but the discipline of touching both sides the same way and saying why.

Full lesson — 20 minutes

1. Name the unknown (4 min)
Read the raven problem and say what number nobody knows. Write R on a card and put it face down on the left of your mat, then build the sentence around it. Say aloud what R stands for before you touch a counter.
Word preview: unknown
Let R be the number of Ravens on the wires when Mandy and Billy stopped by the house.
R minus 6 equals 13.
2. Undo the subtraction (6 min)
Six ravens flew off, so put six counters back on the left side. The rule says you must do the same to the right, so put six on the right too. Count the right side and say the number. That number is R.
Word preview: eliminate
You must eliminate the minus 6.
You can do that by adding 6 to each side of the equation.
3. Undo the addition (6 min)
Now the bat problem. Twelve bats went in, so take twelve counters off the left side, and take twelve off the right as well. Count what is left on the right and say the number. Check it by putting the twelve back and seeing twenty-seven return.
Word preview: subtracting
y plus 12 equals 27.
You can do that by subtracting 12 from each side of the equation.
4. Say why both sides (4 min)
Your partner does one side only and leaves the other alone. Tell them what goes wrong and show it on the mat. Use the words both sides and still balanced in what you say.
The simple rule is, whatever is done to one side of the equal sign must be done to the other side.

Short version — 9 minutes

1. Name the unknown (3 min)
Read the raven problem and say what number nobody knows. Put a card marked R on the left of your mat and build the sentence around it.
Word preview: unknown
R minus 6 equals 13.
2. Undo the subtraction (6 min)
Put six counters back on the left, then six on the right as well. Count the right side aloud. That number is R.
Word preview: eliminate
You can do that by adding 6 to each side of the equation.

Three levels

Support: Stay with the raven problem for the whole lesson and work it twice, once with the teacher naming each move and once alone. The numbers stay 6 and 13; what is reduced is how many problems, not how much of the procedure.
At Grade: Work both additive problems, ravens and bats, and check each answer by rebuilding the original sentence.
Extension: Take the bat problem and change 27 to a number of your choosing under fifty, then work it and say what happened to y and why it moved the way it did.

English learners

Eliminate is the hard word and it does not transfer; students often know remove or take off already and those are safe substitutes when they explain. The idiom get it alone is opaque even to strong English speakers and should be shown with hands before it is used. Rehearse: I take ___ off both sides, so ___ is alone. Let students narrate the moves in their strongest language while their hands do the work, then name only the final number in English.

Materials

Index cards
A paper equation mat divided by a drawn equal sign
Two-colour counters
Word cards: unknown, eliminate, variable

Standards & curriculum

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

2. Both Sides of the Equal Sign Concept · Reading an equation as two sides that must balance

The book opens by making the equal sign a physical claim rather than an instruction: a seesaw with a pumpkin on it, then a run of equations whose two sides are each computed and compared. Students build both sides of the book's own equations in counters on a mat split by an equal sign, total each side separately, and rule the sentence balanced or not balanced. The equal sign says the two sides name the same amount, not that an answer follows; this matters because the book's four printed sentences include 4 plus 1 equals 3 plus 2 and 5 minus 1 equals 3 plus 1, neither of which has a lone number on the right.

Full lesson — 20 minutes

1. Build the seesaw sentence (5 min)
Put four counters on the left of your mat and one on the right of the plus sign, then three and two on the far side of the equal sign. Count each side out loud and say the total you get. Say whether the mat balances, and put a hand flat and level to show it.
Word preview: balanced
A seesaw is like an equation.
Whatever is on one side should be balanced by whatever is on the other side.
2. Total each side separately (6 min)
Take the next sentence, 5 minus 1 equals 3 plus 1, and build it. Start with five counters and take one away on the left; build three and one on the right. Say both totals before you say whether it balances. Do not touch a counter on the right while you work the left.
Word preview: equation
5 minus 1 equals 3 plus 1.
The two sides of each equation are balanced.
3. Sort balanced from broken (5 min)
Your teacher hands you cards with a sentence on each. Build both sides of each one and put the card in the balanced pile or the not balanced pile. For every card in the broken pile, say which side is heavier and by how many counters.
6 plus 2 equals 8.
4. Say the rule in your own words (4 min)
Tell your partner what the equal sign is telling you to check. Use the words both sides and the same amount. Then point at a card from the broken pile and say what you would add to one side to make it balance.
Word preview: equal sign
An equation is a sentence with an equal sign.

Short version — 9 minutes

1. Build the seesaw sentence (5 min)
Put four counters on the left of your mat and one beside them, then three and two on the far side of the equal sign. Count each side aloud and say the total. Say whether the mat balances.
Word preview: balanced
A seesaw is like an equation.
2. Total each side separately (4 min)
Build 5 minus 1 equals 3 plus 1. Say both totals before you rule on it. Keep your hands on one side at a time.
Word preview: equation
5 minus 1 equals 3 plus 1.

Three levels

Support: Work only the sentences whose right side is a single number, 6 plus 2 equals 8 and 4 plus 1 equals 5, so one side is built and the other is counted out as a single pile. Everything else stays: two sides, two totals, one ruling.
At Grade: Work all four printed sentences, including the two with an operation on both sides, and rule each one after saying both totals aloud.
Extension: Write a false sentence of your own that looks balanced at a glance, trade with a partner, and make them find the side that is short and say by how much.

English learners

Balanced transfers directly from playground and kitchen scales in most languages, and students can often demonstrate it with their hands before they can say it. Equal sign does not transfer as a name, and the mathematical use of equals as a claim about two sides rather than a cue to answer is the piece that misleads. Rehearse: This side is ___ and this side is ___, so they balance. Invite students to say the two totals in their strongest language first and only the ruling word in English.

Materials

A paper equation mat divided by a drawn equal sign
Two-colour counters
Index cards
Word cards: balanced, equation, equal sign

Standards & curriculum

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

3. Weigh the Mystery Number Representation · Building a balance scale and using it to find a missing weight

The book's back matter gives a full construction procedure for a coat hanger balance and eight penny weights, then poses an equation to be solved by hanging rather than by arithmetic. Students make the weights, hang the eight-penny weight against the two-penny weight, watch it fail, and try weights until the hanger sits level. The representation is what does the teaching: the unknown is a weight you can hold, and balance is something the hanger reports rather than something a student asserts.

Full lesson — 20 minutes

1. Make the weights (6 min)
Make two piles each of two, four, six and eight pennies. Wrap each pile in tape, punch a hole in one end, and mark it with the number of pennies inside. Count the pennies in a pile twice before you tape it shut, because once it is taped you cannot check it.
To make your weights, make two piles each of two pennies, four pennies, six pennies, and eight pennies.
With the fine point marker, mark each weight with the number of pennies inside.
2. Test the scale (4 min)
Hang the four penny weight on one side and two of the two penny weights on the other. Watch the hanger settle. Say what you see and whether the two sides match, then say why four pennies and two twos should hang the same.
Word preview: balance
Hang a four penny weight on one side.
The two sides should balance.
3. Watch it fail (5 min)
Hang the eight penny weight on the left and the two penny weight on the right. Say which side hangs lower and say how you know the sentence is not finished. Do not guess the missing weight yet.
Hang an eight penny weight on the left side of the scale.
The scale is not balanced.
4. Hang until it balances (5 min)
Try weights on the right side next to the two until the hanger sits level. Say the number on each weight you hung and say what the mystery number is. Write the finished sentence with the number in place of the letter.
Word preview: value
Try hanging different weights on the right side.
What is the value of x?

Short version — 9 minutes

1. Watch it fail (4 min)
Hang the eight penny weight on the left and the two penny weight on the right. Say which side hangs lower and say how you know the sentence is not finished.
The scale is not balanced.
2. Hang until it balances (5 min)
Try weights on the right beside the two until the hanger sits level. Say the number on the weight you hung and name the mystery number.
Word preview: value
What is the value of x?

Three levels

Support: Use a scale an adult has already built and weights already marked, and work only the eight against two problem. The hanging and the ruling stay in the student's hands; only the construction is lifted off.
At Grade: Build the weights, test the scale on four against two and two, then solve the eight equals two plus x problem by hanging.
Extension: After you balance it, take the six penny weight off and find another way to balance the same left side using only twos and fours, then say why more than one arrangement can be right.

English learners

Balance is demonstrable and transfers well; students can rule on a hanger before they can describe it. Hangs lower and settles are the phrases that carry the mathematics here and neither is guessable from a dictionary. Rehearse: This side is heavier, so I add ___ to the other side. Numbers can be spoken in the strongest language throughout, since the hanger, not the sentence, reports the answer.

Materials

Forty pennies
Masking tape
A hole puncher
A fine point marker
A coat hanger balance with two paper clips at its ends
Penny weights of two, four, six and eight pennies, each marked with its number
Pencil and notebook
Word cards: balance, value, weight

Standards & curriculum

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

4. Turn the Story into a Sentence Reasoning · Writing a word problem as an equation with a letter for the unknown

Between the story and the arithmetic the book performs a translation it names out loud: it says what the letter stands for, then writes the sentence. Students do only that translation here, for the two problems whose numbers the book supplies, and stop before solving. The reasoning is deciding which number in the story is the whole and which is the part, because the raven story hands the amount that is left and the bat story hands the amount that arrived, and the two produce different sentences from the same shaped scene.

Full lesson — 20 minutes

1. Say what the letter stands for (5 min)
Read the raven story and finish this sentence out loud: R is the number of ___. Write it on your card. Check it against the book's own line and say whether you named the same thing.
Let R be the number of Ravens on the wires when Mandy and Billy stopped by the house.
2. Sort the numbers (5 min)
The raven story gives you two numbers. Say which one is the amount that left and which is the amount still there. Put the two numbers on cards and say which one goes next to the letter and which one goes after the equal sign.
I saw six birds fly away, Mandy told Billy.
Then I counted 13 birds still on the wires.
3. Write both sentences (6 min)
Write the raven sentence and then the bat sentence. Do not solve either one. Read them back to your partner and say what is different about where the numbers sit.
Word preview: equation
R minus 6 equals 13.
y plus 12 equals 27.
4. Say why one is minus and one is plus (4 min)
Tell your partner why the ravens got a minus and the bats got a plus, using what happened in each story. Then take the kitten story and say what its letter would stand for, without writing the sentence.
Let K be the number of kittens.

Short version — 9 minutes

1. Sort the numbers (4 min)
The raven story gives two numbers. Say which is the amount that left and which is the amount still there, and say where each one goes in the sentence.
Then I counted 13 birds still on the wires.
2. Write both sentences (5 min)
Write the raven sentence and the bat sentence. Do not solve either. Say what is different about where the numbers sit.
Word preview: equation
y plus 12 equals 27.

Three levels

Support: Work the raven story alone, with the letter and the two numbers already written on separate cards, and place the cards into a sentence frame that has the minus and the equal sign printed on it. The decision students make is which number goes where.
At Grade: Write both sentences from the stories with nothing pre-printed, and explain the difference in the sign.
Extension: Write the kitten sentence too, then say why its letter is joined to the 4 with no sign written between them and what that missing sign means.

English learners

Let R be the number of is a mathematical frame with no everyday equivalent, and it is the sentence to rehearse verbatim rather than to paraphrase. Flew away and still on the wires are the words that decide the sign, and students who miss still will build the wrong sentence with correct arithmetic. Rehearse: ___ is the number of ___ at the start. Invite students to retell the raven story in their strongest language before writing anything, so the sign is decided by the story rather than by guessing.

Materials

Index cards
Pencil and notebook
Word cards: unknown, equation

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.

5. The Words That Move the Weight Integrated · Students test four of the book's operation words by acting each one out on a balance mat and saying what a swapped word would make their hands do instead.

Students test four of the book's operation words by acting each one out on a balance mat and saying what a swapped word would make their hands do instead.

Full lesson — 20 minutes

1. Act out the book's words (6 min)
Pairs build R minus 6 equals 13 on the mat and carry out the book's instruction exactly, adding six to each side and saying the number they reach.
2. Swap one word and predict (5 min)
Each pair is given one swapped sentence and says aloud, before touching anything, what their hands will do differently and what the sentence will become.
3. Build the swapped version (5 min)
Pairs perform the swapped instruction on the mat and say whether the sentence still balances, and if not, which side is short and by how much.
4. Report the word that mattered (4 min)
Each pair names their word and tells the class the smallest thing that changed in their hands when the word changed.

Short version — 9 minutes

1. Act out the book's words (6 min)
Pairs build R minus 6 equals 13 on the mat and carry out the book's instruction exactly, adding six to each side and saying the number they reach.
2. Swap one word and predict (5 min)
Each pair is given one swapped sentence and says aloud, before touching anything, what their hands will do differently and what the sentence will become.

Three levels

Support: Work only the each swap, and hear both sentences read aloud before predicting. The mat is prebuilt with R minus 6 equals 13 already laid out, so the whole of the student's attention is on what the one word tells their hands to do.
At grade: Work two swaps, each and eliminate, predicting before building both times and reporting which produced the larger error.
Extension: Take the equals swap and argue whether then could ever be a safe reading of any sentence in this book. Find the printed sentence where it would do least damage and say why the damage is still real.

English learners

Three of the four words are ordinary English carrying mathematical freight, which is the hardest case for a multilingual reader: each, over and equals will all be recognised and all three will be read in their everyday sense. Eliminate is the opposite problem, unfamiliar to nearly everyone and therefore approached carefully. Rehearse the frame The book says ___, so I ___ to both sides. Students should predict in their strongest language and say only the two versions of the instruction in English, since the prediction is the reasoning and the English is the evidence.

Materials

A paper equation mat divided by a drawn equal sign
Two-colour counters
A card carrying one swapped sentence
The four book sentences, each written large with its one word underlined

Standards & curriculum

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

6. The Number the Book Never Prints Integrated · Students find the one weight that levels the hanger, then write the sentence from the book that proves six is the only answer it could have been.

Students find the one weight that levels the hanger, then write the sentence from the book that proves six is the only answer it could have been.

Full lesson — 20 minutes

1. Read the set-up and stop (4 min)
Students read the balance problem as far as the question, hang the eight and the two, and say aloud what the hanger is telling them and what the book has not told them.
2. Find the weight (5 min)
Pairs try weights on the right until the hanger levels, recording each one they try and whether it was too heavy or too light.
3. Prove it had to be six (6 min)
Pairs find the two sentences that fix the answer and say what each one rules out, then explain why no other weight in their set could have worked.
4. Take the next one cold (5 min)
Students take 8 equals 6 plus x, name the weight before hanging anything, and then hang it to check the prediction.

Short version — 9 minutes

1. Read the set-up and stop (4 min)
Students read the balance problem as far as the question, hang the eight and the two, and say aloud what the hanger is telling them and what the book has not told them.
2. Prove it had to be six (6 min)
Pairs find the two sentences that fix the answer and say what each one rules out, then explain why no other weight in their set could have worked.

Three levels

Support: Work with the weights already made and marked, and with the two constraining sentences already set apart on a card. Students hang, find six, and choose which of the two sentences says the sides must weigh the same. The finding and the citing both stay; only the search is removed.
At grade: Hang to find six, locate both constraining sentences unaided, and say what each contributes before moving to the second equation.
Extension: Take 6 plus z equals 8 plus 2 and say why the hanger has to carry two weights on its right before anything can be tried, then find z and say which of the book's sentences you leaned on that you did not need for the first problem.

English learners

The mathematical content here is reachable without much English, since the hanger reports the answer and the numbers are small. The demanding half is the citing, which asks students to say what a sentence contributes rather than what it says. Rehearse the frame This sentence tells me ___, so ___ cannot be the answer. Let students find the number and argue the ruling-out in their strongest language, then deliver only the two sentences and the frame in English, because those are the evidence the teacher is collecting.

Materials

A coat hanger balance with two paper clips
Penny weights of two, four, six and eight pennies, marked
A recording strip for weights tried
The balance problem written out to the question and no further
The two constraining sentences on separate cards

Standards & curriculum

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

7. Did He Tell Them or Not? Integrated · Students take a side on whether the caretaker gave away the number of skeletons, and must produce twenty and the sentences behind it whichever side they take.

Students take a side on whether the caretaker gave away the number of skeletons, and must produce twenty and the sentences behind it whichever side they take.

Full lesson — 20 minutes

1. Build the rooms (5 min)
Students set out four paper rooms and put five counters in each, then say the total and say how they got it.
2. Hear both sides (4 min)
The class hears the two positions stated plainly and each student stands with the one they believe, without speaking yet.
3. Build the case (6 min)
Students find the sentences their side rests on and rehearse an explanation that names the total and says when it became fixed.
4. Explain it to Mandy (5 min)
Students deliver the explanation to a partner playing Mandy, who asked and was never answered, and Mandy says whether she now knows the number and how she came to know it.

Short version — 9 minutes

1. Build the rooms (5 min)
Students set out four paper rooms and put five counters in each, then say the total and say how they got it.
2. Explain it to Mandy (5 min)
Students deliver the explanation to a partner playing Mandy, who asked and was never answered, and Mandy says whether she now knows the number and how she came to know it.

Three levels

Support: Build the four rooms and say the total, then choose a side with both positions read aloud and one supporting sentence already found for each. The student's own work is deciding which side that sentence helps and saying the total inside their explanation.
At grade: Build the rooms, take a side unaided, find the sentences, and deliver an explanation naming the total and the moment it became fixed.
Extension: Argue the side you did not choose. Say what your own side's best sentence looks like from over there, and whether anything the caretaker said would have to change for the other position to become the obvious one.

English learners

Told and said are near-synonyms in everyday English and this lesson turns on prying them apart, which is genuinely hard and is hard for monolingual speakers too. Many languages mark this distinction with different verbs, so students may see it faster than they can say it in English. Rehearse the frame He did not say twenty, but he said ___ and ___, so ___. Build the case in the strongest language and deliver to Mandy in English, since the delivery is what the teacher is collecting.

Materials

Four paper rooms
Counters
The caretaker's lines printed on a strip
The two positions written up side by side
The skeleton scene displayed whole

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.

8. Four names for one thing Vocabulary · Tracking the several names a text gives to one idea and saying why it changes them

This book calls the same thing an unknown, a mystery number and a variable, sometimes stacking two of the names inside a single sentence. A reader who does not notice they are one thing will think three things are being introduced. Students collect the names, find the sentence that finally links them, and read the explanation the book gives for the last one. They finish by choosing which name they would use and defending it. Nothing is solved; the work is following one idea through the several words a writer gives it.

Full lesson — 20 minutes

1. Collect the names given in one sentence (5 min)
Read the printed passage. Two different names for the same thing sit in the first sentence, separated by a comma. Underline both. Then find the third sentence and underline the two names stacked there as well. Write all the names you have found on your term-tracking sheet.
Word preview: unknown, term
An algebra equation has an equal sign and an unknown, a mystery number. Here's an algebra equation. 4 plus x equals 5. x represents the unknown, the mystery number.
2. Find the sentence that adds a fourth name and explains it (6 min)
Read the printed passage. A new name is introduced here, and unlike the others it comes with a reason. Underline the new name and underline the part of the sentence that starts with because. Add both to your sheet. Say aloud what the reason is, in your own words.
Word preview: variable, varies
The unknown or mystery number in algebra is also called the variable, because the value of x, y, z or whatever letter or symbol is used varies from one equation to the next.
3. See all the names used together (5 min)
Read the printed passage. Circle every name for the same idea that appears in it. Say aloud how many different names for one thing this single passage uses, and say whether that makes it clearer or harder to read.
Word preview: term, variable
Once you know how to find the mystery number, the variable in an algebra equation, you can use algebra to solve word problems.
4. Choose the name you would keep (4 min)
Look over your term-tracking sheet. Tell your partner which of the names you would use if you were writing this book, and give one reason. Your partner argues for a different one. Neither of you may say a name is better only because it is shorter.
Word preview: unknown, variable, term, varies

Short version — 9 minutes

1. Collect the names given in one sentence (5 min)
Read the printed passage. Underline the two names for the same thing in the first sentence and the two stacked in the last one. Write them on your term-tracking sheet.
Word preview: unknown, term
An algebra equation has an equal sign and an unknown, a mystery number. Here's an algebra equation. 4 plus x equals 5. x represents the unknown, the mystery number.
2. Find the sentence that adds a fourth name and explains it (4 min)
Read the printed passage. Underline the new name and the part beginning with because. Say the reason in your own words.
Word preview: variable, varies
The unknown or mystery number in algebra is also called the variable, because the value of x, y, z or whatever letter or symbol is used varies from one equation to the next.

Three levels

Support: Work only the first printed passage. Read the first sentence with a partner. Answer aloud: what are the two names, and are they two things or one thing? Write the two names on your sheet.
At Grade: Collect every name from the three printed passages, and give the reason the book prints for the last one.
Extension: The second printed passage explains the name variable using a word that shares its root. Write three sentences about why a name that carries its own explanation might be easier to remember, quoting the printed sentence.

English learners

English uses a bare comma to mean that is, so an unknown, a mystery number looks like a list of two items rather than one thing named twice. Read each pair aloud inserting that is, then read it as printed. The pair variable and varies also share a root that is easier to see than to hear. Rehearsable frame: ___ and ___ are two names for the same thing.

Materials

Mystery Math, the passage printed in this step
Term-tracking sheet
Pencils
Sentence frame on the board
Word cards: unknown, variable, term, varies

Standards & curriculum

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

9. Four headings, one shape Comprehension · Using repeated section headings to see how a whole book is organised

The middle of this book is four sections built to a single template, each announced by a heading that says almost exactly the same words. Once a reader sees the template, the book becomes navigable: you know what each section will contain before reading it. Students collect the headings, notice that one has come through the transcription damaged, and use the pattern held by the other three to say what the damaged one must have announced. Nothing is solved; the work is reading a book's organisation from its headings.

Full lesson — 20 minutes

1. Collect three headings and find the shared words (6 min)
Read the printed passages below. Each of these opens a section of the book. Underline the words that all three have in common, and circle the one word at the start of each that is different. Write the three different words on your outline sheet in order.
Word preview: heading, pattern
Subtraction can help you solve word problems and algebra equations.
Multiplication. Can help you solve word problems and algebra equations.
Division. It can help you solve word problems and algebra equations.
2. Meet the fourth heading, which is damaged (5 min)
Read the printed passage exactly as it stands. Do not change any word. This is the fourth heading in the same set, and its first word has been printed wrongly. Underline the word that does not belong. Say aloud what tells you it is a heading at all, even damaged.
Word preview: heading, section
A dish can help you solve word problems and algebra equations.
3. Use the section itself as evidence (5 min)
Read the printed passage, which comes from inside the damaged section. Underline the sentence that says what is being done to each side. Now say aloud what the damaged heading must have announced, and name the evidence: not what sounds right, but what this passage actually does.
Word preview: section, organise
You must eliminate the minus 6. You can do that by adding 6 to each side of the equation.
4. Predict from a heading (4 min)
Look at your outline sheet. Tell your partner what you would expect to find inside a section headed with one of your collected words, before reading a line of it. Your partner says whether the promise a heading makes is a useful one for a reader.
Word preview: heading, section, pattern, organise

Short version — 9 minutes

1. Collect three headings and find the shared words (5 min)
Read the printed headings. Underline the words all three share and circle the different word at the front of each. Write the three different words on your outline sheet.
Word preview: heading, pattern
Subtraction can help you solve word problems and algebra equations.
Multiplication. Can help you solve word problems and algebra equations.
Division. It can help you solve word problems and algebra equations.
2. Meet the fourth heading, which is damaged (4 min)
Read the printed heading exactly as it stands, changing nothing. Underline the word that does not belong. Say what still tells you it is a heading.
Word preview: heading, section
A dish can help you solve word problems and algebra equations.

Three levels

Support: Work only the first step's three printed headings. Read them aloud one after another with a partner. Say the one word that changes each time. Write the three words on your sheet.
At Grade: Collect all four headings, name the damage in the fourth, and use the printed section text to say what it must have announced.
Extension: The three clean headings punctuate the operation name three different ways. Write three sentences about whether that inconsistency matters to a reader using headings to navigate, quoting two of the printed headings.

English learners

Headings in English often drop words or run as fragments, and two of these are punctuated as though the operation name were a separate sentence. Read each heading as one continuous phrase first so the shared pattern is heard before the punctuation is discussed. Rehearsable frame: This section is about ___. I know because the heading says ___.

Materials

Mystery Math, the passages printed in this step
Outline sheet
Coloured pencils
Mystery Math, the passage printed in this step
Pencils
Sentence frame on the board
Word cards: heading, section, pattern, organise

Standards & curriculum

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

10. Why is there a haunted house in this book? Reasoning · Explaining what a story wrapped around an informational text does for a reader

This book is an explanation with a story built around it: two children, a caretaker and a haunted house supply the problems that the explaining parts then work through. Students separate the story sentences from the explaining sentences, notice how the book moves between them, and argue about whether the story helps or gets in the way. Nothing is solved; the work is reading a text's structure and judging a writer's choice.

Full lesson — 20 minutes

1. Sort a passage into story and explaining (6 min)
Read the printed passage. Draw two columns headed Story and Explaining. Put each sentence into one of the columns and be ready to defend any that were hard to place. Say aloud which sentence is the hinge, where the book turns from one to the other.
Word preview: frame, setting
Mandy and Billy stopped by a large creepy haunted house. Lots of Ravens were on the telephone wires beside the house. The Ravens called and then one by one they flew away. I saw six birds fly away, Mandy told Billy. Then I counted 13 birds still on the wires.
2. Find the sentence that hands over to the explaining (5 min)
Read the printed passage. Underline the sentence that takes what happened in the story and turns it into something to work on. Say aloud what changes in the writing after that sentence: who is speaking, and who is being spoken to.
Word preview: explain, frame
Mandy and Billy's problem can be written as an algebra equation. Let R be the number of Ravens on the wires when Mandy and Billy stopped by the house.
3. See the story used to hold a reader's attention (5 min)
Read the printed passage. A character here refuses to answer and offers something else instead. Underline the refusal and underline the offer. Say aloud what this does to a reader who wants to know the answer.
Word preview: purpose
I won't tell you, Igor said and laughed, but I'll give you an algebra problem. Solve the problem and you'll know how many skeletons there are.
4. Argue for or against the haunted house (4 min)
Take a side with your partner: one of you argues the haunted house helps a reader, the other argues it gets in the way. Give one reason each, drawn from the sentences you sorted into your columns. Then swap sides and give one reason for the position you just argued against.
Word preview: frame, setting, explain, purpose

Short version — 9 minutes

1. Sort a passage into story and explaining (5 min)
Read the printed passage. Draw two columns headed Story and Explaining and place each sentence in one. Say which sentence was hardest to place.
Word preview: frame, setting
Mandy and Billy stopped by a large creepy haunted house. Lots of Ravens were on the telephone wires beside the house. The Ravens called and then one by one they flew away. I saw six birds fly away, Mandy told Billy. Then I counted 13 birds still on the wires.
2. Find the sentence that hands over to the explaining (4 min)
Read the printed passage. Underline the sentence that turns the story into something to work on. Say what changes in the writing after it.
Word preview: explain, frame
Mandy and Billy's problem can be written as an algebra equation. Let R be the number of Ravens on the wires when Mandy and Billy stopped by the house.

Three levels

Support: Work only the first printed passage. Read it with a partner. Answer aloud: where are Mandy and Billy, and what did they see? Then say whether this sounds like a story or like a lesson.
At Grade: Sort the first printed passage into two columns, find the handover sentence in the second, and say what the refusal in the third does to a reader.
Extension: The third printed passage has a character refuse to answer a question. Write three sentences about why a writer of an explaining book might put a refusal in a character's mouth rather than simply moving on, quoting the printed sentences.

English learners

This book reports speech without quotation marks, so a line like I saw six birds fly away, Mandy told Billy gives the speaker only after the words, and the I is not the writer. Read each such line twice, once naming the speaker first. Rehearsable frame: ___ said that ___. This part is story / this part is explaining.

Materials

Mystery Math, the passage printed in this step
Two-column chart
Pencils
Sentence frame on the board
Word cards: frame, setting, explain, purpose

Standards & curriculum

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

11. Egor, Igor, Eager Language · Deciding whether differently spelled names refer to one person or to several

The caretaker of the haunted house is named three different ways in this transcription, and nothing in the book announces that they are one person. A reader has to decide from the evidence, and the evidence is what each one is doing and where. Students collect the three spellings with their sentences, weigh what would follow if they were three people, and reach a decision they can defend. They also practise writing about a character whose name cannot be settled. Nothing is solved; the work is reading names as evidence.

Full lesson — 20 minutes

1. Meet the caretaker and write down his name (5 min)
Read the printed passage. Underline the caretaker's name and copy it exactly onto your name chart, along with what he is doing in this passage. Copy the spelling exactly as printed, letter for letter.
Word preview: character, spelling
Egor is the caretaker of the haunted house. He told Mandian Billy, there were bats flying around in here before I started my lunch.
2. Meet a second spelling and add it (5 min)
Read the printed passage. Underline the name here and copy it onto your chart exactly as printed, with what he is doing. Say aloud whether this could be the same person as the one in your first row, and name the evidence either way.
Word preview: evidence
Mandy asked Igor how many skeletons are in the house. I won't tell you, Igor said and laughed, but I'll give you an algebra problem.
3. Meet a third spelling and settle it (6 min)
Read the printed passage. Two different spellings appear in it, and both belong to the same speaker. Underline both and add them to your chart. Now write one sentence on your chart deciding how many people the caretaker is, and one sentence naming the evidence you used. You may not decide by which spelling looks most like a name.
Word preview: decide, spelling
Eager told Mandy and Billy I have a black cat and my cat had kittens. I won't tell you how many kittens I have, but I will tell you that the kittens have 28 legs total.
4. Write about him without choosing a spelling (4 min)
Write one sentence about the caretaker without using any of the three spellings. Read it to your partner. Your partner says whether your sentence would still be true if the book turned out to mean three different people.
Word preview: character, spelling, evidence, decide

Short version — 9 minutes

1. Meet the caretaker and write down his name (5 min)
Read the printed passage. Underline the caretaker's name and copy it exactly onto your name chart with what he is doing.
Word preview: character, spelling
Egor is the caretaker of the haunted house. He told Mandian Billy, there were bats flying around in here before I started my lunch.
2. Meet a second spelling and add it (4 min)
Read the printed passage. Copy this spelling onto your chart with what he is doing. Say whether it could be the same person, and name your evidence.
Word preview: evidence
Mandy asked Igor how many skeletons are in the house. I won't tell you, Igor said and laughed, but I'll give you an algebra problem.

Three levels

Support: Work with the first two printed passages only. Copy the two names onto your chart. Answer aloud: do these two people do the same kind of job in the same house? Then say whether you think they are one person.
At Grade: Collect all three spellings with their sentences, decide how many people the caretaker is, and write down the evidence you used.
Extension: The second printed passage also runs two other characters' names together into a single word. Write three sentences about how a careful reader should record a name that the page prints inconsistently, using the printed passages as your examples.

English learners

Learners meeting unfamiliar English names cannot rely on knowing which forms are ordinary, so Eager looking like a common adjective is a real trap rather than a joke. Say plainly that all three are printing variants of one name and that the deciding evidence is what the person does, not how the letters look. Rehearsable frame: I think ___ and ___ are the same person, because both of them ___.

Materials

Mystery Math, the passage printed in this step
Name chart
Pencils
Word cards: character, spelling, evidence, decide

Standards & curriculum

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

12. The seesaw that never leaves Comprehension · Following one comparison a writer returns to and saying what it explains each time

This book opens on a seesaw and comes back to the same idea of balance at the very end with a hanger and some pennies. The comparison is not decoration; it carries the book's single most important claim, which is stated in almost the same words in three separate places. Students trace the comparison from its first appearance to its last, quote the sentence that recurs, and say what the comparison lets a writer avoid explaining. Nothing is solved; the work is following one idea across a whole text.

Full lesson — 20 minutes

1. Read the opening comparison (5 min)
Read the printed passage. Underline the sentence that makes the comparison. Then underline the two sentences that say the same thing about each side of it. Say aloud what a reader is expected to already know about seesaws.
Word preview: balance, compare
A seesaw is like an equation. A seesaw must be balanced. An equation must be balanced too. Whatever is on one side should be balanced by whatever is on the other side.
2. Find the claim restated as a rule (5 min)
Read the printed passage. Here the same idea about balance arrives without any seesaw at all. Underline the rule. Say aloud what the rule and the opening comparison have in common, and what the rule adds that the comparison did not.
Word preview: claim, return
The simple rule is, whatever is done to one side of the equal sign must be done to the other side.
3. Find the comparison returning at the end (6 min)
Read the printed passage from the last part of the book. The comparison is back, with a different object standing in for the seesaw. Underline the sentence that makes it. Say aloud why a writer might close a book by returning to the idea it opened with.
Word preview: return, balance
Many years ago small items were weighed on balance scales. Balance scales are like equations. When the scale is in balance, the weight on one side of the scale equals the weight on the other side.
4. Say what the comparison saved the writer (4 min)
Tell your partner one thing this writer never had to explain because a reader already understands seesaws. Then say whether a reader who had never been on one would still follow the book. Your partner gives a different example.
Word preview: balance, compare, return, claim

Short version — 9 minutes

1. Read the opening comparison (5 min)
Read the printed passage. Underline the sentence making the comparison and the two that say the same thing about each side. Say what a reader is expected to know about seesaws already.
Word preview: balance, compare
A seesaw is like an equation. A seesaw must be balanced. An equation must be balanced too. Whatever is on one side should be balanced by whatever is on the other side.
2. Find the comparison returning at the end (4 min)
Read the printed passage from the last part of the book. Underline the sentence that makes the comparison again. Say why a writer might close with the idea the book opened on.
Word preview: return, balance
Many years ago small items were weighed on balance scales. Balance scales are like equations. When the scale is in balance, the weight on one side of the scale equals the weight on the other side.

Three levels

Support: Work only the first printed passage. Read the first three sentences with a partner. Answer aloud: what two things are being compared, and what one word is said about both of them?
At Grade: Trace the comparison from the first printed passage through the rule in the second to its return in the third, and say what each one adds.
Extension: The first and third printed passages make the same comparison with different objects. Write three sentences about why a writer would swap the object rather than repeat the seesaw, quoting the sentence that makes the comparison in each.

English learners

Whatever is on one side and whatever is done to one side are two long noun phrases built from a word learners usually meet as a question word, and the sentences are hard to parse before they are hard to understand. Read each one in two halves, pausing at the verb. Invite students to describe a seesaw in their strongest language first. Rehearsable frame: A ___ is like an equation, because both must be ___.

Materials

Mystery Math, the passage printed in this step
Pencils
Sentence frame on the board
Word cards: balance, compare, return, claim

Standards & curriculum

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