The Great Graph Contest

$The Great Graph Contest book cover$

Grade 2
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.

1Two Squares and the Words That Say What They Are
2Fifteen and Nine, Side by Side
3The Taller Stack Only Wins If the Pieces Match
4Both Goes in the Middle, Neither Goes Outside
5Ask, Write It Down, Then Build It

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.

6More Is Two Groups, Most Is All of Them
7The Judge Never Did the Math
8Six More and Six Fewer Are the Same Six

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.

9I Wonder: The Sentence That Starts Every Investigation in This Book
10Think, Collect, Use, Put: How the Back of the Book Tells You What to Do
11Excuse Me, May I Ask You a Question? How Beezy Talks to Strangers
12He Cut, He Drew, He Put: How the Back of the Book Retells What Happened
13Venn, Then, End: A Word This Book Spells Three Different Ways

Both exports carry any edits you have made. Edits are saved in this browser only — nobody else sees them, and they are not sent anywhere.

Skill lessons

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

1. Two Squares and the Words That Say What They Are Representation · Sorting a collection into two groups by an attribute you choose, and labelling them

Gonk is handed a pile of rocks and nothing else, and the first thing he does is decide what to look at: smooth or rough. The book then shows the whole procedure in its closing pages, including the labels and the reason they are needed. Students get their own unsorted pile, choose the attribute themselves, place every object into one of two marked squares, and write the two labels and the title. The lesson is over the sorting, not over a finished picture: nothing tells a child which pile a rock belongs in except the rock.

Full lesson — 20 minutes

1. Choose what you are sorting by (5 min)
Take the pile of buttons at your table and turn them over with your hands before you decide anything. Find one thing about them that splits the whole pile in two, so that every single button goes to one side or the other. Say your attribute out loud to your partner and let them try to find a button that fits neither.
Word preview: smooth, rough
I wonder if there are more smooth rocks or rough ones.
2. Put every one on a square (6 min)
Set your two paper squares side by side. Move the buttons one at a time onto the square where they belong, and do not skip any. When a button is hard to decide, hold it up and say which side you are putting it on and why, then put it down and leave it there.
Word preview: square
I'll put the smooth ones on one square and the rough ones on the other square.
3. Write the labels (5 min)
Write one label card for each square naming what is on it, and one title card saying what the whole graph is about. Put the cards where a person walking past could read them without asking you. Then hand your graph to another pair and let them tell you what it shows from the cards alone.
Word preview: label, title
Oh, I have to make a labels too.
He made labels for the graph title and for the two groups of rocks.
4. Say which square has more (4 min)
Look at your two squares and say which one has more buttons on it. Then find the pair in the room whose two squares look closest to the same, and say what you would have to do to be sure about theirs. Say the sentence the book says about that: you would have to count.
Word preview: more
It is easy to see that more of the rocks are smooth but if a similar number of rocks were on each square, it would be hard to tell which group was larger.
You would have to count all of the rocks.

Short version — 9 minutes

1. Choose what you are sorting by (4 min)
Turn the buttons over with your hands. Find one thing about them that splits the whole pile in two, so every button goes to one side or the other. Say it out loud and let your partner try to find a button that fits neither.
I wonder if there are more smooth rocks or rough ones.
2. Put every one on a square (5 min)
Set your two squares side by side and move the buttons across one at a time. Do not skip any. When one is hard to decide, say which side you are putting it on before you put it down.
I'll put the smooth ones on one square and the rough ones on the other square.

Three levels

Support: Work from a pile of twelve buttons that split cleanly, so no button sits on the fence and the child's whole attention goes to placing every one and naming the two groups. The child still chooses the attribute and still writes both labels; only the size of the pile and the number of hard cases come down.
At Grade: Sort twenty-four mixed buttons by an attribute you choose, place every one on a square, write two labels and a title, and say which square has more.
Extension: Sort the same pile a second time by a different attribute, so the buttons that were together are now apart. Write the second pair of labels, then say which sorting answers a question somebody would actually ask, and what question the other one answers instead.

English learners

Smooth and rough are felt before they are said, so let hands do the sorting first and attach the English words to a square a child is already pointing at. The words carrying the mathematical load here are square, label and more; more is the one to rehearse, because comparing groups is language-independent but the English phrase this square has more is not. A usable frame is: this square has more ___ than that square. Children may argue over a hard button in their strongest language and give only the finished label and the closing sentence in English.

Materials

Mixed button collection, about twenty-four per pair
Two large paper squares per pair
Blank label cards, three per pair
Word cards: label, more, rough, smooth, square, title

Standards & curriculum

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

2. Fifteen and Nine, Side by Side Concept · Comparing two counts within twenty by building and matching rows

The rock graph is the one place in this book where both groups are actually counted: fifteen smooth and nine rough. The book prints the two numbers and never puts them together, and it never says how much bigger one group is. Students build the two rows from the book's own numbers, line them up from a common end, and find the six left over by matching one to one. Nobody subtracts; the leftover is seen, and saying so is what the closing step is for.

Full lesson — 20 minutes

1. Build fifteen and build nine (5 min)
Count fifteen cubes into one row and nine cubes into another row, saying each number as a cube goes down. Line both rows up from the same end of the table so the left ends are even. Count each row again to check, and say the two numbers to your partner in the order the book gives them.
Word preview: count
1314 there are 15 smooth rocks.
There are nine rough rocks.
2. Match them one to one (6 min)
Slide the rows together so each cube in the short row sits directly beside a cube in the long row. Touch each matched pair as you go. When the short row runs out, put your finger on the first cube that has no partner and leave it there.
Word preview: match
There are nine rough rocks.
3. Count what is left over (5 min)
Count only the cubes with no partner and say that number. Say which row they came from. Then say the whole thing in one sentence: which group has more, and how many more it has.
Word preview: more, left over
My graph shows that more of the rocks are smooth.
4. Say it the other way round (4 min)
Keep the rows exactly where they are and put your finger back on the same leftover cubes. Now say the sentence about the short row instead: how many fewer the rough rocks are. Both sentences are about the same cubes, so do not move anything while you swap them.
Word preview: fewer
I wonder if there are more smooth rocks or rough ones.

Short version — 9 minutes

1. Build fifteen and build nine (4 min)
Count fifteen cubes into one row and nine into another, saying each number as a cube goes down. Line both rows up from the same end so the left ends are even, then count each row again to check.
1314 there are 15 smooth rocks.
There are nine rough rocks.
2. Match them one to one (5 min)
Slide the rows together so each cube in the short row sits beside a cube in the long row, touching each pair as you go. When the short row runs out, count the cubes with no partner and say which group has more and how many more.
My graph shows that more of the rocks are smooth.

Three levels

Support: Build the nine first and hand the child a pre-counted row of fifteen, so the whole of the work goes into the matching and the leftover rather than into two accurate counts. The child still slides the rows together, still finds the six unpartnered cubes, and still says both sentences over them.
At Grade: Build both rows from the book's two numbers, match them one to one, count the six left over, and say both the more sentence and the fewer sentence over the same unmatched cubes.
Extension: Without moving the cubes, say what the two rows would have to look like for there to be no leftover at all, and name two different ways to get there: adding to the short row or taking from the long one. Say why those two ways do not end with the same two numbers even though both end with a match.

English learners

Number and one-to-one matching travel across languages, and most children will find the six leftover cubes long before they can say the sentence about them. Take the match first and attach the words afterwards. The hard part is that English says the same arrangement two ways, more than and fewer than, and fewer is the one that gets lost. Rehearse the pair back to back over the same cubes: smooth has six more than rough, rough has six fewer than smooth. Children may count in their strongest language and give the two comparison sentences in English.

Materials

Interlocking cubes, twenty-five per pair
A long strip of paper ruled into two rows
Word cards: fewer, match, more

Standards & curriculum

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

3. The Taller Stack Only Wins If the Pieces Match Representation · Building a bar graph from real objects in three categories, with a fair unit

Beezy looks at a plate of cookies and decides for herself that there are three kinds, then stacks each kind separately so height stands in for number. The book gives the whole method and then gives the condition that makes it honest: the cookies have to be about the same thickness. Students build three stacks from mixed objects, read the tallest, and then rebuild after a thick piece is slipped in, so the fairness condition is something they catch rather than something they are told.

Full lesson — 20 minutes

1. Find the kinds (4 min)
Look through the tray of counters at your table and decide how many different kinds there are. Do not let anyone tell you; sort a few until the kinds are obvious, then say your three kinds aloud so your partner can check that every counter fits one of them.
Word preview: kind
I see three kinds of cookies.
I wonder if there are more chocolate chip, oatmeal, or sugar cookies.
2. Stack each kind (6 min)
Build one stack for each kind, straight up from the base line, with every stack starting at the same line. Put every counter into a stack, none left in the tray. Keep the stacks side by side and close enough to see over the tops.
Word preview: stack
To see which kind of cookie was most common, Beezy piled up each type in a separate stack.
I'll stack them up and find out.
3. Read the tallest (4 min)
Look across the tops of the three stacks and say which kind there are most of, without counting anything. Then count that stack and say its number. Say the sentence that connects the two: the stack is tallest, so there are more of those.
Word preview: most, taller
If a stack is taller, that means there are more of those cookies.
The graph shows there are more chocolate chip cookies than the other two kinds.
4. Slip in a thick one (6 min)
Take the two thick blocks and add one to the shortest stack. Look across the tops again and say which stack is tallest now. Then count all three stacks and say whether the tallest stack really has the most counters in it. Tell your partner what went wrong and what rule would stop it.
Word preview: thickness, accurate
The cookies must be about the same thickness for the results to be accurate.

Short version — 9 minutes

1. Find the kinds (3 min)
Look through the tray of counters and decide how many different kinds there are. Sort a few until the kinds are obvious, then say your three kinds aloud so your partner can check that every counter fits one of them.
I see three kinds of cookies.
2. Stack each kind (6 min)
Build one stack for each kind, straight up from the base line, with every stack starting at the same line and every counter in a stack. Look across the tops and say which kind there are most of, then count that stack to check.
To see which kind of cookie was most common, Beezy piled up each type in a separate stack.
If a stack is taller, that means there are more of those cookies.

Three levels

Support: Give the child two kinds instead of three and about sixteen counters, so the tray sorts quickly and both stacks stay short enough to see over. The thick block still goes in and the child still catches it; only the number of categories and the height of the stacks come down.
At Grade: Sort about thirty counters into three kinds you named yourself, stack each kind from a common base line, read the tallest by eye and confirm by counting, then catch what the thick block does to the reading.
Extension: Set up a tray where the tallest stack is not the largest group and the fault is not a thick piece but stacks that start at different lines. Hand it to another pair without saying anything is wrong, and see whether they catch it. Then say what a person reading a stack graph has to check before believing it.

English learners

Taller and more are two different words for what a child will see as one thing, and English keeps them apart: taller is about the stack, more is about the counters. Say both over the same stack every time. Thickness and accurate are the words most likely to be new; thickness can be shown by holding one counter and one block edge on, which needs no English at all. A usable frame is: the ___ stack is tallest, so there are more ___. Children may sort and argue in their strongest language and give the reading sentence in English.

Materials

Tray of flat counters in three colours, about thirty per pair
A flat board or tabletop with a marked base line
Two thick blocks the same footprint as the counters
Word cards: accurate, kind, most, stack, taller, thickness

Standards & curriculum

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

4. Both Goes in the Middle, Neither Goes Outside Concept · Sorting into two overlapping groups, including both and neither

The bathing suits have flowers, or bugs, or flowers and bugs, and the book adds the fourth case in a single line: a suit with neither goes outside both circles. That fourth region is the whole of the difficulty and the whole of the lesson. Students lay two string loops that overlap, decide the two attributes themselves, and place every card in one of four places, saying the region name as the card goes down. Nothing here is read off a finished diagram; the cards start in a heap.

Full lesson — 20 minutes

1. Lay two loops that overlap (4 min)
Lay your two string loops on the table so they cross and leave a lens-shaped space in the middle. Point to the four places a card could go: the left part only, the right part only, the middle, and the table outside both loops. Say each of the four aloud before you touch a card.
Word preview: overlap
He formed two big circles of string, making them overlap in the middle.
2. Name your two groups (4 min)
Look through the card deck and pick the two things you are going to sort by, so that some cards have one, some have the other, some have both and at least one has neither. Write a label for each loop. Check with your partner that a card exists for every one of the four places.
Word preview: both
Hmm, some of these suits have a pattern of flowers.
Some of them have bugs, and some of them both flowers and bugs.
3. Place every card and say where (7 min)
Take the cards one at a time and put each one where it belongs, saying the place out loud as you set it down: left only, right only, both, or neither. Do not leave a card in your hand because it is hard. When you disagree with your partner, hold the card up and each say which place and why before it goes down.
Word preview: middle
The suits with flowers are on the left circle.
The suits with bugs are in the right circle.
The suits with both are in the middle where the circle is overlap.
4. Defend the outside pile (5 min)
Find the cards you put outside both loops and say, for each one, both of the things it does not have. Then have your partner try to move one of them into a loop; hold your ground with the card in your hand if it belongs outside. Say why outside is a real place on this graph and not a leftover heap.
Word preview: neither, outside
What if the suit doesn't have bugs or flowers?
Then it goes outside of both circles.

Short version — 9 minutes

1. Lay two loops that overlap (3 min)
Lay your two string loops so they cross and leave a lens-shaped space in the middle. Point to the four places a card could go: left only, right only, the middle, and outside both loops. Say all four aloud before you touch a card.
He formed two big circles of string, making them overlap in the middle.
2. Place every card and say where (6 min)
Take the cards one at a time and put each where it belongs, saying the place out loud as you set it down: left only, right only, both, or neither. Do not leave a hard card in your hand. When you disagree, hold the card up and each say which place and why.
The suits with both are in the middle where the circle is overlap.
Then it goes outside of both circles.

Three levels

Support: Hand the child a deck of twelve where the both cards are visibly both and only one card belongs outside, and place the first card together while naming its region. The child still places every remaining card and still says the region name each time; only the number of hard cases comes down, not the four regions.
At Grade: Choose the two attributes, label both loops, and place all twenty cards into left only, right only, both or neither, saying each region as the card goes down and defending the outside pile.
Extension: Take a placed diagram from another pair with the labels turned face down, and work out from the cards alone what the two labels must have been. Then find a card whose placement would change if the two labels were swapped, and say why the middle would not move.

English learners

Both and neither are the two words this lesson lives on and they are the two most likely to be missing, because many languages carry neither as a negated either rather than as one word. Attach both to the middle space and neither to the tabletop outside, and point every time the word is said, so the word has a place rather than a definition. Two frames worth rehearsing: this one has both, so it goes in the middle, and this one has neither, so it goes outside. Children may discuss a disputed card in their strongest language and name the region in English as the card goes down.

Materials

Two loops of string per pair
A deck of about twenty picture cards carrying two attributes
Blank label cards, two per pair
Word cards: both, middle, neither, outside, overlap

Standards & curriculum

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

5. Ask, Write It Down, Then Build It Application · Asking a survey question, recording each answer, and building columns from the record

Beezy walks a flower market asking one question and writing every answer down, and the book closes by handing that whole method to the reader: think of a question, collect data and write it down, then build. This is the only lesson in the book where the data does not exist until students make it. Students ask their own question, keep a written record as answers come in, and then stand one same-sized marker per answer in the right column, so the column heights come out of the record rather than out of a guess.

Full lesson — 20 minutes

1. Write one question and its answers (5 min)
Write one question you can ask everybody in the room, and write the three answers a person is allowed to give. Try it on your partner first. If their answer does not fit any of your three, fix the question or fix the answers before you ask anybody else.
Word preview: question, answer
To make your own graph, think of a question to ask.
What are you planning to do with your flower?
2. Ask and record every answer (6 min)
Go round and ask your question, and make one mark on your sheet for each person as they answer. Mark it while they are still standing there, not afterwards from memory. Keep going until you have asked at least twelve people, and do not skip a person whose answer surprises you.
Word preview: record, survey
Beezy took a survey to find out what shoppers planned to do with their new flowers.
She wrote down their answers to keep track of the data.
Collect data and write it down.
3. Build the columns from the record (5 min)
Set your column base card down with your three answers written along the bottom. Read your sheet mark by mark and stand one paper square in the right column for each mark. Every square is the same size, so do not stretch one to fill a gap. Count the squares in each column against the marks on your sheet when you are done.
Word preview: column
To complete this bar graph, she made flower shapes, all the same size put in three colors, and for each answer she put a color-coded flower in its correct column.
4. Title it and say what it shows (4 min)
Write your question across the top of the graph as its title, and check that each column is labelled with the answer it holds. Then show it to a pair who was not asked, and let them tell you what most people said. If they cannot tell, add the label that was missing.
Word preview: title, label
Put a title and labels on your graph so people will know what it is about.
As with all graphs, it is important to put labels on it so people understand what the graph is about.

Short version — 9 minutes

1. Ask and record every answer (5 min)
Ask your question round the room and make one mark on your sheet for each person as they answer. Mark it while they are still standing there, not afterwards from memory. Ask at least twelve people and do not skip a surprising answer.
Beezy took a survey to find out what shoppers planned to do with their new flowers.
She wrote down their answers to keep track of the data.
2. Build the columns from the record (4 min)
Read your sheet mark by mark and stand one paper square in the right column for each mark. Every square is the same size, so do not stretch one to fill a gap. Count the squares in each column against the marks on your sheet when you are done.
To complete this bar graph, she made flower shapes, all the same size put in three colors, and for each answer she put a color-coded flower in its correct column.

Three levels

Support: Give the child a question with two answers instead of three and a recording sheet already ruled into those two columns, so the marking has a place to go and no answer has to be sorted on the spot. The child still asks every person, still makes the mark while the person is there, and still builds the columns square by square from their own sheet.
At Grade: Write a three-answer question, ask at least twelve people, mark each answer as it comes, then build the columns one same-sized square per mark and title and label the finished graph.
Extension: After the graph is built, ask six more people and add their answers, keeping the same square size. Say which column moved and whether the answer to your question changed. Then say how many more people you would have to ask for the second-place column to overtake the first, and what on your sheet tells you that.

English learners

This lesson asks a child to ask strangers a question in English, which is the heaviest language demand in the book, so let the question be written and carried rather than remembered. A child may hold up the sheet and let the person point at their own answer, which records the data honestly with no speaking at all. Survey and record are the new words and both are shown by the act. A frame worth rehearsing before anyone leaves the table is: can I ask you a question? Children may write their recording sheet in their strongest language, since the marks are counted rather than read, and label the finished columns in English.

Materials

Clipboard with a blank recording sheet
Pencil
Paper squares, all the same size, thirty per pair
Column base card with three labelled columns
Blank label cards, four per pair
Word cards: answer, column, question, record, survey, title

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. More Is Two Groups, Most Is All of Them Integrated · Students find that swapping one small word changes how many stacks they have to look at, and build a sort where more is true and most is false at the same time.

Students find that swapping one small word changes how many stacks they have to look at, and build a sort where more is true and most is false at the same time.

Full lesson — 20 minutes

1. Test the book's sentence over two rows (5 min)
Students build fifteen counters and nine counters into two rows from the book's rock counts, match them one to one and say the book's sentence about them. They then say the swapped sentence with most in place of more and decide whether it is also true of these two rows.
2. Say which word the graph will take (4 min)
Students are shown three graph set-ups without counts - two squares, three stacks, four columns - and say for each one which of the two words a sentence about it could use, before anything is counted. Competing answers are left standing and written on the board.
3. Build the sort that breaks them apart (7 min)
Each pair sorts twenty-four counters into three groups of their own choosing and stacks them from a common base line. They count all three, then test both sentences on their own sort: which group has more than the others, and whether any group is most of the whole twenty-four. They find the case where more is true and most is false and hold it up.
4. Say the sentence that fits (4 min)
Each pair says one true sentence about their own stacks using whichever word fits, and says out loud why the other word makes the sentence false, pointing at the stacks that make it false. A listening pair rebuilds the claim from the sentence alone by pointing at the right stacks.

Short version — 9 minutes

1. Say which word the graph will take (4 min)
Students are shown three graph set-ups without counts - two squares, three stacks, four columns - and say for each one which of the two words a sentence about it could use, before anything is counted. Competing answers are left standing and written on the board.
2. Build the sort that breaks them apart (7 min)
Each pair sorts twenty-four counters into three groups of their own choosing and stacks them from a common base line. They count all three, then test both sentences on their own sort: which group has more than the others, and whether any group is most of the whole twenty-four. They find the case where more is true and most is false and hold it up.

Three levels

Support: Keep the pair at two groups and the book's own numbers, fifteen and nine, and let the child test both words over one pair of rows rather than building a new sort. The child still says both sentences and still says which one the rows support; the second sort is what comes off, so the language demand is untouched and the counting load drops.
At grade: Test both sentences over the book's two rows, then build a three-group sort of twenty-four, count all three groups, and produce the case where more is true and most is false, saying the fitting sentence over your own stacks.
Extension: Build a sort where most IS true, and say what had to be true of the three numbers to get there. Then say whether a group can be most without being more than every other group one at a time, and settle it with counters rather than with an opinion.

English learners

More and most are a comparative and a superlative of the same word, and many languages mark that difference somewhere other than on the word itself, so a child may hear one sound where English intends two. Say the two sentences back to back over the same stacks with the same rhythm and let the stacks carry the difference. Number, matching and ranking are language-independent and most children will find the group that beats the others before they can name it, so accept the pointing first and attach the word afterwards. Two frames are worth rehearsing: this group has more than that group, and this group is most of all of them. Children may count and argue in their strongest language and give the closing sentence in English.

Materials

Counters, thirty per pair
Base line card for building three stacks
The two versions of the rock sentence, written large one above the other
Three unlabelled graph set-ups: two squares, three stacks, four columns

Standards & curriculum

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

7. The Judge Never Did the Math Integrated · Students score two of the book's graphs on the judge's own criterion of correct math and argue their score to him out loud, with the counts in the sentence.

Students score two of the book's graphs on the judge's own criterion of correct math and argue their score to him out loud, with the counts in the sentence.

Full lesson — 20 minutes

1. Hear the criterion and the ending (4 min)
Students hear the judge's three criteria and the ending in which he declares a tie, and say what he never did. They say aloud which of the three criteria a person could settle with counters and which two they could not, and the answers are left on the board unresolved.
2. Build the two graphs and count them (7 min)
Half the pairs build the rock sort from the book's two counts, fifteen and nine, in two matched rows. The other half build a three-kind stack graph from a tray and count only one kind, as the book does. Every pair writes down which numbers their graph actually gives a reader.
3. Take a position (4 min)
Each pair chooses which of the two graphs earns more points for correct math and finds the counts that fund their choice. They say the case to their partner once, and the partner's only job is to tell them whether a number was in it.
4. Say your score to the judge (5 min)
Each student says their score aloud to the judge, naming the graph, the points and the counts the graph does or does not supply. A student holding the opposing position answers with their own counts. Cases without a number in them are said again.

Short version — 9 minutes

1. Build the two graphs and count them (7 min)
Half the pairs build the rock sort from the book's two counts, fifteen and nine, in two matched rows. The other half build a three-kind stack graph from a tray and count only one kind, as the book does. Every pair writes down which numbers their graph actually gives a reader.
2. Say your score to the judge (5 min)
Each student says their score aloud to the judge, naming the graph, the points and the counts the graph does or does not supply. A student holding the opposing position answers with their own counts. Cases without a number in them are said again.

Three levels

Support: Hand the pair a frame that carries the number rather than a smaller argument: I give the ___ graph more points because it counted ___ and ___, and the other one only counted ___. The child still builds both graphs, still finds the counts and still says the case to the judge; what comes down is having to assemble the sentence from nothing while holding the quantities in mind.
At grade: Build one of the two graphs, find which counts it gives a reader and which it withholds, take a position on the judge's criterion and argue it aloud with at least one count inside the sentence.
Extension: Argue the case you did not choose, as strongly as you can, and then say which of the two cases you now think is better and what changed your mind. Then say what the judge would have had to be told about the egg graph for it to score well, and whether the book anywhere says it.

English learners

This lesson asks for an argued case, which is the heaviest language demand in the book, so let the numbers do the arguing wherever they can - a child who says fifteen and nine and points at the two rows has made the case even with very little English around it. Counting and matching are language-independent; what is not is the scoring register, the because that links a number to a judgement. Rehearse one frame before anybody speaks: I give it ___ points because it counted ___ and ___. Children may work out their position in their strongest language and give only the scoring sentence in English, and a partner may repeat a case back in either language to check the number survived.

Materials

Counters, thirty per pair
Base line card for building three stacks
Recording slip for the counts a graph gives
The judge's three criteria, written large
The ending line in which the contest is declared a tie

Standards & curriculum

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

8. Six More and Six Fewer Are the Same Six Integrated · Students build the book's two rock counts as matched rows, find the six that have no partner, and say the one arrangement in both directions without moving anything.

Students build the book's two rock counts as matched rows, find the six that have no partner, and say the one arrangement in both directions without moving anything.

Full lesson — 20 minutes

1. Take the two counts from the book (4 min)
Students hear the two rock sentences and say the two numbers back, then say which group the book says there are more of. They say what the book does not tell them about the rough rocks, and that question is left standing.
2. Build both rows and match them (6 min)
Students count fifteen counters into one row and nine into another, line both up from the same end, and slide them together so each counter in the short row has a partner. They put a finger on the first counter with no partner and count the ones left over.
3. Say it both ways over the same six (6 min)
Without moving a counter, students say how many more the smooth row has, then say how many fewer the rough row has, keeping a finger on the same unmatched counters through both sentences. They say aloud that the two sentences are about the same six.
4. Rebuild from a sentence (4 min)
One partner turns away and hears only a comparison sentence and the smaller count, and builds both rows from that alone. The rows are compared with the original, and the pair says which word in the sentence told them which row to make longer.

Short version — 9 minutes

1. Build both rows and match them (6 min)
Students count fifteen counters into one row and nine into another, line both up from the same end, and slide them together so each counter in the short row has a partner. They put a finger on the first counter with no partner and count the ones left over.
2. Say it both ways over the same six (6 min)
Without moving a counter, students say how many more the smooth row has, then say how many fewer the rough row has, keeping a finger on the same unmatched counters through both sentences. They say aloud that the two sentences are about the same six.

Three levels

Support: Give the child a pre-counted row of fifteen and have them build only the nine, so the whole of the effort goes into the matching and into holding still while both sentences are said. The child still finds the six, still says both directions and still keeps a finger on the same counters; only one of the two counts is handed over.
At grade: Build both rows from the book's counts, match them one to one, count the six left over, say both the more and the fewer sentence over the unmoved counters, and rebuild a partner's rows from a spoken sentence.
Extension: Find a different pair of counts that would give the same six left over, build it, and say both sentences about it. Then say what is the same about every such pair and what is different, and whether a partner hearing only six more could ever know which two numbers you used.

English learners

Number and one-to-one matching cross languages intact, and nearly every child will find the six unmatched counters before they can say a sentence about them, so take the match first and attach the words after. The difficulty is entirely in the English: fewer is low-frequency, it is often replaced by less, and the comparative than construction reverses which noun comes first for the same fact. Say the two sentences back to back over the unmoved counters with the same rhythm every time. Two frames are worth rehearsing: smooth has six more than rough, and rough has six fewer than smooth. Children may count in their strongest language and give the two comparison sentences in English.

Materials

Counters, twenty-five per pair
Two-row comparison mat
The two rock-count sentences, written large one above the other

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. I Wonder: The Sentence That Starts Every Investigation in This Book Language · The Question a Writer Asks Before Investigating

Three times in this book a character stops and says a sentence beginning I wonder, and each time the sentence after it says what they will do about it. Students read two of these, identify the wondering sentence and the doing sentence, and say how the second answers the first. They finish by writing a wondering sentence of their own about the classroom. Nothing is graphed or tallied; the work is recognising the question that opens an investigation.

Full lesson — 20 minutes

1. Find the wondering sentence (6 min)
The teacher reads the passage below once, then you read it silently. Underline in the air the sentence that begins with the words I wonder. Read that sentence aloud to a partner. Then say what the character does not know yet.
Word preview: wonder
I wonder if there are more smooth rocks or rough ones. I'll put the smooth ones on one square and the rough ones on the other square. Oh, I have to make a labels too.
2. Find the sentence that answers it (5 min)
Read the passage below again. This time find the sentence that starts with I'll. Say aloud what the character has decided to do. Then explain to your partner how the doing sentence is connected to the wondering sentence.
Word preview: plan
I wonder if there are more smooth rocks or rough ones. I'll put the smooth ones on one square and the rough ones on the other square. Oh, I have to make a labels too.
3. Spot the same move somewhere else (5 min)
Read the passage below. A different character is doing the same thing here. Point to the wondering sentence and then to the doing sentence. Say aloud whether they come in the same order as they did before.
Word preview: order
Let me think. I see three kinds of cookies. I wonder if there are more chocolate chip, oatmeal, or sugar cookies. I'll stack them up and find out.
4. Write a wondering sentence of your own (4 min)
Write one sentence that starts I wonder about something in this classroom you do not know. Then write a second sentence that starts I'll and says how you would find out. Read both to your partner.
Word preview: investigate

Short version — 9 minutes

1. Find the wondering sentence (5 min)
The teacher reads the passage below. Find the sentence that begins I wonder and read it aloud. Say what the character does not know yet.
Word preview: wonder
I wonder if there are more smooth rocks or rough ones. I'll put the smooth ones on one square and the rough ones on the other square. Oh, I have to make a labels too.
2. Find the sentence that answers it (4 min)
Read the passage below again. Find the sentence that starts with I'll and say what the character has decided to do about the question.
Word preview: plan
I wonder if there are more smooth rocks or rough ones. I'll put the smooth ones on one square and the rough ones on the other square. Oh, I have to make a labels too.

Three levels

Support: In step 1, read the printed passage with the teacher and point to the two words I wonder. Say the whole sentence after the teacher. Then answer aloud: is the character sure or not sure?
At Grade: Read the printed passage in step 1, name the wondering sentence and the doing sentence, and say in your own words how the second one answers the first.
Extension: The printed passage in step 3 makes the same move with a different character. Say two or three sentences about why a writer might repeat the same sentence shape each time a character starts something new.

English learners

I wonder if is a whole English frame for not knowing, and the if inside it is not the if of a condition — a learner who reads it that way will look for a consequence that never comes. Say I don't know whether ___ and then I wonder if ___ so the two are heard as the same move. Invite students to say, in their strongest language, that they do not know something and want to find out. Rehearsable frame: I wonder if ___. I'll ___ and find out.

Materials

The Great Graph Contest, the passage printed in this step
highlighter or finger
pencil and paper
Word cards: wonder, plan, order, investigate

Standards & curriculum

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

10. Think, Collect, Use, Put: How the Back of the Book Tells You What to Do Language · Reading a Set of Steps and Following Them

The last page of this book stops telling a story and starts telling the reader what to do, in four short commands. Students read it, find where each instruction starts, say what makes these sentences sound different from the story sentences, and put the steps in order without looking. They finish by turning one step into a full sentence about themselves. Nothing is computed; the work is reading procedural writing and noticing how it is worded.

Full lesson — 20 minutes

1. Read the steps and find where each one starts (6 min)
The teacher reads the passage below once. Then read it yourself. Each instruction starts with a word that tells you to do something. Point to each of those starting words in turn and read them aloud in order.
Word preview: steps
To make your own graph, think of a question to ask. What is my family's favorite snack food? Collect data and write it down. Use real objects and or art supplies to create your graph. Put a title and labels on your graph so people will know what it is about.
2. Hear how it is different from a story sentence (5 min)
Read both passages below. One tells you what somebody did. One tells you what to do. Say aloud which is which. Then say the one thing the instruction passage never says that the story passage does say.
Word preview: instruction
To make your own graph, think of a question to ask. What is my family's favorite snack food? Collect data and write it down. Use real objects and or art supplies to create your graph. Put a title and labels on your graph so people will know what it is about.
She wrote down their answers to keep track of the data. She made a tulip shape out of poster board and then wrote the title question on top.
3. Put the steps back in order (5 min)
Read the passage below one more time, then turn it face down. Tell your partner the four things you are told to do, in the right order. Your partner turns the passage back over and says whether you kept the order the book used.
Word preview: order
To make your own graph, think of a question to ask. What is my family's favorite snack food? Collect data and write it down. Use real objects and or art supplies to create your graph. Put a title and labels on your graph so people will know what it is about.
4. Say a step as a sentence about you (4 min)
Pick one of the steps and say it as a full sentence about yourself, starting with I will. Say what your question would be. Then listen to your partner's.
Word preview: follow

Short version — 9 minutes

1. Read the steps and find where each one starts (5 min)
The teacher reads the passage below. Point to the word that starts each instruction and read those words aloud in order.
Word preview: steps
To make your own graph, think of a question to ask. What is my family's favorite snack food? Collect data and write it down. Use real objects and or art supplies to create your graph. Put a title and labels on your graph so people will know what it is about.
2. Put the steps back in order (4 min)
Read the passage below, then turn it face down and tell your partner the four things you are told to do, in order.
Word preview: order
To make your own graph, think of a question to ask. What is my family's favorite snack food? Collect data and write it down. Use real objects and or art supplies to create your graph. Put a title and labels on your graph so people will know what it is about.

Three levels

Support: In step 1, read the printed passage with the teacher and point to the first word, To. Then point to the word Collect. Say those two instructions after the teacher.
At Grade: Read the printed passage in step 1, name the word that starts each instruction, then in step 3 retell the four steps in the order the book gave them.
Extension: The printed passages in step 2 sit on the same page of the same book but are worded completely differently. Say two or three sentences about why the writer changed the wording for the last page.

English learners

English instructions drop the subject entirely — Collect data, not You collect data — so a learner may read them as an unfinished sentence or as a statement about someone else. Read each instruction twice, once as the book has it and once with You added at the front, so the missing word is heard as missing on purpose. Invite students to give an instruction in their strongest language and say whether it names the person. Rehearsable frame: First ___. Then ___.

Materials

The Great Graph Contest, the passage printed in this step
highlighter or finger
two passage strips
pencil and paper
partner talk cards
Word cards: steps, instruction, order, follow

Standards & curriculum

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

11. Excuse Me, May I Ask You a Question? How Beezy Talks to Strangers Language · Asking a Polite Question and Listening to the Answer

Beezy asks four strangers almost the same question and gets four different answers. Students read the exchanges, find the polite words she uses before asking, notice how she changes the wording each time, and then ask each other a question the same way. They finish by saying which answer surprised them. Nothing is tallied; the work is the language of asking and listening.

Full lesson — 20 minutes

1. Find the polite words (6 min)
The teacher reads the passage below once. Then read it together. Find the two words Beezy says before she asks anything, and read them aloud. Then say why somebody says those words first.
Word preview: polite
Excuse me, may I ask you a question? What are you planning to do with your flower? I'm going to plant it in my garden.
2. Notice she does not say it the same way twice (5 min)
Read the passage below. Beezy asks three more people here. Point to each question. Say aloud one word she changes each time, and say why she might change it depending on who she is talking to.
Word preview: question
Sir, what do you plan to do with this plant? As a birthday gift for my friend. What will you do with this flower? I'll plant it in my yard. So what will you do with your new plant? Eat it!
3. Ask it yourself (5 min)
Read the passage below once more with a partner. Then take turns: one of you is Beezy and asks the question politely, and the other gives an answer that is not in the book. Swap over and go again.
Word preview: answer
Excuse me, may I ask you a question? What are you planning to do with your flower? I'm going to plant it in my garden.
4. Say which answer surprised you (4 min)
Talk with your partner about the answers the shoppers gave. Say which one you did not expect and why. Use a whole sentence starting I did not expect ___ because ___.
Word preview: listen

Short version — 9 minutes

1. Find the polite words (5 min)
The teacher reads the passage below. Find the words Beezy says before she asks anything and read them aloud. Say why somebody says those first.
Word preview: polite
Excuse me, may I ask you a question? What are you planning to do with your flower? I'm going to plant it in my garden.
2. Notice she does not say it the same way twice (4 min)
Read the passage below. Point to each question Beezy asks. Say one word she changes between them.
Word preview: question
Sir, what do you plan to do with this plant? As a birthday gift for my friend. What will you do with this flower? I'll plant it in my yard. So what will you do with your new plant? Eat it!

Three levels

Support: In step 1, read the printed passage with the teacher and point to the words Excuse me. Say them aloud twice. Then say the question after the teacher, one part at a time.
At Grade: Read the printed passages in steps 1 and 2, name the polite words Beezy uses, and say one way she changes the question between one shopper and the next.
Extension: In the printed passage in step 2 the last shopper answers with two words that do not fit the others. Say two or three sentences about what that answer tells you about asking real people questions.

English learners

English softens a request with a stack of politeness before the question itself — Excuse me, may I, please — and a learner who goes straight to the question can sound abrupt without meaning to. Practise the opening words on their own, before any question is attached. Invite students to say how a person is asked politely in their strongest language, and say which words do that work. Rehearsable frame: Excuse me, may I ask you ___?

Materials

The Great Graph Contest, the passage printed in this step
highlighter or finger
partner talk cards
Word cards: polite, question, answer, listen

Standards & curriculum

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

12. He Cut, He Drew, He Put: How the Back of the Book Retells What Happened Language · Explaining How Something Was Made, Step by Step

The back of this book retells things the reader has already seen, but as an explanation instead of a scene. Students read two of these retellings, list the actions in order, and then find the sentence in one of them that gives a warning rather than an action. They finish by explaining how they made something. Nothing is computed or compared by amount; the work is reading an explanation and separating the doing from the advice.

Full lesson — 20 minutes

1. List the actions in order (6 min)
The teacher reads the passage below once. Then read it yourself. Say aloud the three things this person did, in the order the passage gives them. Start each one with He.
Word preview: explain
He cut out paper rectangles all the same size, and drew a picture of each baby. He put the babies in one of two groups. Either reptiles or birds.
2. Find the sentence that is not an action (5 min)
Read the passage below. Most of it says what somebody did, but one sentence gives a warning about doing it wrong. Point to that sentence and read it aloud. Say what would go wrong if you ignored it.
Word preview: warning
This bar graph is also made of real objects, cookies in this case. To see which kind of cookie was most common, Beezy piled up each type in a separate stack. If a stack is taller, that means there are more of those cookies. The cookies must be about the same thickness for the results to be accurate.
3. Find the advice that applies to all of them (5 min)
Read the short passage below. This one sentence is advice for every graph in the book, not just one. Read it aloud. Then say in your own words who the advice is really meant to help.
Word preview: advice
As with all graphs, it is important to put labels on it so people understand what the graph is about.
4. Explain something you made (4 min)
Tell your partner how you made something recently, using three sentences that each start with I. Then add one sentence of warning about what somebody should be careful of.
Word preview: process

Short version — 9 minutes

1. List the actions in order (5 min)
The teacher reads the passage below. Say the three things this person did, in order, each starting with He.
Word preview: explain
He cut out paper rectangles all the same size, and drew a picture of each baby. He put the babies in one of two groups. Either reptiles or birds.
2. Find the sentence that is not an action (4 min)
Read the passage below. Find the sentence that gives a warning instead of an action and read it aloud. Say what would go wrong without it.
Word preview: warning
This bar graph is also made of real objects, cookies in this case. To see which kind of cookie was most common, Beezy piled up each type in a separate stack. If a stack is taller, that means there are more of those cookies. The cookies must be about the same thickness for the results to be accurate.

Three levels

Support: In step 1, read the printed passage with the teacher and point to each sentence that starts with He. Say the first action aloud twice.
At Grade: Read the printed passage in step 1 and list the actions in order, then in step 2 find the one sentence that warns instead of describing.
Extension: The printed passage in step 2 ends by saying what must be true for the results to be accurate. Say two or three sentences about why an explanation would include something like that at the end rather than the beginning.

English learners

An explanation in English moves in the past tense while the advice inside it switches to must or should, and that tense change is the only signal that the sentence has stopped describing and started warning. Read one action sentence and one warning sentence back to back and name which is which. Invite students to explain, in their strongest language, how something is made, and add one warning. Rehearsable frame: First he ___. But it must ___.

Materials

The Great Graph Contest, the passage printed in this step
highlighter or finger
partner talk cards
Word cards: explain, warning, advice, process

Standards & curriculum

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

13. Venn, Then, End: A Word This Book Spells Three Different Ways Language · Special Words a Book Gives You, and Checking Them

A book about graphs has to hand the reader technical names, and this transcript hands over one name three different ways: correctly once in the story and wrongly in both places at the back where it is supposed to be defined. Students read the three passages side by side, say which spelling is the real one and how they can tell, and then use the definition that is right even though its first word is wrong. Nothing is calculated; the work is reading technical words carefully and checking a term against how it is used.

Full lesson — 20 minutes

1. Meet the word where the book gets it right (6 min)
The teacher reads the passage below once. Then read it yourself. Find the two-word name for this kind of diagram and read it aloud. Say what the passage tells you goes in the left circle.
Word preview: term
Here is a Venn diagram. The suits with flowers are on the left circle.
2. Meet the same word gone wrong (5 min)
Read the two short passages below. Both are from the back of the book and both are supposed to name the same diagram you just met. Read the first word of each one aloud. Say whether either matches the name from step 1.
Word preview: spelling
Then diagrams show how things are alike and different.
End diagram. It has two or more overlapping circles or other shapes.
3. Use the definition anyway (5 min)
Read the two passages below again, side by side. The names are wrong but the rest of each sentence still describes something real. Say aloud, in your own words, what this kind of diagram is and what it does, using only what these passages tell you.
Word preview: define
Then diagrams show how things are alike and different.
End diagram. It has two or more overlapping circles or other shapes.
4. Say how you would check a word (4 min)
Talk with your partner. If a book gave you a word and you were not sure it was right, say two things you could do to check it. Say them as full sentences starting I could.
Word preview: check

Short version — 9 minutes

1. Meet the word where the book gets it right (5 min)
The teacher reads the passage below. Find the two-word name for this kind of diagram and read it aloud. Say what goes in the left circle.
Word preview: term
Here is a Venn diagram. The suits with flowers are on the left circle.
2. Meet the same word gone wrong (4 min)
Read the two short passages below. Read the first word of each aloud. Say whether either matches the name you just read.
Word preview: spelling
Then diagrams show how things are alike and different.
End diagram. It has two or more overlapping circles or other shapes.

Three levels

Support: In step 1, read the printed passage with the teacher and point to the name Venn. Say it aloud twice. Then answer aloud: does the diagram have circles?
At Grade: Read the printed passages in steps 1 and 2 and say which one spells the name correctly, using what the sentences around it are describing as your evidence.
Extension: The printed passages in step 2 get the name wrong in both places where the book is defining it, but right in step 1 where it is only mentioned. Say two or three sentences about why a reader should not simply trust the first spelling they see.

English learners

A technical term is a name, not a describable word, so a learner cannot repair a wrong one from context the way they might repair an ordinary word — they have to compare it against another place it appears. Say the correct name clearly and write it up before the two wrong versions are read. Invite students to name something in their strongest language that has one right name and several common mistakes. Rehearsable frame: The book says ___, but the right word is ___.

Materials

The Great Graph Contest, the passage printed in this step
highlighter or finger
two passage strips
partner talk cards
Word cards: term, spelling, define, check

Standards & curriculum

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