Grandma's Button Box

$Grandma's Button Box book cover$

Grade 1
5 skill lessons

Math

Skill lessons

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

1The Rule That Leaves Nothing Over
2Twelve Compartments and Only Seven Piles
3One Colour, One Compartment, Count to Twelve
4One Handful, Three Charts
5Find the Button for Grandma's Sweater

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.

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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.

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Skill lessons

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

1. The Rule That Leaves Nothing Over Concept · Sorting one set by a single attribute so that every button lands in exactly one group

Kelly's cousins try three rules on one pile of buttons and the first one breaks in a way children can see and count. Sorting by shape gives Timmy his round buttons and Brendan his square ones, and then leaves Kelly holding ducks, boats, cowboy boots and a pineapple with nowhere to put them. Students run the same rule on their own tray, drop every button no shape group will take into a cup, and count the cup out loud. Then they tip everything back and run the colour rule, where the cup ends up empty. A rule that sorts has to name a group for every button in the tray, and the count in the cup is how a child finds out whether it does.

Full lesson — 20 minutes

1. Pour out the buttons and say what is different (4 min)
Pour your tray of buttons out flat and move nothing yet. Take turns saying one thing that is true of some of these buttons but not of all of them. Say four different things before anyone touches a button.
Word preview: compartment
Soon all the buttons were in a big pile.
Wait, said Kelly, we have to put them back in the right compartments.
2. Sort by shape and count what will not fit (5 min)
Sort the whole tray by shape. Start a group for round, one for square, one for triangle and one for diamond, and put any button that fits none of them in the stray cup. When the tray is empty, count the stray cup out loud.
Word preview: everything else, stray
Timmy picked out all the round buttons.
Kelly started to pick out everything else.
How do I sort these?" she asked.
3. Say which rule left buttons out (4 min)
Hold up your stray cup and say the count in one sentence: the shape rule left this many buttons with no group. Say what the buttons in the cup have in common. Listen for whether your partner agrees that they have nothing in common at all.
We tried sorting them by shape, said Kelly, but that didn't work, said Timmy.
4. Sort the same buttons by colour and check for strays (7 min)
Tip every group and the stray cup back together and sort the same buttons again, this time by colour. Every button gets a colour plate and the stray cup has to end up empty. Count each plate, then count the stray cup and say that count out loud even though it is nothing.
Sorting them by color, said Kelly.
We put them back by color, said Kelly.

Short version — 9 minutes

1. Pour out the buttons and say what is different (4 min)
Pour the buttons out flat and move nothing. Take turns saying one thing that is true of some of them but not all of them, twice each.
Word preview: compartment
Soon all the buttons were in a big pile.
2. Sort by shape and count what will not fit (5 min)
Sort the tray by shape into round, square, triangle and diamond, and drop anything that fits none of them in the stray cup. Count the stray cup out loud when the tray is empty.
Word preview: everything else, stray
Timmy picked out all the round buttons.
Kelly started to pick out everything else.

Three levels

Support: Hand the child a tray of a dozen buttons rather than thirty, chosen so that four of them are plainly round and four plainly square. Everything else stays whole: the two shape groups, the stray cup, and the count of the cup said out loud. Add buttons a few at a time and let the child recount the cup after each handful.
At Grade: Sort thirty buttons by shape with a stray cup, count the cup, then sort the same thirty by colour and count the cup again. Say both cup counts aloud and say which rule left nothing over.
Extension: Invent a rule that leaves exactly two buttons in the stray cup, hand your tray and your rule to another pair, and see whether their cup comes out at two as well. Then say what you would have to change about the rule, not the buttons, to empty the cup.

English learners

Sorting is done with hands, so a child at the very start of English can run the whole rule and be seen to be right without saying a word. Two pieces of language need work before the counting does. The book names its leftover group as everything else, which defines a group by what it is not - several languages build that with a negative verb rather than a noun phrase, and a child who hears it as some other things will not put every unclaimed button in the cup. And compartment is a long word for a small hole, so hold an egg carton while you say it. Rehearse one frame and reuse it for every rule: the ___ rule left ___ buttons out. Children may argue about a doubtful button in their strongest language and give only the frame in English.

Materials

A tray of about thirty mixed buttons for each pair
A cup labelled Strays, one per pair
Twelve small paper plates, so each colour group has its own place
Word cards: compartment, everything else, stray

Standards & curriculum

These lessons are being matched against curricula now.

2. Twelve Compartments and Only Seven Piles Reasoning · Matching groups to compartments one to one, and counting the compartments left empty

This is the sentence the whole book turns on: twelve compartments and only seven sizes. The children have already built the seven piles and named them from teeny to humongous, and Brandon's line is what tells them the size rule is finished before it starts. Students build the seven piles, set one pile into one compartment of a twelve-space tray, and put a finger in each compartment that has nothing in it. Then they tip the piles back, sort the same buttons by colour, and find no empty compartments at all. The reasoning is the argument they make afterwards: a rule fits this box only when its group count and the compartment count come out the same, and the empty compartments are how you show it.

Full lesson — 20 minutes

1. Build the seven size piles (4 min)
Sort your buttons into seven piles by size and lay one of Kelly's seven size cards beside each pile, from teeny up to humongous. Every button goes in the pile whose card fits it, and no pile may be left with nothing in it. Count your piles by touching each one.
Word preview: humongous
After a while they had seven piles of buttons.
Let's see, said Kelly, we've got teeny, small, medium, large, extra-large, jumbo, and humongous.
2. Put one pile in each compartment and count the empties (5 min)
Set one size pile into one compartment of the twelve-space tray and keep going until every pile has a compartment of its own. Now put a finger in each compartment that has nothing in it and count those out loud. Say your count of empty compartments before anybody reads Brandon's line.
Word preview: compartments
There are 12 compartments, said Brandon, and only 7 sizes.
3. Do it again with the colour groups (7 min)
Tip the seven piles back together and sort the same buttons by colour instead, taking Sarah and Kelly's six colours first and then Brandon and Timmy's six. Set one colour group into each compartment. Count the empty compartments again and say that count out loud too.
Sarah and Kelly picked out the buttons that were white, pink, purple, yellow, orange, and brown.
Brandon and Timmy picked out the buttons that were red, blue, green, silver, gold, and black.
A color for every compartment, Brandon said.
4. Say which rule fits the box (4 min)
Say in one sentence which rule filled the tray and which rule left compartments with nothing in them, and give both of your empty counts as the reason. If your partner disagrees, put the piles back in the tray and count the empties again together.
Kelly sighed, this isn't right either.
There must be another way, she said.

Short version — 9 minutes

1. Build the seven size piles (4 min)
Sort the buttons into seven piles by size and lay one size card beside each pile, teeny up to humongous. Count the piles by touching each one.
Word preview: humongous
After a while they had seven piles of buttons.
Let's see, said Kelly, we've got teeny, small, medium, large, extra-large, jumbo, and humongous.
2. Put one pile in each compartment and count the empties (5 min)
Set one size pile into one compartment until every pile has its own. Put a finger in each compartment with nothing in it and count those out loud before anybody reads Brandon's line.
Word preview: compartments
There are 12 compartments, said Brandon, and only 7 sizes.

Three levels

Support: Use a six-compartment tray and three size piles rather than twelve and seven, so the empty count is three and can be held in one hand. The work stays whole: one pile to one compartment, a finger in every empty compartment, and the count said aloud. Move up to the twelve-space tray once the child has said three without recounting twice.
At Grade: Build seven size piles, set them one to a compartment in the twelve-space tray, and count the empty compartments. Do it again with the colour groups and say both empty counts, then say which rule fits the box.
Extension: Say how many size piles the children would have needed for no compartment to be empty, and say how you know without setting any buttons in the tray. Then put the seven size cards in order from teeny to humongous and say which two piles you would split to get there.

English learners

The counting here is done with a finger in an empty hole, which needs no English at all, so start every child there. Three things carry the meaning and none of them is a numeral. Only is the book's single comparison word and it does the work of a whole phrase - a child who hears just seven sizes hears no problem at all, so say the line twice with a hand over the five empty compartments. Compartment names a hole in a box and has no everyday use elsewhere. And empty is being used as a count here, not a description: five compartments are empty is a number. Rehearse one frame and reuse it: the ___ rule leaves ___ compartments empty. Children may argue about which rule fits in their strongest language and give only the frame in English.

Materials

A tray of about thirty mixed buttons for each pair
Seven size cards reading teeny, small, medium, large, extra-large, jumbo and humongous
An egg carton or ice-cube tray with twelve compartments, one per pair
Word cards: humongous, compartments

Standards & curriculum

These lessons are being matched against curricula now.

3. One Colour, One Compartment, Count to Twelve Fluency · Counting to twelve with one-to-one matching, and putting six with six

The book hands over one addition and one match. Sarah and Kelly pick out six colours, Brandon and Timmy pick out six more, and Kelly reads the total as twelve - and then Brandon says a colour for every compartment, which puts those twelve against the twelve holes in the box one for one. Students lay a row of six buttons for each team, count each row by touch, push the rows into one line and count it to twelve, then say six and six make twelve while sliding the rows apart and together. They finish by dropping one button of each colour into its own compartment, counting up as the buttons land and counting back down as they come out. The fluency is one touch, one number word, and a total that comes out at twelve every time.

Full lesson — 20 minutes

1. Count each team's colours (5 min)
Lay out one button for each colour Sarah and Kelly picked, in a straight row, and count the row by touching one button per number word. Build a second row underneath for the six colours Brandon and Timmy picked and count that one the same way. Say how many are in each row with your hand flat over the row.
Word preview: purple, silver
Sarah and Kelly picked out the buttons that were white, pink, purple, yellow, orange, and brown.
Brandon and Timmy picked out the buttons that were red, blue, green, silver, gold, and black.
2. Push the rows together and count to twelve (4 min)
Slide the second row onto the end of the first so all the buttons make one line along the paper strip, one button to a square. Count the line by touching one button per number word and stop on the last button. Say the number you stopped on, then say the two row counts you started with.
We've got 12 colors said Kelly.
3. Say six with six (5 min)
Say the sentence six and six make twelve while you slide the two rows apart and push them together again. Now break the line of twelve into two rows a different way, count both rows, and say that sentence too. Keep the line of twelve on the strip so every sentence can be checked against it.
4. Give every colour its own compartment (6 min)
Drop one button of each colour into its own compartment in the twelve-space tray, counting out loud as each one lands. Check that no compartment holds two buttons and no compartment is left empty. Then lift them out one at a time, counting back down from twelve to nothing.
Word preview: every
A color for every compartment, Brandon said.
Wait, said Kelly, we have to put them back in the right compartments.

Short version — 9 minutes

1. Count each team's colours (5 min)
Lay one button for each of Sarah and Kelly's six colours in a row and count it by touch, then build and count a second row for Brandon and Timmy's six. Say each row count with your hand flat over the row.
Word preview: purple, silver
Sarah and Kelly picked out the buttons that were white, pink, purple, yellow, orange, and brown.
Brandon and Timmy picked out the buttons that were red, blue, green, silver, gold, and black.
2. Push the rows together and count to twelve (4 min)
Slide the second row onto the end of the first, one button to a square, and count the whole line by touch. Say the number you stopped on and then the two row counts you started with.
We've got 12 colors said Kelly.

Three levels

Support: Start with one row of six and count it three times, touching one button per number word, before the second row is laid at all. Keep the touching rule exactly as it is - one touch, one number - and add the second row only once six comes out the same three times running. Count the joined line with the child's finger under yours.
At Grade: Count each row of six by touch, push them into one line and count to twelve, and say six and six make twelve. Then drop one button of each colour into its own compartment, counting up as they land.
Extension: Fill the tray, then take out any three buttons and say how many compartments are empty without counting the holes one by one. Put them back and say the total again. Then find every way to break your twelve into two rows and say each one as a sentence.

English learners

Counting by touch is the same act in every language, and a child with no English can do the whole first row on day one. What needs rehearsing is the colour vocabulary, because twelve colour words arrive at once and six of them - purple, silver, gold, brown, orange, pink - are the ones least likely to have been taught yet. Hold each button up as the word is said, and let the child answer by pointing rather than naming for as long as they need to. The number words are worth a separate pass: eleven and twelve break the pattern the teens follow, so count the line aloud together twice before anyone counts it alone. Rehearse one frame and reuse it: six and six make ___. Children may say the colour names in their strongest language while giving the count in English.

Materials

A set of twelve buttons for each pair, one in each of the book's twelve colours
A strip of paper ruled into twelve squares, one per pair
An egg carton or ice-cube tray with twelve compartments, one per pair
Word cards: purple, silver, every

Standards & curriculum

These lessons are being matched against curricula now.

4. One Handful, Three Charts Representation · Recording one set of buttons under three sorting rules and comparing how many groups each rule makes

The back page hands a class its own procedure: you can sort these buttons in different ways, and then three lines showing what each way looks like - by shape all round, by colour all yellow, by size all large. Students take one handful of buttons, count it once and never change it, then lay that same handful out three times in rows: shape rows, colour rows, size rows. A number card goes beside every row and another beside the count of rows, so three charts sit side by side with the same total at the top and a different number of rows underneath. The point is that the rule chooses the rows; the buttons stay put.

Full lesson — 20 minutes

1. Take one handful and count it (5 min)
Take one handful of buttons from the box, tip it into your own tray and count it by touching each button once. Say the count, put that number card at the top of your paper, and do not add or take away a single button for the rest of the lesson.
Word preview: chart
Sorting chart, you can sort these buttons in different ways.
2. Build the shape chart (4 min)
Sort your handful into shape groups and lay each group along its own row on the paper. Count each row and set a number card beside it, then count the rows and set a number card for that. Say how many rows the shape rule made.
Sort them by shape, all round.
3. Build the colour chart and the size chart with the same buttons (5 min)
Sweep the handful back together and lay it out again by colour, one group to a row, then a third time by size. Put a number card beside every row and one for how many rows each rule made. The handful never changes; only the rows do.
Sort them by color, all yellow.
Sort them by size, all large.
4. Read the three charts against each other (6 min)
Lay your three charts side by side and read the row counts aloud, rule by rule. Say which rule made the most rows and which made the fewest, and check that the number card at the top is still the same for all three. Then take the book's hint, turn your buttons over and count the ones with two holes, and say whether holes would make a fourth chart.
Word preview: holes
Can you think of another way to sort them?
Hint, check the holes.

Short version — 9 minutes

1. Build the shape chart (4 min)
Lay your counted handful out in shape rows, one group to a row. Set a number card beside each row and one for how many rows the shape rule made.
Sort them by shape, all round.
2. Build the colour chart and the size chart with the same buttons (5 min)
Sweep the same handful together and lay it out again by colour, then a third time by size, with a number card beside every row. Say how many rows each rule made and check the handful never changed.
Sort them by color, all yellow.
Sort them by size, all large.

Three levels

Support: Give the child a handful of ten and only two rules, shape and colour. The recording stays whole - a number card beside every row and a number card for the rows - and the handful is counted again out loud at the start of each chart, so the child hears that ten did not change when the rows did. Add the size chart once the two charts are read side by side.
At Grade: Count one handful, then lay it out three times, by shape, by colour and by size, with a number card beside every row and a number card for the rows. Read the three charts side by side and say which rule made the most rows.
Extension: Predict the number of rows before you sort. Say how many rows you think the size rule will make, sort, and say whether you were over or under. Then find a rule that gives your handful exactly two rows, and one that gives it as many rows as there are buttons.

English learners

The three charts are built with hands and read with a finger, so the mathematics is available to a child who is not speaking English yet. The language that matters is the word row and the word rule, because both are new and both name something the child can point at - lay a row and say row, hold up a size card and say rule. The back page's three lines are worth reading aloud as they are written, because each one puts the rule and an example together in five words: by shape, all round. Rehearse one frame and reuse it for every chart: sorting by ___ makes ___ rows. Children may name the shapes and colours in their strongest language and give the row counts in English.

Materials

A box of mixed buttons for the class to take handfuls from
A tray and a sheet of paper for each pair
Number cards from 0 to 20, one set per pair
Word cards: chart, holes

Standards & curriculum

These lessons are being matched against curricula now.

5. Find the Button for Grandma's Sweater Application · Using a sorted collection to find a button that matches on two attributes, and comparing how many buttons each search touched

Grandma gives the reason sorting is worth the trouble: she stopped looking for new buttons because finding anything in that box took so long. Students run both searches for themselves. First they hunt a named colour and size in a jumbled box, moving one button at a time into a line so the line records how many they had to look at. Then they hunt a second button in a set already sorted by colour and count that line too. They hold candidates against a grey felt sweater and say wrong colour or wrong size until one is right on both, then compare their two line counts and say how many fewer buttons the sorted tray made them handle.

Full lesson — 20 minutes

1. Search the jumbled box and count what you touch (4 min)
Your partner holds up a button and names its colour and its size. Find its twin in the jumbled box, moving one button at a time into a line as you look at it. Stop the moment you find the twin and count your line.
Word preview: jumbled
They were always just jumbled together.
I never bothered to look for new buttons because it always took so long to find anything in that button box.
2. Search the sorted tray and count again (5 min)
Your partner names the colour and the size of a second button. This time go straight to that colour's compartment and move one button at a time into a line as you look at it. Stop when you find the twin and count this line too.
It won't take long at all.
3. Say wrong colour, then say wrong size (7 min)
Take turns holding a button against the grey felt and saying either wrong colour or wrong size, and put every rejected button back where it came from. Keep going until one button is right on both counts, then say what makes it right. Count how many you turned down for colour and how many for size, and say both numbers.
Wrong color said Brendan.
Wrong size said Kelly.
They're almost perfect.
4. Say which search was shorter (4 min)
Say your two line counts in one sentence and say which was smaller. Then say how many fewer buttons the sorted tray made you look at. Last, say whether the sorted tray would still be quicker if the button you wanted happened to be the very last one in its compartment.
Word preview: sorted
I think I'll keep my buttons sorted from now on," she said.

Short version — 9 minutes

1. Search the jumbled box and count what you touch (4 min)
Your partner names a button's colour and size. Find its twin in the jumbled box, moving one button at a time into a line as you look at it, and count the line when you stop.
Word preview: jumbled
I never bothered to look for new buttons because it always took so long to find anything in that button box.
2. Search the sorted tray and count again (5 min)
Your partner names a second button's colour and size. Go straight to that colour's compartment, move one button at a time into a line as you look at it, and count this line too. Say which line was shorter.
It won't take long at all.

Three levels

Support: Name only the colour, not the colour and the size, so one attribute decides the search. Both searches stay whole and both lines are still counted, which is the whole point. Add the size once the child has said which of two counts is smaller without recounting either line.
At Grade: Run both searches, count both lines, and say which was smaller and by how many. Reject candidates aloud on colour and on size until one button is right on both.
Extension: Say what would have to be true for the jumbled box to win, then set it up and test it: put the wanted button on the very top of the jumbled box and at the back of its compartment, run both searches again and report both line counts. Say why one short search does not settle which box is quicker.

English learners

A search is silent work, so a child can take a full turn in this lesson while saying nothing but a colour word. The language is a rejection, which is short and worth teaching exactly as the book writes it: wrong colour, wrong size. Both are two words and both are said while holding the button against the felt, so the meaning is visible at the moment it is spoken. Note that a rejection in English puts wrong before the attribute, where several languages put the attribute first, so a child may say colour wrong and should be taken as correct. Rehearse one frame for the ending: the sorted tray was shorter by ___ buttons. Children may explain why in their strongest language.

Materials

A box of about forty mixed buttons, jumbled, for each pair
A second set of the same forty buttons, already sorted by colour into a twelve-compartment tray
A square of grey felt for the sweater, one per pair
Word cards: jumbled, sorted

Standards & curriculum

These lessons are being matched against curricula now.