If the Shoe Fits

$If the Shoe Fits book cover$

Grade 1
4 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.

1Five Paper Clips Long
2The Same Shoe, Two Numbers
3Will It Fit, and With How Much to Spare
4One Size, and It Stays That Size

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.

No reading and language lessons for this book yet.

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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. Five Paper Clips Long Concept · Measuring a length by laying same-size units end to end and counting them

Albert lays a line of paper clips along a people's shoe and the book reads the number off for us without ever showing the line being laid. Here children lay it. Each pair takes clips that are all one size, puts the first clip's end against the heel end of a paper shoe, touches every new clip against the end of the last one, stops at the toe and counts aloud. The number that comes out is not written on the shoe and not written on the clips: it is how many copies of one clip it takes to get from one end of the shoe to the other, and it only comes out right if nothing overlaps and nothing is skipped. Children then measure the three things Groucho got to first, and close with a clip line somebody laid with gaps in it, so they see a count come out too small and can say what caused it.

Full lesson — 20 minutes

1. Lay the clips with no gaps (6 min)
Take clips out of the pot one at a time and lay them along your paper shoe, starting with the end of the first clip touching the heel end. Put each new clip so its end touches the end of the one before it, with no space between them and no clip sitting on top of another. Stop when you reach the toe. Count the clips out loud, touching each one as you say its number, and say the last number again on its own.
Word preview: clip, count
Albert had a paperclip collection.
They were all the exact same size.
2. Say the whole sentence and write the number (4 min)
Say the whole thing out loud to your partner the way the book says it, the thing first and then the number and then the words paper clips long. Then write just the number on the first line of your measuring card, next to the word shoe. If you say only the number and not the words paper clips, your partner says wait, and you say it again.
Word preview: long
It was five paper clips long.
3. Measure the three things from the yard (5 min)
Take the feather, the ball and the bun out of the envelope. These are the things Groucho got to first. Measure each one with the same clips, laying them end to end with no gaps the way you did on the shoe, and count out loud. Say each one as a whole sentence and write its number on your card. Then say which of the three took the most clips.
Word preview: measure
A huge striped feather, a pink rubber ball, a dropped hot dog bun.
4. Check a clip line that was laid wrong (5 min)
Look at the printed card. Somebody has already laid clips along the same shoe and counted four. Count the drawn clips yourself, then lay your own clips on your own shoe again with no gaps and count those. Say both numbers out loud, then say which number belongs to the shoe and point at what went wrong on the card.
Word preview: gap
Wanda measured the shoe.

Short version — 9 minutes

1. Lay the clips with no gaps (5 min)
Lay clips along your paper shoe from the heel end, each new clip touching the end of the one before it, with no space between them. Stop at the toe. Count them out loud, touching each one.
Word preview: clip, count
They were all the exact same size.
2. Say the whole sentence and write the number (4 min)
Say it out loud the way the book does, the thing and then the number and then the words paper clips long. Write the number on your measuring card next to the word shoe.
Word preview: long
It was five paper clips long.

Three levels

Support: Work with the shoe and the ball only, using the two cards that have a clip track printed along them, so each clip drops against the last one and a gap is hard to leave. Count out loud, touching each clip, and say the whole sentence before writing anything. The laying and the counting are exactly what everybody else does; the track only holds the clips still.
At Grade: Measure the shoe and all three yard things with same-size clips laid end to end, say each measurement as a whole sentence with the words paper clips long in it, write the four numbers on the card, and settle the gap card by relaying the shoe.
Extension: Measure the bun with the clips, then measure it again with the clips spaced a finger apart on purpose, counting only the clips that fit inside the bun. Say both numbers, say which one is the bun's length, and say why the other one came out smaller than it should be. Then say what would happen to the number if the clips were allowed to lie on top of each other instead, and try it to see whether you were right.

English learners

Counting and laying carry across languages, and neither will be the hard part here. What has to be rehearsed is the English order in five paper clips long, where the number comes first, then the thing you measured with, then the word long right at the end, because several languages put the length word first or attach it to the number. Say the frame aloud together with the clips in view, the ___ is ___ paper clips long, before anyone writes. Children who are new to English can count the clips in their strongest language while touching them and then say the whole sentence in English, and the touching is what proves the count either way. The word long is worth naming twice, because it is the ordinary word for a big amount of time as well as the word for a length.

Materials

A pot of fifteen paper clips, all exactly the same size, one pot per pair
A paper shoe cut to exactly five of the clips in the pot, one per pair
A measuring card per pair, ruled with four lines headed thing and paper clips, with shoe, feather, ball and bun already printed down the first column
An envelope of three paper things from the yard per pair, cut to six, two and four of the same clips, labelled feather, ball and bun
A printed card showing the same paper shoe with four clips drawn along it and a gap left between each pair of clips, one per pair
A shoe card and a ball card per pair with a clip track printed along each, the same lengths as the plain ones, for pairs working at Support
Word cards: measure, long, same size

Standards & curriculum

These lessons are being matched against curricula now.

2. The Same Shoe, Two Numbers Reasoning · Measuring one object with two different units and comparing the two counts

The book measures one shoe three times and gets ten, then eight, then five, and nobody ever says the shoe changed. Children put that in their own hands: they lay clips along a paper shoe and count five, take them off, lay mouse-foot cards along the same shoe and count ten, and then hold one clip against one foot to see why. Both numbers are right and the shoe did not change between them, because a count answers a question about the unit as much as about the thing measured. The last step turns that into a prediction: children hold a cheese-stick card against a clip, say before laying anything whether it will take more or fewer than five, and then lay eight of them and find out.

Full lesson — 20 minutes

1. Lay the clips and count them (5 min)
Lay same-size paper clips end to end along your paper shoe, from the heel end to the toe, with no gaps. Count them out loud and say the whole sentence: the shoe is five paper clips long. Leave the clips where they are while your partner counts them again.
Word preview: clip
It was five paper clips long.
2. Lay the mouse feet along the same shoe (6 min)
Take the clips off and put the mouse-foot cards along the very same shoe instead, heel end to toe, each foot touching the last one, no gaps. Count them out loud. Now say both numbers about one shoe: it is five paper clips long and it is ten mouse feet long. Nobody cut the shoe and nobody stretched it, so say out loud what did change between your two counts.
Word preview: foot, count
She measured with her feet.
10 Wanda feet.
3. Put one clip beside one mouse foot (4 min)
Take one clip and one foot card and lay them side by side with their left ends level. Say which one is longer. Then say which one you needed more of to reach the toe. Say the two facts together in one breath to your partner: the foot is shorter, so it took more of them.
Word preview: longer, shorter
Your feet are bigger than mine!
That's why we got different numbers.
4. Guess first, then lay the cheese sticks (5 min)
Hold one cheese-stick card next to one clip and next to one foot card. Before you lay anything, say out loud whether it will take more than five or fewer than five sticks to reach the toe, and say why. Then lay the sticks along the shoe and count them. Say whether your guess was right and what told you.
Word preview: more, fewer
He held up a cheese stick.
It was exactly eight cheese sticks long.

Short version — 9 minutes

1. Lay the clips and count them (4 min)
Lay same-size clips end to end along your paper shoe with no gaps and count them out loud. Say the sentence: the shoe is five paper clips long.
Word preview: clip
It was five paper clips long.
2. Lay the mouse feet along the same shoe (5 min)
Take the clips off and lay the mouse-foot cards along the same shoe instead, no gaps, and count them. Say both numbers about the one shoe, then say what changed between your two counts, since the shoe did not.
Word preview: foot
10 Wanda feet.

Three levels

Support: Work with the clips and the mouse feet only, and lay each set inside its own printed track on the two-track shoe so no gap can creep in. Count each set out loud, touching every piece, and say the two numbers one after the other with your hand flat on the shoe between them, so the shoe is felt to be the same shoe both times. The two counts are the same two everybody else produces.
At Grade: Lay all three units along one paper shoe, produce five, ten and eight, hold the units against each other to say which is longest and which is shortest, and predict the cheese-stick count before laying it.
Extension: Put the three units in a row from shortest to longest by holding them against each other, then touch each one and say the count it gave. Say out loud what you notice about the order of the units and the order of the three numbers, and then say what count you would expect from a unit longer than a paper clip. Do not work it out with numbers; say more than five or fewer than five, and say what makes you sure.

English learners

The comparison itself is visible on the desk and is not where the difficulty sits. English builds this comparison with the thing first, then the comparing word ending in -er, then than, as in the foot is shorter than the clip, and many languages use a separate word meaning more and put the two things the other way round, so a child who has the units right can still assemble the sentence backwards. Rehearse both frames aloud with the two units held side by side, the ___ is longer than the ___ and the ___ is shorter than the ___, before either sentence is expected on its own. Invite children to say which unit is longer in their strongest language first while holding the two pieces, then say it in English. The word foot needs saying plainly too: in this book it is a mouse's foot, a part of a mouse, and not a measuring word.

Materials

A pot of fifteen paper clips, all exactly the same size, one pot per pair
A paper shoe cut to exactly five of the clips in the pot, one per pair
An envelope of twelve mouse-foot cards per pair, cut so that ten of them reach from the heel to the toe of the same paper shoe
An envelope of ten cheese-stick cards per pair, cut so that eight of them reach from the heel to the toe of the same paper shoe
A second paper shoe per pair with a clip track printed along one edge and a mouse-foot track along the other, for pairs working at Support
Word cards: longer, shorter, more, fewer

Standards & curriculum

These lessons are being matched against curricula now.

3. Will It Fit, and With How Much to Spare Application · Deciding whether one thing fits inside another by measuring both in the same unit

Wanda will not carry the shoe across the yard until she knows it will fit, and the book settles it with two numbers in one unit: seven paper clips for the playroom, five for the shoe, two clips to spare. Children produce all three. They lay clips along a playroom strip and count seven, lay the same clips along the paper shoe and count five, then lay the shoe on the strip with their ends level, like two children standing back to back, and fill the strip that sticks out past the toe, which takes exactly two clips. Nobody takes five away from seven; the two is a leftover a child can put a finger on. The last step hands them a boot that is nine clips long so that the same method returns the other answer, and the two clips move from the spare end to the too-long end.

Full lesson — 20 minutes

1. Measure the shoe and the playroom strip (7 min)
Lay same-size clips end to end along the playroom strip, no gaps, and count them out loud. Take them off and do the very same thing along the paper shoe. Say both sentences: the playroom is seven paper clips long and the shoe is five paper clips long. Do not move the strip and the shoe next to each other yet.
Word preview: measure
The playroom was seven paper clips long.
It was five paper clips long.
2. Lay the shoe on the playroom and count what is left (6 min)
Now put the shoe on the playroom strip with the heel end and the end of the strip level, like two children standing back to back. Look at the part of the strip that sticks out past the toe. Fill that part with clips, laid end to end with no gaps, and count them. Say out loud whether the shoe fits and how many clips are left over.
Word preview: fit, left over
It would fit in the playroom with two paper clips to spare.
3. Say it to another pair (3 min)
Say the whole thing to another pair without pointing at anything: the shoe fits in the playroom with two paper clips to spare. Then let them say it back to you. If either of you says only it fits, the other one asks how many clips are left, and the sentence gets said again with the number in it.
Word preview: to spare
It fit perfectly.
4. Try the boot that does not fit (4 min)
Take the big boot out and measure it with the same clips. Say its number. Then lay the boot on the playroom strip with the ends level and look at what happens at the far end. Fill the part of the boot that hangs off the strip with clips and count them. Say out loud whether the boot fits and how many clips too long it is.
Word preview: too long
I don't want to get there and find out it doesn't fit.

Short version — 9 minutes

1. Measure the shoe and the playroom strip (5 min)
Lay same-size clips end to end along the playroom strip with no gaps and count them. Take them off and do the same along the paper shoe. Say both numbers out loud with the words paper clips long in them.
Word preview: measure
The playroom was seven paper clips long.
2. Lay the shoe on the playroom and count what is left (4 min)
Put the shoe on the strip with the heel end and the end of the strip level. Fill the part of the strip sticking out past the toe with clips and count them. Say whether it fits and how many clips are left over.
Word preview: fit, left over
It would fit in the playroom with two paper clips to spare.

Three levels

Support: Start with the shoe already lying on the playroom strip with the ends level, and only measure the part sticking out past the toe. Count those clips out loud and say the sentence with the number in it. Then go back and measure the whole strip and the whole shoe, so the seven and the five arrive after the two rather than before it. Every count is a count everybody else makes.
At Grade: Measure both objects in the same clips, produce seven and five, lay one on the other from a level start, fill the leftover with two clips, and say the whole fitting sentence with its number to another pair.
Extension: Build a playroom the boot would fit in with two clips to spare. Lay the boot on the strip from a level start, fill the part of the boot hanging past the end of the strip with clips, then put two more clips beyond the boot's toe. Count every clip you have laid past the end of the strip: that is how much strip you have to add. Tape on that much spare strip, trim it, then measure the new playroom and lay the boot in it to check the two clips are really there. Say aloud how you knew how much to add before you taped anything.

English learners

The mathematics here is visible the moment the two things are laid together, and it is the sentence that carries the load. English puts the leftover at the end of the sentence in a phrase that looks like an afterthought, with two paper clips to spare, and that phrase is doing the arithmetic, so it cannot be dropped. Rehearse the whole frame aloud with the pieces in view, the ___ fits in the ___ with ___ paper clips to spare, and rehearse the other one beside it, the ___ does not fit, it is ___ paper clips too long. Let children say whether it fits in their strongest language first while their finger is on the leftover clips, then say the whole English sentence. The word fit is worth a moment of its own, because it is used for clothes and for belonging as well as for one thing going inside another.

Materials

A pot of fifteen paper clips, all exactly the same size, one pot per pair
A paper shoe cut to exactly five of the clips in the pot, one per pair
A playroom strip per pair, cut to exactly seven of the clips in the pot and labelled playroom
A second paper shoe per pair, cut to exactly nine of the same clips and labelled the big boot
A spare strip six clips long, scissors and a roll of tape per pair, for pairs working at Extension
Word cards: fit, to spare, left over

Standards & curriculum

These lessons are being matched against curricula now.

4. One Size, and It Stays That Size Reasoning · Testing whether a set of measuring units can be trusted before measuring with it

Wanda states the rule for a measuring unit in one sentence and names the two ways the mice have already broken it: mouse feet are not one size, and a cheese stick does not stay the same size. Children test both. With a pot of matching clips, both partners measure the same shoe and get the same number, twice over. With a pot of jumbled long and short clips, a child does not even get their own number back on a second try, which is the sharper version of what happened to Albert and Wanda's feet. Then a whole cheese-stick card gives eight and a bitten one gives ten for a shoe nobody touched, so the pair has to name what actually changed. They finish by putting a yes or a no on each of the three and saying which rule it kept, with their own two counts as the reason.

Full lesson — 20 minutes

1. Both of you measure with the matching pot (4 min)
One of you lays clips from Pot A along the paper shoe, end to end with no gaps, counts them out loud and says the number. Take them all off. Now the other one does exactly the same thing with the same pot. Say your two numbers to each other. Write both numbers in the Pot A box on your pot card.
Word preview: same size
They were all the exact same size.
2. Both of you measure with the jumbled pot (6 min)
Now use Pot B, and take the next clip off the top of the pile every time instead of choosing which one you want. Lay them along the same shoe with no gaps and count. If the last clip goes past the toe, count it and say that it hung over. Say your number. Take them off, put them back and do it a second time yourself, and say whether you got your own number back, and write both of your tries in the Pot B box. Then let your partner do both turns.
Word preview: different
That's why we got different numbers.
3. Measure with the whole stick, then with the bitten one (5 min)
Lay the whole cheese-stick cards along the shoe, no gaps, and count them. Say the number and keep it in your head. Now put those away and lay the bitten cards along the very same shoe and count those. Say both numbers out loud and write them in the cheese sticks box, then say what got smaller between the two counts. It was not the shoe, so put your finger on the thing that did.
Word preview: shorter
Did you eat part of the cheese stick?
It seemed shorter.
4. Sort the three of them and say why (5 min)
Put a yes card or a no card on Pot A, on Pot B and on the cheese sticks. For each one, say out loud which of Wanda's two rules it keeps or breaks: it has to be one size, and it has to stay the same size. Use your own numbers as the reason, not just the words, so say the two counts that made you decide.
Word preview: one size
It has to be one size, not like mouse feet, and it has to stay the same size, not like a cheese stick.

Short version — 9 minutes

1. Both of you measure with the matching pot (4 min)
Each of you in turn lays clips from Pot A along the same paper shoe with no gaps and counts them out loud. Say your two numbers to each other and write both of them in the Pot A box on your pot card.
Word preview: same size
They were all the exact same size.
2. Both of you measure with the jumbled pot (5 min)
Now use Pot B, taking the next clip off the top of the pile every time. Count what you laid, say your number, then measure the same shoe a second time and say whether your own number came back.
Word preview: different
That's why we got different numbers.

Three levels

Support: Work with the two pots only and leave the cheese sticks out. Start every clip line on the black mark at the heel and say each number out loud as soon as it is counted, before it goes in the box, so nobody is holding four numbers in their head at once. Read the two Pot A numbers back side by side, then the two Pot B numbers, and say which pair matches. The measuring is the same measuring everybody else does.
At Grade: Produce four counts with the two pots and two more with the whole and bitten sticks, then put a yes or a no on each of the three and say aloud which of Wanda's rules decided it, naming the counts that showed it.
Extension: Pot B is not allowed, but make it allowed: take clips out of it until what is left could be trusted, say how you chose which ones to take out, and then prove it by measuring the shoe twice and getting your number back. Then say whether the bitten stick could be trusted from now on, and what it could never be used for again.

English learners

Nothing about laying a unit and counting it depends on English, and children new to the language often see the jumbled pot for what it is before anyone has said a word about it. The sentence is where the work sits. Two English pieces here are easy to lose: same size is two words doing one job, and stay the same is a verb that means not changing rather than not moving, which is confusing when the clips are being moved about the whole time. Rehearse both aloud while holding the pieces, these are all one size and this one did not stay the same size, and let children say why a pot cannot be trusted in their strongest language first, with the two counts in front of them, before saying it in English. Yes and no cards let the decision be given before the reason, so the reason is not what stops a child taking part.

Materials

Pot A: fifteen paper clips, all exactly the same size, one pot per pair
A paper shoe cut to exactly five of the Pot A clips, one per pair
A pot card per pair with three boxes on it, headed Pot A, Pot B and cheese sticks, each box holding four lines for numbers
Pot B: fifteen paper clips jumbled together, eight of them long and seven of them half that length, one pot per pair
Eight whole cheese-stick cards and ten bitten ones per pair, in two colours, cut so that the eight whole cards, or the ten bitten ones, reach from the heel to the toe of the same paper shoe
Three yes-and-no cards per pair, one for each pot and one for the cheese stick
Word cards: one size, same size, different sizes

Standards & curriculum

These lessons are being matched against curricula now.