Dealing with Addition

$Dealing with Addition book cover$

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.

1Every Way to Make Five
2Count the Symbols or Add the Corners
3Three Cards, Four Cards, One Total
4Capture with One Card or with Two
5The Bigger the Total, the More Ways

Math + reading

Math through the reading

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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. Every Way to Make Five Reasoning · Finding every different way one hand of cards makes a total of five

The book lays out seven cards and claims that exactly five different picks from them add to five, then names all five. Students hold the same seven cards and find the five picks themselves. The hard part is not the adding, which stays inside five; it is deciding when two picks are the same pick, because the hand holds two 2's and three aces and the book rules that swapping one for its twin does not buy you a new way.

Full lesson — 20 minutes

1. Lay out the book's hand (4 min)
Deal yourselves the book's seven cards face up in a row: a 5, a 3, two 2's and three aces. Point at each card and say what it is worth, remembering that an ace is worth one. Put a mat with a big 5 on it in the middle of the table. Everything you pick has to add up to that 5.
Word preview: ace
Use the cards below and pick all the different ways to get a total of 5.
2. Find a way, then another (6 min)
Find one pick that adds to five and slide those cards onto the mat. Say the sum aloud, card by card, and let your partner check it. Slide them back and find a different pick. Keep going, one pick at a time, and lay a paper strip on the table for every pick you both agree on.
Word preview: combination
You can pick just the 5 of hearts.
Or you could put together a 3 and a 2.
3 plus 2 equals 5.
You can also pick both of the twos and any ace.
3. Decide when two picks are the same way (5 min)
Make three and a 2, then put that 2 back and make three and the other 2. Ask your partner: is that a new way or the same way said twice? The book answers it. Read the answer, then test it again with the aces, swapping one ace for another inside a pick you already have. Say the rule back in your own words.
Word preview: same, different
Either of the 2's will work.
You could use the ace from any suit and the problem would be the same.
4. Say you have them all (5 min)
Count your paper strips. If you have fewer than five, hunt for the missing ones by starting from the biggest card you have not used yet. If you have more than five, two of your strips are the same way wearing different suits, so find them and take one away. When you have exactly five, read them out in order and say the sentence: these are all of them.
Or you can pick a 2 and all 3 aces.
2 plus 1 plus 1 plus 1 equals 5.
All of these combinations give you a total of 5.

Short version — 9 minutes

1. Find a way, then another (5 min)
Lay out the 5, the 3, both 2's and the three aces. Find one pick that adds to five, say the sum aloud, and lay a paper strip down for it. Slide the cards back and find a different pick.
Word preview: combination
Or you could put together a 3 and a 2.
3 plus 2 equals 5.
2. Decide when two picks are the same way (4 min)
Make three and a 2, then swap in the other 2. Ask your partner whether that is a new way. Read what the book says, then swap one ace for another inside a pick you already have and say the rule back in your own words.
Word preview: same, different
Either of the 2's will work.

Three levels

Support: Work the same seven cards but drop one ace, so the hand is a 5, a 3, two 2's and two aces and the picks that use three aces disappear. Find four ways instead of five, and keep the strips on the table where they can be seen rather than counted from memory.
At Grade: Seven cards, five ways found one at a time on the mat, the twin-card rule tested on the 2's and again on the aces, and the five strips read back as a finished list.
Extension: Take the 5 out of the hand and leave the 3, both 2's and three aces. Say how many ways are left before you look, then find them and say whether you were right. Then put the 5 back and add a 4, and say what the 4 can and cannot join to make five.

English learners

The mathematics here is a rule about sameness, and English says it with two small words that sound alike in a noisy room: either and both. Separate them with hands before you separate them with sound, one card lifted for either and two cards lifted for both, and keep the gesture available all lesson. Same and different are the words to put on cards, because the whole lesson turns on them and a child can be completely right while pointing rather than saying. A rehearsable frame runs that is the same way because blank, and it is worth hearing four or five times. A student may sort the strips into keep and repeat piles in silence and be understood; invite the reason in the strongest language first, then only the frame in English.

Materials

Seven playing cards per pair: a 5, a 3, two 2's and three aces
A blank mat with a large 5 written at the top, one per pair
Five paper strips per pair, one for each way found
Pencil per student
Word cards: different, same, combination

Standards & curriculum

These lessons are being matched against curricula now.

2. Count the Symbols or Add the Corners Concept · Finding one total two ways and showing the two ways agree

The book puts two cards side by side and says there are two roads to their total: count the big hearts printed down the middle of both cards, or add the two small numbers in the corners. It then promises the roads meet. Students walk both roads on the same cards and check the promise themselves, first on two cards and then on three, so that adding is not a rule handed down but a shortcut they watched replace a count they had already made.

Full lesson — 20 minutes

1. Read the book's two ways (3 min)
Listen to the two sentences that name the two ways, and put a hand on your head for counting and a hand on the table for adding. Say which way you would use if the cards were face up in front of you right now. Nobody is right yet; the book says the two ways land in the same place and you are going to test that.
Word preview: total
Some players like to count the big symbols on each card.
Others like to add the numbers in the corner of each card.
Either way, you get the same answer.
2. Count the hearts on two cards (5 min)
Take a 2 and a 3 out of your deck and lay them side by side. Touch every big heart in the middle of both cards, one touch per number word, and say the count out loud so your partner can hear the last number. Write nothing yet. Say the total to your partner and have them count it again from the other end to check you.
What is the total number of big hearts on these two cards?
Find out by counting the hearts in the middle of both cards.
3. Add the corner numbers instead (6 min)
Turn the same two cards so you can see only the little numbers in the corners. Cover the middles with your hand. Say two plus three and write the total in the last box of your strip. Now uncover the middles and check the total against the count you just made. Say out loud whether the two ways agreed.
Word preview: corner
Or by adding the numbers in the corners.
Two plus three equals five.
The total is always five.
4. Try it with three cards (6 min)
Add a 4 to your 2 and your 3 so there are three cards in the row. Add the corner numbers first this time, one box each, and write the total. Then count every big symbol across all three cards to check it. Tell your partner which way was quicker and whether the quicker way got the same number.
Word preview: symbol
First, add the numbers in the corners to get the total.
Then, count the big symbols.
Whether you add or count, the total of these cards is always 9.

Short version — 9 minutes

1. Count the hearts on two cards (3 min)
Lay a 2 and a 3 side by side. Touch every big heart down the middle of both cards, one touch per number word, and say the last number aloud. Have your partner count back the other way to check you.
Find out by counting the hearts in the middle of both cards.
2. Add the corner numbers instead (6 min)
Cover the middles of the same two cards and read only the corner numbers. Say two plus three, write the total, then uncover and check it against your count. Say aloud whether the two ways agreed.
Word preview: corner
Two plus three equals five.
The total is always five.

Three levels

Support: Stay on two cards for the whole lesson and keep the numbers small, an ace and a 2, then an ace and a 3. Count the middles first every time and add the corners second, so the answer is already known before the adding starts and the adding only has to match it.
At Grade: Two cards counted and then added, then three cards added and then counted, with the total written on the strip and said aloud both times.
Extension: Build a row of four cards whose corners you can add but whose middles are slow to count, a 4, a 3, a 2 and an ace. Add first, then count to check, and time both. Say which way you would want if the row were ten cards long and why, and say what has to be true about the corner numbers for the shortcut to be safe.

English learners

The book's two verbs sit close together in English and far apart in the hands: count is one touch per object, add is one number joined to another with no touching at all. Show both with the cards before either word is asked for, because a child who has touched the hearts and then covered them has the difference whether or not the English has arrived. Number words to nine will already be there in a first language, so let a student count the hearts aloud in their strongest language and then say only the total in English. A rehearsable frame runs I counted blank and I added blank and I got the same. Corner and middle are the two words to put on cards, because both are ordinary words being used to point at a specific patch of a card.

Materials

Printed source passage in this step
A deck of playing cards per pair of students, picture cards set aside
Recording strip with a box for each card and one box for the total, one per student
Pencil per student
Word cards: total, corner, symbol

Standards & curriculum

These lessons are being matched against curricula now.

3. Three Cards, Four Cards, One Total Fluency · Adding three and four one-digit cards to a total of eight or ten

Most first-grade adding stops at two numbers. This book does not: its lists for eight and for ten are full of sums with three and four cards in them, and every one of the eighteen printed sums in those two lists is correct. Students build the sums with real cards, add them left to right, and then check their own totals against the book's list, which for these two totals can be trusted card for card.

Full lesson — 20 minutes

1. Warm up on two cards (4 min)
Deal each pair a small stack of cards, ace through seven. Draw two, lay them down, and say the sum without writing anything. Do six of these fast, taking turns. If a sum makes eight or ten, hold those two cards up for the room to see.
Word preview: plus, equals
5 plus 3 equals 8.
7 plus 1 equals 8.
6 plus 4 equals 10.
7 plus 3 equals 10.
2. Add three cards (6 min)
Now draw three cards at a time. Line them up left to right, add the first two and say that number out loud, then add the third to it and say the total. Write only the total on your strip. Say the whole sum back to your partner from the cards, not from memory.
4 plus 2 plus 2 equals 8.
3 plus 3 plus 2 equals 8.
6 plus 3 plus 1 equals 10.
3. Add four cards (6 min)
Deal four cards. Add them left to right, saying each running number out loud so your partner hears where you are. When you have the total, slide the four cards apart and add them again starting from the other end. Say whether you got the same total both times.
Word preview: total
3 plus 2 plus 2 plus 1 equals 8.
5 plus 2 plus 2 plus 1 equals 10.
4 plus 3 plus 2 plus 1 equals 10.
4. Check the book's list (4 min)
The book prints its own list of sums for eight and for ten. Read them one at a time and put a thumb up if your cards agree and a thumb down if they do not. Build any sum you are unsure of and count it out.
Here are 8 different ways to get 8.
Here are 10 different ways to get 10.

Short version — 9 minutes

1. Add three cards (4 min)
Draw three cards. Line them up left to right, add the first two aloud, then add the third and say the total. Write only the total. Say the whole sum back from the cards.
Word preview: plus, equals
4 plus 2 plus 2 equals 8.
6 plus 3 plus 1 equals 10.
2. Add four cards (5 min)
Deal four cards and add them left to right, saying each running number aloud. Then slide them apart and add from the other end. Say whether both totals matched.
Word preview: total
3 plus 2 plus 2 plus 1 equals 8.
4 plus 3 plus 2 plus 1 equals 10.

Three levels

Support: Keep every sum at three cards and put an ace in each hand, so one of the three steps is always adding one. Say the running number after each card and touch the card you have just used, so the place in the sum is visible and does not have to be held in the head.
At Grade: Two cards fast, then three cards with the running total said aloud, then four cards added from both ends and the two totals compared.
Extension: Deal four cards and find the order that makes them easiest to add, then say why that order helped. Try making a pair that adds to ten first and joining the rest to it. Then take one card away from a four-card sum that made ten and say what card would have to replace it to make ten again.

English learners

Plus and equals are the two words that carry the whole lesson, and both are said far more often than they are read here, so put them on cards and point at them while the sum is spoken. The number words themselves usually transfer intact, so a student can say the running total in a first language and only the final total in English and still show everything this lesson asks for. The run-on shape of a long English sum, three plus two plus two plus one equals eight, is the piece that is genuinely new, and it is easiest to hear when a finger moves along the row of cards at the same speed as the voice. Invite a student to say a sum in their strongest language first, then say it again touching each card as the English words come.

Materials

Playing cards ace through seven, two of each, per pair of students
Recording strip with a box for each card and one box for the total, one per student
Pencil per student
Printed source passage in this step
Word cards: plus, equals, total

Standards & curriculum

These lessons are being matched against curricula now.

4. Capture with One Card or with Two Application · Matching a card's value with one card or with a group of cards that adds to it

The book closes with a game it built out of everything in front of it, and the game is one question asked over and over: what on this table adds up to what is in my hand? Students learn the three captures the rules allow, take each of them once from a set-up the book itself describes, and then play. A pair is a match of one value to one value; a combination is a match of one value to a sum, and that is where the adding lives.

Full lesson — 20 minutes

1. Learn the three ways to capture (4 min)
Listen to the rules for taking cards and count the three ways on your fingers. Say each one back: one card for one card, cards on the table for one card in my hand, cards in my hand for one card on the table. Keep your fingers up while you say them.
Word preview: value, match
There are three ways a player may capture cards.
A pair is the easiest way to take a card.
Each player tries to match the value of a card or cards in his or her hand to the value of a card or cards in the center row.
2. Take a pair (4 min)
Set up the table exactly as the book does: put a four of clubs in the middle and hold a four of hearts. Say why they match, using the word value and not the word suit. Take both cards and put them face down in your capture pile. Do it twice more with different numbers.
Word preview: capture
If you have a four of hearts and there's a four of clubs in the center, take both cards and put them face down to the side.
3. Take a table combination (6 min)
Now put two fours in the middle and hold an eight. Add the two table cards out loud before you take anything. Say the sum and say why the eight matches it. Take all three cards. Then set up one of your own: put two cards in the middle, find the one card in your hand that matches their sum, and let your partner check the adding before you take.
A table combination is made by finding two or more cards on the table that add up to the value of one card in your hand.
If there are two fours in the center and you have an eight in your hand, you win all three cards.
4. Take a hand combination (6 min)
Turn it around. Hold a two, a three and a four, and put a nine in the middle. Add your three cards out loud and say whether they match the nine. Take all four cards. Play three more turns each, and every time you capture, say the sum out loud before your hand touches a card.
A hand combination is one by finding two or more cards in your hand that add up to the value of one card on the table.
If you have a two, a three, and a four in your hand, and there is a nine in the row on the table, you win all four cards.

Short version — 9 minutes

1. Take a table combination (4 min)
Put two fours in the middle and hold an eight. Add the two table cards out loud, say why the eight matches their sum, and take all three cards into your pile.
Word preview: value, match
If there are two fours in the center and you have an eight in your hand, you win all three cards.
2. Take a hand combination (5 min)
Hold a two, a three and a four, and put a nine in the middle. Add your three cards out loud, say whether they match the nine, and take all four cards. Then play two turns each, saying every sum before you touch a card.
Word preview: capture
If you have a two, a three, and a four in your hand, and there is a nine in the row on the table, you win all four cards.

Three levels

Support: Play with cards ace through five only, so every sum stays inside ten and most captures are pairs. Lay the two table cards you are adding side by side and push them together as you say the sum, so the joining is something the hands do before the mouth does it.
At Grade: All three captures taken once from the book's own set-ups, then free play with the sum said aloud before any card is taken.
Extension: Deal a row of four cards face up and a hand of four, and find every capture available before taking any of them. Say which one takes the most cards and take that one. Then say what would have to be in the middle for your whole hand to be captured in one turn.

English learners

Value is the word to spend time on, because the cards give the mathematics away for free and the English is the only hard part: a four of hearts and a four of clubs are plainly the same to the eye long before a child can say why in English. Let the hands answer first, two cards held up together, and put value, match and capture on cards where they can be pointed at during play. A rehearsable frame runs these two make blank, so I can take the blank. Number words to ten usually transfer, so a student may say the sum in their strongest language and the frame in English and have shown everything. The turn-taking talk of the game will carry the vocabulary further than any drill does.

Materials

Printed source passage in this step
A deck of playing cards per pair of students, picture cards set aside
A capture pile tray or paper plate per student
Word cards: value, match, capture

Standards & curriculum

These lessons are being matched against curricula now.

5. The Bigger the Total, the More Ways Reasoning · Comparing how many ways two different totals can be made

The book makes a claim about its own ten pages: bigger totals can be made in more ways. Then it prints the count for every total from one to ten and lets the claim stand on them. Students turn two of those counts into two stacks of cards, stand the stacks side by side, and match them off one against one until one stack runs out, so the comparison is read off the leftover rather than worked out.

Full lesson — 20 minutes

1. Read the book's claim (3 min)
Listen to the one sentence where the book says what it has noticed about its own pages. Say it back in your own words to your partner. Then guess: does four have more ways than ten, or fewer? Hold up a fist for more and a flat hand for fewer, and remember which you chose.
Word preview: larger
The larger the total, the more ways there are to get it.
2. Stack four beside ten (7 min)
The book says how many ways there are for four and how many for ten. Write one index card for each way of making four and stand them in a stack, then do the same for ten in a second stack. Do not write the sums, just one card per way. Stand the two stacks side by side on the table so both are the same width.
The cards on this page give you four different ways to get a total of four.
With these cards, there are 10 different ways to make 10.
3. Do it again with two and eight (5 min)
Build two more stacks the same way, one for two and one for eight, using the counts the book gives. Stand all four stacks in a row from shortest to tallest and say the four totals out loud in that order. Say whether the order of the stacks matches the order of the totals.
Here are two different ways to get two.
There are 8 different ways to get 8 with these cards.
4. Say how many more ways (5 min)
Put the four-stack and the ten-stack flat on the table in two rows, one card beside one card, starting from the same end. Point at the cards in the ten row that have nothing beside them and count only those. Say the sentence with both numbers in it: ten has that many more ways than four.
Word preview: more, fewer

Short version — 9 minutes

1. Stack four beside ten (5 min)
Write one index card for each way of making four and stand them in a stack, then do the same for ten. Stand the two stacks side by side, both the same width, and say which is taller.
Word preview: larger
The cards on this page give you four different ways to get a total of four.
With these cards, there are 10 different ways to make 10.
2. Say how many more ways (4 min)
Lay both stacks flat in two rows, one card beside one card from the same end. Count only the cards in the ten row with nothing beside them, and say the sentence with both numbers in it.
Word preview: more, fewer

Three levels

Support: Use two and four instead of four and ten, so the rows are short enough to see whole without counting twice. Lay the cards flat from the start rather than standing them, and put a finger on each matched pair before saying how many are left over.
At Grade: Four stacks built from the book's own counts, stood shortest to tallest, then the four row and the ten row matched card against card and the leftover counted and said in a sentence with both numbers.
Extension: Build the stack for every total from one to ten and stand them all in a row. Say what the row of stacks looks like from the side and what that shape tells you. Then say whether you would expect eleven to have eleven ways, and say what you would need to see before you believed it.

English learners

This lesson needs one word the book never uses. It supplies larger and more and stops there, so fewer has to come from the classroom, and the two rows of cards are the safest place to get it: the short row is the fewer one, pointed at before it is named. Than is the other import and it is the harder one, because it does the joining work that a first language may do with word order or a case ending instead. A rehearsable frame runs ten has blank more ways than four, and a student who points at the leftover cards and says only the number has shown the mathematics completely. Take the reason in the strongest language first, then swap in the frame.

Materials

Printed source passage in this step
Index cards, about twenty per pair of students
Pencil per student
Word cards: larger, more, fewer

Standards & curriculum

These lessons are being matched against curricula now.