A unit of the course: the story, then chapter by chapter — sections, numbered lessons, a source or the numbers to read, three checks each — a review per chapter, and the wrap-up at the end.
Drawn scene: a pond at golden hour with ducks on the water and three flying off, lily pads joined like a number bond, and reeds at the edges
2Unit
Adding and Subtracting
Operations
You have two cookies. A friend gives you three more. How many now? Your sister takes one. How many are left? These are adding and subtracting questions. You meet them every day, at lunch, at recess and at the store.
In this unit you will put groups together and take groups apart. You will learn what the equal sign really means. You will find a missing number in any spot. Then you will learn quick tricks: doubles, making ten and fact families.
By the end, you will know your facts within 20. You will solve story problems with two steps. And you will check your answer a second way, so you know it is right.
How we figured it out
Step 1
Put two groups together and count them all
Step 2
Count on from the first number instead of starting at 1
Step 3
Take some away and count what is left
Step 4
Compare two groups to find how many more
Step 5
Split a whole into two parts with a number bond
Step 6
Read the equal sign as the same as, and find a missing number
Step 7
Learn doubles and the pairs that make ten
Step 8
Use near doubles and make ten to add within 20
Step 9
Think addition to subtract, and build fact families
Step 10
Solve two-step stories and check the answer a second way
3
Chapter
Putting Together and Taking Apart
Addition and Subtraction
Big questionHow do numbers change when we put groups together or take some away?
The story
Nine Ducks on the Pond
Count the ducks before and after some fly away.
Nine ducks float on a pond in a Chicago park. A girl named Rosa counts them from the path. One, two, three, all the way to nine. She writes 9 on her hand with her finger so she will not forget.
A dog barks. Four ducks flap their wings and fly away. Rosa looks again. Some ducks are gone. How many stay on the water? She counts them: five ducks. Nine take away four is five.
Later, two ducks come back. Rosa counts again. Five and two more. Now there are seven ducks. The number went down, then it went up. Taking away and putting together, right there on the pond.
Talk about itHow could Rosa know there are 5 ducks without counting every duck again?
Section 1
Putting Together
3.1
Adding Puts Groups Together
Main ideaAdding puts two groups together to find how many in all.
Mia has 3 red apples. Ben has 2 green apples. Put them in one basket. Count them all: 1, 2, 3, 4, 5. There are 5 apples in all. We the two groups.
We write it like this: 3 + 2 = 5. The + sign means put together. The answer is called the . Five is the sum of 3 and 2.
Try 4 + 3. Start with 4 blocks. Add 3 more blocks. Count them all. You get 7. So 4 + 3 = 7.
Words to know
add
to put groups together and find how many in all
sum
the answer when you add; 3 + 2 = 5, so 5 is the sum
Check yourself
1. Ana has 2 cats. Leo has 4 cats. How many cats in all?
Why: 2 + 4 = 6. Count on from 2: 3, 4, 5, 6.
2. Which sign means put together?
Why: The + sign means add, or put together. The − sign means take away.
3. What is 3 + 3?
Why: 3 blocks and 3 more blocks make 6 blocks. 3 + 3 = 6.
3.2
Adding More to a Group
Main ideaWhen more come, say the first number and count on.
Six birds sit on a fence. Two more birds land. How many birds now? Start at 6. Count on: 7, 8. There are 8 birds. 6 + 2 = 8.
You do not need to count from 1. Say the first number. Then count on for the other part. This is called . It is faster.
Try 5 + 3. Say 5. Count on three times: 6, 7, 8. The sum is 8. Check it with fingers. Five fingers and three more make 8.
Words to know
counting on
start at one number and count up from there; for 6 + 2, say 6, then 7, 8
Check yourself
1. 7 fish are in a tank. 2 more go in. How many fish now?
Why: Say 7, then count on: 8, 9. So 7 + 2 = 9.
2. To find 8 + 3 by counting on, what number do you say first?
Why: Start at 8. Then count on three times: 9, 10, 11.
3. What is 5 + 4?
Why: Say 5, then count on four times: 6, 7, 8, 9. So 5 + 4 = 9.
Section 2
Taking Apart
3.3
Taking Away
Main ideaSubtracting takes some away and finds how many are left.
Sam has 7 grapes. He eats 3. How many are left? Start with 7. Take away 3. Count what is left: 4. We . 7 − 3 = 4.
The − sign means take away. The answer is called the . Four is the difference between 7 and 3.
Try 9 − 4. Draw 9 circles. Cross out 4. Count the circles not crossed out. There are 5. So 9 − 4 = 5.
Words to know
subtract
to take some away and find how many are left
difference
the answer when you subtract; 7 − 3 = 4, so 4 is the difference
Check yourself
1. There are 6 balloons. 2 pop. How many are left?
Why: 6 − 2 = 4. Count back from 6: 5, 4.
2. Which sign means take away?
Why: The − sign means subtract, or take away.
3. What is 10 − 6?
Why: Draw 10 circles. Cross out 6. Four are left. 10 − 6 = 4.
3.4
How Many More?
Main ideaSubtract to compare two groups and find how many more.
Jo has 8 stickers. Kim has 5. Who has more? Jo. How many more? Line them up. Match each of Kim’s stickers to one of Jo’s. Three of Jo’s stickers have no match. Jo has 3 more.
We can subtract to . 8 − 5 = 3. The bigger number goes first. Then take away the smaller number. The difference tells how many .
Try it. A tower has 6 blocks. Another has 2. How many more in the tall tower? 6 − 2 = 4. The tall tower has 4 more blocks.
Words to know
compare
to look at two groups and find which is bigger and by how much
more
a bigger amount; 8 is more than 5
Check yourself
1. Ria has 9 shells. Tom has 4. How many more does Ria have?
Why: 9 − 4 = 5. Match 4 of Ria's shells to Tom's. Five are left over.
2. The pet table shows 6 dogs and 4 cats. How many more dogs than cats?
Why: 6 − 4 = 2. There are 2 more dogs than cats.
3. Which number sentence compares 7 and 3?
Why: To compare, put the bigger number first and subtract. 7 − 3 = 4.
3.5
Parts and the Whole
Main ideaA number bond shows a whole and its two parts.
Hold up 7 fingers. Keep 3 down. The parts are 7 and 3. The is 10. A shows this. The whole sits on top. The two parts sit below. 10 splits into 7 and 3.
The parts always add up to the whole. 7 + 3 = 10. The whole minus one gives the other part. 10 − 7 = 3.
Find the parts of 5. 1 and 4. 2 and 3. 0 and 5. Each pair makes 5. Try it with 5 counters. Split them two ways.
Words to know
number bond
a picture with a whole and its two parts; 10 has parts 7 and 3
whole
the total; the big number in a number bond
part
one piece of the whole; 7 and 3 are parts of 10
Check yourself
1. The whole is 8. One part is 5. What is the other part?
Why: 8 − 5 = 3. Check: 5 + 3 = 8.
2. Which pair of parts makes 7?
Why: 4 + 3 = 7. The others make 6 and 8.
3. A number bond has whole 9 and part 6. What is the missing part?
Why: 9 − 6 = 3. Check: 6 + 3 = 9.
Section 3
Equals and Missing Numbers
3.6
What Equals Means
Main ideaThe equal sign means both sides are the same amount.
Two plates. One has 3 crackers and 2 more. The other has 5 crackers. Both plates hold 5. They are . 3 + 2 = 5. The = sign means the same as.
The equal sign is not just an answer sign. It says both sides match. 5 = 3 + 2 is . 4 + 1 = 3 + 2 is true too. Both sides make 5.
Is 6 = 2 + 3 true? Count 2 + 3. That is 5. Six is not 5. So it is false. Check both sides every time.
Words to know
equal
the same amount; 3 + 2 = 5 means 3 + 2 is the same as 5
true
correct; both sides of the equal sign really match
Check yourself
1. Which sentence is true?
Why: 4 + 3 = 7. Count on from 4: 5, 6, 7.
2. What does the = sign mean?
Why: The equal sign says both sides are the same amount.
3. Is 2 + 4 = 3 + 3 true?
Why: 2 + 4 = 6 and 3 + 3 = 6. Both sides are 6, so it is true.
3.7
Find the Missing Number
Main ideaA missing number can be in any spot; use parts and wholes to find it.
Dan has 3 marbles. He gets some more. Now he has 7. How many did he get? 3 + ? = 7. Count on from 3 to 7: 4, 5, 6, 7. That is 4 jumps. So 3 + 4 = 7.
The can be in any spot. ? + 2 = 6. Think: what and 2 make 6? Four. Or 8 − ? = 5. Think: 8 take away what leaves 5? Three, since 5 + 3 = 8.
Use a number bond. The whole is 7. One part is 3. The other part is 7 − 3 = 4. Subtracting finds the missing part.
Words to know
missing number
the number you do not know yet, shown by a ? or a box
unknown
another name for the missing number
Check yourself
1. 5 + ? = 9. What is the missing number?
Why: Count on from 5 to 9: 6, 7, 8, 9. Four jumps. 5 + 4 = 9.
2. ? + 6 = 10. What is the missing number?
Why: 10 − 6 = 4. Check: 4 + 6 = 10.
3. 8 − ? = 2. What is the missing number?
Why: 8 take away 6 leaves 2. Check: 2 + 6 = 8.
3.8
Doubles and Making Ten
Main ideaDoubles and pairs that make ten are facts worth knowing by heart.
Two hands. Five fingers each. 5 + 5 = 10. That is a . Both parts are the same. 2 + 2 = 4. 3 + 3 = 6. 4 + 4 = 8. Doubles are quick to learn.
Pairs that are handy too. Hold up 6 fingers. How many are down? Four. So 6 + 4 = 10. Other pairs: 9 and 1, 8 and 2, 7 and 3, 5 and 5.
What goes with 8 to make 10? Hold up 8 fingers. Two are down. 8 + 2 = 10. Check by counting on from 8: 9, 10. Yes.
Words to know
double
adding a number to itself, like 4 + 4 = 8
make ten
two numbers that add up to 10, like 7 and 3
Check yourself
1. What is 4 + 4?
Why: 4 + 4 = 8. It is a double: 4 fingers and 4 fingers.
2. What goes with 7 to make 10?
Why: 7 + 3 = 10. Hold up 7 fingers; 3 are down.
3. Which one is a double?
Why: A double adds a number to itself. 6 + 6 = 12.
Chapter review
Putting Together and Taking Apart
0 / 6
1. There are 4 ducks. 3 more swim over. How many ducks now?
Why: 4 + 3 = 7. Count on from 4: 5, 6, 7.
2. There are 9 ducks. 4 fly away. How many are left?
Why: 9 − 4 = 5. Count back from 9: 8, 7, 6, 5.
3. Which sign means the same as?
Why: The = sign means both sides are the same amount.
4. The whole is 10. One part is 6. What is the other part?
Why: 10 − 6 = 4. Check: 6 + 4 = 10.
5. 2 + ? = 8. What is the missing number?
Why: Count on from 2 to 8: 3, 4, 5, 6, 7, 8. Six jumps. 2 + 6 = 8.
6. Lucy has 7 shells. Max has 3. How many more does Lucy have?
Why: 7 − 3 = 4. Lucy has 4 more shells than Max.
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4
Chapter
Facts Within 20 and Good Strategies
Fluency
Big questionWhat tricks help you know adding and subtracting facts fast?
The story
The Fact House on the Wall
A paper house holds four facts that all belong together.
Mr. Ortiz's first-grade class has a paper house on the wall. The roof says 10. The two windows say 6 and 4. The door has four lines on it. Each line is a number fact. The class reads the house every morning.
Deshawn reads the door out loud. 6 + 4 = 10. 4 + 6 = 10. 10 − 6 = 4. 10 − 4 = 6. Every line uses the same three numbers. That is why the facts live in one house. They are a family.
On Friday the roof number changes to 13. The windows say 8 and 5. Deshawn writes the four new facts by himself. He knows one fact, so he knows all four. The house makes facts easy to remember.
Talk about itWhy do the three numbers in the house make exactly four facts?
Section 1
Counting On and Back
4.1
Count On to Add
Main ideaTo add a small number, start with the big number and count on.
Nine kids wait in line for the slide. Three more join. Say 9. : 10, 11, 12. There are 12 kids. 9 + 3 = 12.
Always start with the bigger number. For 2 + 8, say 8 first. Count on: 9, 10. The sum is 10. The does not change the sum. 2 + 8 = 8 + 2.
Use counting on for 1, 2 or 3. For bigger numbers, use another trick. Try 11 + 2. Say 11. Then 12, 13. So 11 + 2 = 13.
Words to know
count on
start at the bigger number and count up from there
order
which number comes first; 2 + 8 and 8 + 2 have the same sum
Check yourself
1. What is 12 + 3?
Why: Say 12, then count on: 13, 14, 15. So 12 + 3 = 15.
2. To add 3 + 9 by counting on, which number do you say first?
Why: Start with the bigger number, 9. Then count on: 10, 11, 12.
3. What is 15 + 2?
Why: Say 15, then count on: 16, 17. So 15 + 2 = 17.
4.2
Count Back to Subtract
Main ideaTo take away a small number, start at the whole and count back.
Eleven cookies sit on a tray. Grandpa eats 2. Say 11. : 10, 9. Nine cookies are left. 11 − 2 = 9.
Count back only for 1, 2 or 3. Use your fingers to keep track. Each finger is one step back. For 13 − 3, say 13. Back: 12, 11, 10. The difference is 10.
A common mistake is to say the start number as a step. 11 − 2 is not 10. Start at 11. Step to 10, then to 9. Two steps. The answer is 9.
Words to know
count back
start at the whole and count down one step for each one taken away
Check yourself
1. What is 14 − 3?
Why: Say 14, then count back: 13, 12, 11. So 14 − 3 = 11.
2. Nina has 17 beads. She gives away 2. How many are left?
Why: Count back from 17: 16, 15. So 17 − 2 = 15.
3. What is 12 − 1?
Why: One step back from 12 is 11. So 12 − 1 = 11.
Section 2
Ten and Doubles Tricks
4.3
Near Doubles
Main ideaIf you know a double, you can find the fact right next to it.
You know 6 + 6 = 12. What is 6 + 7? Seven is one more than 6. So the sum is one more than 12. 6 + 7 = 13. That is a .
Try 8 + 9. Think 8 + 8 = 16. Nine is one more than 8. So 8 + 9 = 17. Or think 9 + 9 = 18 and take one away. That gives 17 again.
Know these doubles. 6 + 6 = 12. 7 + 7 = 14. 8 + 8 = 16. 9 + 9 = 18. 10 + 10 = 20. A near double is one more or one less.
Words to know
near double
a fact one more or one less than a double, like 6 + 7
Check yourself
1. What is 7 + 8?
Why: 7 + 7 = 14. One more is 15. So 7 + 8 = 15.
2. Which double helps you find 5 + 6?
Why: 5 + 5 = 10, and 5 + 6 is one more: 11.
3. What is 9 + 8?
Why: 9 + 9 = 18. One less is 17. So 9 + 8 = 17.
4.4
Make Ten to Add
Main ideaBreak one number so the other becomes 10, then add the rest.
Add 8 + 5. Eight is close to 10. It needs 2 more. Take 2 from the 5. Now 8 + 2 = 10. Three are left from the 5. 10 + 3 = 13. So 8 + 5 = 13. This is called .
Picture a . Eight dots fill 8 spots. Two spots are empty. Move 2 dots from the 5 to fill them. The frame is full: 10. Three dots wait outside. Ten and 3 is 13.
Try 9 + 6. Nine needs 1. Take 1 from 6. 9 + 1 = 10. Five are left. 10 + 5 = 15. So 9 + 6 = 15. Check by counting on from 9: 10, 11, 12, 13, 14, 15. Yes.
Words to know
make ten
break one number so a part of it fills the other number up to 10
ten frame
a box with 10 spots in two rows of 5
Check yourself
1. Add 8 + 4 by making ten. How many do you move from the 4?
Why: 8 needs 2 to make 10. Move 2 from the 4. Then 10 + 2 = 12.
2. What is 9 + 7?
Why: 9 + 1 = 10. Six are left. 10 + 6 = 16. So 9 + 7 = 16.
3. What is 7 + 5?
Why: 7 + 3 = 10. Two are left. 10 + 2 = 12. So 7 + 5 = 12.
4.5
Think Addition to Subtract
Main ideaTo subtract, ask what you add to the part to reach the whole.
What is 13 − 9? Think: 9 plus what makes 13? from 9: 10, 11, 12, 13. Four jumps. 9 + 4 = 13. So 13 − 9 = 4.
Adding and subtracting each other. 9 + 4 = 13. So 13 − 9 = 4. And 13 − 4 = 9. All three facts share the same parts.
Try 15 − 8. Think 8 + ? = 15. From 8, jump 2 to reach 10. Then jump 5 to reach 15. 2 + 5 = 7. So 15 − 8 = 7. Check: 8 + 7 = 15. Yes.
Words to know
count up
start at the part and count to the whole to find the difference
Why: Count up from 9: 10, 11, 12, 13, 14. Five jumps. 9 + 5 = 14, so 14 − 9 = 5.
2. To find 11 − 7, which adding question helps?
Why: Ask 7 plus what makes 11? That is 4. So 11 − 7 = 4.
3. What is 16 − 8?
Why: 8 + 8 = 16, a double. So 16 − 8 = 8.
Section 3
Fact Families and Two Steps
4.6
Fact Families
Main ideaThree numbers make a family of two adding facts and two subtracting facts.
Take 4, 6 and 10. Ten is the whole. Four and 6 are the parts. Write four facts: 4 + 6 = 10. 6 + 4 = 10. 10 − 4 = 6. 10 − 6 = 4. This is a .
The whole is always the sum. The whole comes first in the subtracting facts. If you know one fact, you know all four.
Try 5, 8 and 13. Adding: 5 + 8 = 13 and 8 + 5 = 13. Subtracting: 13 − 5 = 8 and 13 − 8 = 5. A double like 7 + 7 = 14 has only two facts. Both parts match.
Words to know
fact family
four facts that use the same three numbers, two adding and two subtracting
Check yourself
1. Which fact is in the family of 3, 9 and 12?
Why: 12 is the whole. 12 − 3 = 9 is true. The whole comes first when subtracting.
2. A family has 2 + 7 = 9. Which subtracting fact belongs?
Why: The whole is 9. 9 − 7 = 2 uses the same three numbers.
3. How many facts are in the family of 6, 8 and 14?
Why: 6 + 8, 8 + 6, 14 − 6 and 14 − 8. That is four facts.
4.7
Two-Step Story Problems
Main ideaSolve one step at a time, then check by a second way.
Ava has 8 crayons. She gets 5 more. Then she gives 3 to Ben. How many now? Step 1: 8 + 5 = 13. Step 2: 13 − 3 = 10. Ava has 10 crayons. This is a .
Read the story twice. Find the first thing that happens. Do that step. Then use its answer for the next step. Write both number sentences.
by a second way. Ava got 5 and gave away 3. That is 2 more overall. 8 + 2 = 10. Same answer. Two ways, same answer, so it is right.
Words to know
two-step problem
a story problem with two things to do, one after the other
check
solve again a different way to see if the answers match
Check yourself
1. Joe has 6 cars. He gets 4 more. Then he loses 2. How many now?
Why: 6 + 4 = 10. Then 10 − 2 = 8.
2. 15 birds sit in a tree. 6 fly away. Then 3 come back. What is the first step?
Why: First 6 fly away, so subtract: 15 − 6 = 9. Then add the 3 that come back.
3. 15 birds. 6 fly away. Then 3 come back. How many birds now?
Why: 15 − 6 = 9. Then 9 + 3 = 12.
Chapter review
Facts Within 20 and Good Strategies
0 / 6
1. What is 13 + 3?
Why: Say 13, then count on: 14, 15, 16. So 13 + 3 = 16.
2. What is 17 − 8?
Why: Think 8 + ? = 17. From 8, jump 2 to 10, then 7 to 17. 2 + 7 = 9.
3. Which trick fits 8 + 8 best?
Why: 8 + 8 is a double. Both parts are the same. 8 + 8 = 16.
4. Which fact belongs to the family of 4, 7 and 11?
Why: 11 is the whole. 11 − 7 = 4 is true.
5. 9 + 6: take 1 from the 6 to make ten. What is left to add?
Why: 6 − 1 = 5. Then 10 + 5 = 15. So 9 + 6 = 15.
6. Ken has 10 stickers. He gives 4 away. Then he gets 7. How many now?
Why: 10 − 4 = 6. Then 6 + 7 = 13.
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★
Unit wrap-up
Adding and Subtracting
Twelve words, twelve meanings
0 / 8
Tap a word, then tap its meaning. A right pair locks in green.
Words
Meanings
Unit test
Fifteen questions across the unit
0 / 10
1. What is 3 + 4?
Why: Say 4, then count on: 5, 6, 7. So 3 + 4 = 7.
2. What is 9 − 5?
Why: Draw 9 circles. Cross out 5. Four are left. 9 − 5 = 4.
3. The whole is 10. One part is 3. What is the other part?
Why: 10 − 3 = 7. Check: 3 + 7 = 10.
4. Which sentence is true?
Why: 2 + 3 = 5, so both sides are 5. The others make 4 and 6.
5. 4 + ? = 9. What is the missing number?
Why: Count on from 4 to 9: 5, 6, 7, 8, 9. Five jumps. 4 + 5 = 9.
6. What is 7 + 7?
Why: 7 + 7 is a double. 7 + 7 = 14.
7. What is 8 + 6?
Why: Make ten: 8 + 2 = 10. Four are left. 10 + 4 = 14.
8. What is 12 − 5?
Why: Think 5 + ? = 12. From 5, jump 5 to 10, then 2 to 12. 5 + 2 = 7.
9. Which fact is in the family with 6 + 9 = 15?
Why: The whole is 15. 15 − 6 = 9 uses the same three numbers.
10. Bo has 9 rocks. He finds 5 more. Then he gives 6 away. How many now?
Why: 9 + 5 = 14. Then 14 − 6 = 8.
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Spiral review
Five questions from earlier units
0 / 5
1. (Unit 1) Which has fewer: 6 cats or 8 dogs?
Why: 6 is smaller than 8. The cats are the smaller group.
2. (Unit 1) Count by fives: 20, 25, 30, what comes next?
Why: Each jump adds five. 30 and 5 more is 35.
3. (Unit 1) What number is 5 tens and 3 ones?
Why: 5 tens is 50. 50 and 3 is 53. Tens go first.
4. (Unit 1) Which number means none?
Why: Zero means none. We write it 0.
5. (Unit 1) Start at 15. Count on 2 more. What number do you say last?
Why: Start at 15, then say 16, 17. The last number is 17.
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Write it
Mia has 7 stickers. She gets 6 more. Then she gives 4 to a friend. How many stickers does Mia have now? Solve it one step at a time. Then check your answer a second way.
Write your answer first.
Write a number sentence for step 1.
Write a number sentence for step 2.
Tell which trick you used, like make ten or count on.
Check it a second way and say if it matches.
0 wordsSaved on this device as you type.
Practice rooms
Rooms already on the site that belong to this unit — cards, quizzes, a lab.
Every lesson keeps its own three checks; a lesson is ticked when all three are right. Chapter reviews, the unit test and its spiral review (five questions from earlier units in this band) score on the page. When the site is connected to your sheet, or the link carries ?dest=, each one also has a Send box: the first-try score, the standards, the supports used, the attempt number and the minutes go to your sheet as an IEP data point.
Print this page for a paper copy of the readings, the sources, the words and the questions; the answers print as dashed boxes under each question.
Fact-check notes for this course live in the handoff: quotes marked (paraphrased) were set that way on purpose.