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 lemonade stand at the end of a driveway under a shady tree, with stacks of paper cups in tens and a big glass jar of buttons on the table
3Unit
Place Value to 1,000
Number
How many buttons fit in a jar? How many cups of lemonade can you sell in a weekend? Big numbers are everywhere. This unit shows you how big numbers are built. Every number up to 1,000 is made of hundreds, tens and ones.
You will read and write numbers to 1,000. You will compare them with >, < and =. You will count by 5s, 10s and 100s. Then you will add and subtract big numbers by trading tens and ones. And you will explain why your way works.
How we figured it out
Step 1
Count buttons one by one and lose your place
Step 2
Make groups of ten so counting goes faster
Step 3
Ten groups of ten make one hundred
Step 4
Ten hundreds fill the jar: one thousand
Step 5
Write a number as hundreds, tens and ones
Step 6
Compare two numbers with >, < and =
Step 7
Skip count by 5s, 10s and 100s
Step 8
Add cups sold: tens with tens, ones with ones
Step 9
Trade ten ones for a ten when there are too many
Step 10
Trade a ten for ten ones so you can subtract
Step 11
Add and subtract hundreds with drawings
Step 12
Explain your strategy and check it another way
5
Chapter
Hundreds, Tens and Ones
Place Value
Big questionHow can three little digits stand for a number as big as 1,000?
The story
The Button Jar
A big jar of buttons sits on a shelf. Nobody knows how many are inside.
Mrs. Diaz keeps a big glass jar on the shelf. It is full of buttons. Red ones, blue ones, tiny white ones. One day she asks the class a question. How many buttons are in the jar? Everyone guesses. Ten! A hundred! A million!
Two friends, Kai and Rosa, pour the buttons out. Kai starts to count. One, two, three. At forty-two, someone sneezes. Kai loses his place. He has to start again. Rosa has an idea. Let's make groups of ten, she says.
They make piles of ten buttons. Ten piles of ten make one hundred. They put each hundred in a paper cup. Soon the table is covered with cups. They stop and count the cups. Ten cups. That is ten hundreds. Ten hundreds make one thousand!
Mrs. Diaz smiles. You did not count 1,000 buttons one by one, she says. You counted hundreds, tens and ones. That is how big numbers work. Every big number is just groups. Groups of one hundred, groups of ten and some left over.
Talk about itWhy did making groups of ten help Kai and Rosa count faster than counting one by one?
Section 1
Building Big Numbers
5.1
Hundreds, Tens and Ones
Main ideaA three-digit number is made of hundreds, tens and ones.
Think of base-ten blocks. A little cube is one. A rod of ten cubes is a . A flat square of ten rods is a . A hundred has 100 little cubes in it.
Look at 347. The 3 is in the hundreds place. It means 3 hundreds, or 300. The 4 is in the tens place. It means 4 tens, or 40. The 7 is in the ones place. It means 7 ones.
The place tells you the value. A 3 in the hundreds place is 300. A 3 in the ones place is just 3. Same digit, different job. Always ask: which place is it in?
Words to know
hundred
a group of ten tens, or 100 ones
ten
a group of ten ones
place
the spot a digit sits in, which tells its value
Check yourself
1. In 582, what does the 5 stand for?
Why: The 5 is in the hundreds place. It means 5 hundreds, or 500.
2. How many tens make one hundred?
Why: Ten rods of ten make one flat hundred. 10 tens = 100.
3. Which number has 4 hundreds, 0 tens and 9 ones?
Why: 4 hundreds is 400. 0 tens is 0. 9 ones is 9. 400 + 0 + 9 = 409.
5.2
Expanded Form
Main ideaExpanded form breaks a number into hundreds plus tens plus ones.
You can stretch a number out. This is called . Take 347. It has 3 hundreds, 4 tens and 7 ones. So 347 = 300 + 40 + 7.
Try 615. The 6 means 600. The 1 means 10. The 5 means 5. Write it as 600 + 10 + 5. Add it back up. 600 + 10 = 610. Then 610 + 5 = 615. It matches.
Watch out for zeros. In 508, the 0 means 0 tens. So 508 = 500 + 8. Some students write 500 + 0 + 8. That is fine too. Just do not write 58!
Words to know
expanded form
a number written as hundreds plus tens plus ones, like 300 + 40 + 7
Check yourself
1. What is 729 in expanded form?
Why: 7 hundreds is 700. 2 tens is 20. 9 ones is 9. So 700 + 20 + 9.
2. What number is 400 + 50 + 1?
Why: 400 + 50 = 450. Then 450 + 1 = 451.
3. What is 306 in expanded form?
Why: 306 has 3 hundreds, 0 tens and 6 ones. So 300 + 6.
5.3
Reading and Writing Numbers
Main ideaSay the hundreds, then the tens and ones, to read a number up to 1,000.
To read 347, say the hundreds first. Three hundred. Then say the rest like a two-digit number. Forty-seven. Three hundred forty-seven. Do not say ’and’ in the middle.
Now write a number from words. Five hundred twelve. Five hundred is 500. Twelve is 12. Put them together: 512. Be careful with ’twelve’. It is one ten and two ones.
One is written 1,000. It is ten hundreds. The comma helps your eye. Nine hundred ninety-nine is 999. One more makes 1,000.
Words to know
digit
one of the symbols 0 to 9 used to write numbers
thousand
ten hundreds, written 1,000
Check yourself
1. How do you write six hundred forty-two?
Why: Six hundred is 600. Forty-two is 42. 600 + 42 = 642.
2. How do you say 803?
Why: The 8 is 800. Then 0 tens and 3 ones. Eight hundred three.
3. What number comes right after 999?
Why: 999 + 1 = 1,000. Ten hundreds make one thousand.
Section 2
Comparing Numbers
5.4
Which Number Is Bigger?
Main ideaCompare the hundreds first, then the tens, then the ones.
Kai has 348 buttons. Rosa has 352. Who has more? Let’s . Look at the hundreds first. Both have 3 hundreds. It is a tie. Move to the tens.
Kai has 4 tens. Rosa has 5 tens. 5 tens is more than 4 tens. So 352 is bigger than 348. You do not even need the ones. The tens settled it.
A common mistake is to look at the ones first. 348 has an 8. 352 has a 2. But 8 ones is only 8. One ten is worth 10. Bigger places win. Start on the left.
Words to know
compare
to look at two numbers and tell which is bigger, smaller or the same
Check yourself
1. Which is bigger, 476 or 481?
Why: Both have 4 hundreds. 8 tens is more than 7 tens. 481 is bigger.
2. Which is smaller, 209 or 190?
Why: 209 has 2 hundreds. 190 has only 1 hundred. 190 is smaller.
3. To compare 635 and 638, which place do you need to check last?
Why: The hundreds tie at 6. The tens tie at 3. The ones decide it. 8 is more than 5, so 638 is bigger.
5.5
The Signs >, < and =
Main ideaUse > for greater than, < for less than and = for equal to.
Three signs help you compare. The sign > means . The sign < means . The sign = means . The open side of > or < always faces the bigger number.
Compare 352 and 348. 352 is greater. Write 352 > 348. Now flip it. 348 is less than 352. Write 348 < 352. Both say the same thing.
What about 500 and 500? They are the same. Write 500 = 500. Think of the sign as a hungry mouth. It opens to eat the bigger number.
Words to know
greater than
bigger than; the sign is >
less than
smaller than; the sign is <
equal to
the same amount; the sign is =
Check yourself
1. Which sign goes in 415 ? 451?
Why: The hundreds tie. 1 ten is less than 5 tens. So 415 < 451.
2. What does 890 > 809 mean?
Why: The sign > means greater than. 9 tens beats 0 tens, so 890 is greater.
3. Which is true?
Why: 300 + 40 is 340. So 340 = 340. They are equal.
Section 3
Counting and Patterns
5.6
Counting by 5s, 10s and 100s
Main ideaSkip counting adds the same amount each time: 5, 10 or 100.
To means to count by jumps. Count by 5s: 5, 10, 15, 20, 25. Count by 10s: 10, 20, 30, 40, 50. Count by 100s: 100, 200, 300, 400, 500.
You can start anywhere. Start at 340 and count by 10s. 340, 350, 360, 370. Only the tens digit changes. Start at 340 and count by 100s. 340, 440, 540. Only the hundreds digit changes.
Skip counting is fast. Rosa has 6 cups of 100 buttons. She counts 100, 200, 300, 400, 500, 600. Six jumps of 100 is 600. Much faster than counting one by one.
Words to know
skip count
to count by jumps of the same size, like 5, 10, 15, 20
Check yourself
1. Count by 5s: 35, 40, 45, ___. What comes next?
Why: 45 + 5 = 50. Each jump adds 5.
2. Count by 10s from 570: 570, 580, ___. What comes next?
Why: 580 + 10 = 590. Only the tens digit changes.
3. Count by 100s: 250, 350, 450, ___. What comes next?
Why: 450 + 100 = 550. The hundreds digit goes up by 1.
5.7
100 More and 100 Less
Main ideaAdding or taking away 100 changes only the hundreds digit.
What is 100 than 462? Add one hundred. The hundreds digit goes from 4 to 5. The tens and ones stay the same. 462 + 100 = 562.
What is 100 than 462? Take one hundred away. The hundreds digit goes from 4 to 3. 462 − 100 = 362. The 6 and the 2 do not move.
The same trick works for 10. 10 more than 462 is 472. 10 less than 462 is 452. Only the tens digit changes. Be careful near 9 tens: 10 more than 495 is 505.
Words to know
more
a bigger amount; 100 more means add 100
less
a smaller amount; 100 less means take away 100
Check yourself
1. What is 100 more than 738?
Why: 738 + 100 = 838. Only the hundreds digit changes, from 7 to 8.
2. What is 100 less than 520?
Why: 520 − 100 = 420. The hundreds digit drops from 5 to 4.
3. What is 10 more than 293?
Why: 293 + 10 = 303. 9 tens plus 1 ten is 10 tens, which makes a new hundred.
5.8
Even and Odd Numbers
Main ideaEven numbers make pairs with none left over; odd numbers have one left over.
Put 8 buttons in pairs. You get 4 pairs. None are left over. So 8 is . Put 7 buttons in pairs. You get 3 pairs and 1 left over. So 7 is .
Here is a fast check. Look at the ones digit only. If it is 0, 2, 4, 6 or 8, the number is even. If it is 1, 3, 5, 7 or 9, the number is odd. So 346 is even. 231 is odd.
Even numbers are doubles. 8 is 4 + 4. 10 is 5 + 5. 12 is 6 + 6. Odd numbers cannot split into two equal groups. Try to split 9 in half. You get 4 and 5, not a match.
Words to know
even
a number that makes pairs with none left over, like 2, 4, 6
odd
a number that leaves one out when you make pairs, like 1, 3, 5
Check yourself
1. Which number is even?
Why: 18 ends in 8. It makes 9 pairs with none left over. 18 is even.
2. Which number is odd?
Why: 31 ends in 1. Pairs leave one out. 31 is odd.
3. Which number is a double, like 6 = 3 + 3?
Why: 14 = 7 + 7. It is even. 9 and 11 cannot be split into two equal groups.
Chapter review
Hundreds, Tens and Ones
0 / 6
1. What number is 5 hundreds, 7 tens and 3 ones?
Why: 500 + 70 + 3 = 573.
2. What is 840 in expanded form?
Why: 8 hundreds is 800. 4 tens is 40. There are 0 ones. So 800 + 40.
3. Which sign goes in 596 ? 603?
Why: 596 has 5 hundreds. 603 has 6 hundreds. So 596 < 603.
4. Count by 5s: 90, 95, 100, ___. What comes next?
Why: 100 + 5 = 105. Each jump adds 5.
5. What is 100 less than 907?
Why: 907 − 100 = 807. The hundreds digit drops from 9 to 8.
6. Which number is odd?
Why: 489 ends in 9, so it is odd. Numbers that end in 0 or 4 are even.
Send it to your teacher
6
Chapter
Adding and Subtracting Bigger Numbers
Operations
Big questionHow do hundreds, tens and ones help us add and subtract big numbers?
The story
The Lemonade Stand
Two days of sales, two cards with numbers and one big question: how many cups in all?
It is a hot weekend in July. Kai and Rosa set up a lemonade stand on the corner. A cup costs 50 cents. Saturday is busy. Cars stop. Neighbors walk over. By dinner they have sold 48 cups. Rosa writes 48 on a card.
Sunday is a little slower. Clouds roll in after lunch. Still, they sell 36 cups. Rosa writes 36 on a second card. Kai looks at the two cards. How many cups did we sell in all? he asks. Rosa starts to count on her fingers. That will take forever.
Then Rosa remembers the button jar. Tens and ones! she says. 48 is 4 tens and 8 ones. 36 is 3 tens and 6 ones. Add the tens: 7 tens. Add the ones: 14 ones. But 14 ones is a ten and 4 more. So that is 8 tens and 4 ones. Eighty-four cups!
Kai checks it another way. 48 plus 30 is 78. Then 78 plus 6 is 84. Same answer. They high-five. Then Kai asks a harder question. We had 100 cups at the start. How many are left? That is a subtraction problem. And it is next.
Talk about itRosa and Kai got 84 two different ways. Why is it smart to check an answer with a second way?
Section 1
Adding Within 100
6.1
Tens With Tens, Ones With Ones
Main ideaTo add two-digit numbers, add the tens together and the ones together.
Let’s 32 + 45. Break each number apart. 32 is 3 tens and 2 ones. 45 is 4 tens and 5 ones. Add the tens: 3 tens + 4 tens = 7 tens. Add the ones: 2 + 5 = 7. So 32 + 45 = 77.
Picture the rods and cubes. Put 3 rods next to 4 rods. That is 7 rods. Put 2 cubes next to 5 cubes. That is 7 cubes. 7 rods and 7 cubes show 77. The is 77.
A common mistake is to add a ten to a one. In 32 + 45, do not add 3 + 5. The 3 is tens and the 5 is ones. Tens go with tens. Ones go with ones.
Why: 4 tens + 8 tens = 12 tens. That is 1 hundred and 2 tens. 3 + 2 + 1 = 6 hundreds. So 620.
6.7
Mental Math with 10s and 100s
Main ideaYou can add or subtract 10 or 100 in your head by changing one digit.
Rosa sold 48 cups. Then 10 more. She uses . She adds a ten in her head. 48 + 10 = 58. Then 10 more: 68. Only the tens digit changes. No paper needed.
Do the same with hundreds. 325 + 100 = 425. 325 − 100 = 225. Only the hundreds digit moves. Try 640 − 200. Two hundreds down: 540, 440. So 640 − 200 = 440.
Break bigger jumps into tens. 57 + 30 is three tens more. 67, 77, 87. So 57 + 30 = 87. And 92 − 40 is four tens back. 82, 72, 62, 52. So 92 − 40 = 52.
Words to know
mental math
doing math in your head without writing it down
Check yourself
1. What is 76 + 20?
Why: Two tens more: 86, then 96. So 76 + 20 = 96.
2. What is 483 − 100?
Why: One hundred less. The 4 becomes 3. So 383.
3. What is 250 + 300?
Why: Three hundreds more: 350, 450, 550. So 250 + 300 = 550.
6.8
Why the Strategy Works
Main ideaA good strategy works because it keeps the tens and ones in their places.
Kai adds 48 + 36 by jumping. 48 + 30 = 78. Then 78 + 6 = 84. Why does this work? Because 36 is just 30 and 6. Adding 30 and then 6 is the same as adding 36.
Rosa uses a different way. She makes 48 into 50. She takes 2 from 36 to do it. 50 + 34 = 84. Same answer! Moving 2 from one number to the other does not change the total.
When you a strategy, say what you did to the tens and ones. Say why the total did not change. Then check with a different way. If both ways match, you can trust the answer.
Words to know
strategy
a plan or way to solve a problem
explain
to tell how you did something and why it works
Check yourself
1. Rosa solves 57 + 25 as 60 + 22. Why does this work?
Why: 57 + 3 = 60 and 25 − 3 = 22. The total is still 82.
2. Kai adds 64 + 23 by jumping the tens first. What is his first jump?
Why: Jump the tens first: 64 + 20 = 84. Then 84 + 3 = 87.
3. Kai gets 84 one way and 74 another way. What should he do?
Why: Two different answers means one has a mistake. Check each step of both ways again.
Chapter review
Adding and Subtracting Bigger Numbers
0 / 6
1. What is 34 + 52?
Why: 3 + 5 = 8 tens. 4 + 2 = 6 ones. So 86.
2. What is 47 + 38?
Why: 7 + 8 = 15. Trade ten ones for a ten. 4 + 3 + 1 = 8 tens. So 85.
3. What is 85 − 42?
Why: 8 − 4 = 4 tens. 5 − 2 = 3 ones. So 43.
4. What is 70 − 26?
Why: Trade: 6 tens and 10 ones. 10 − 6 = 4. 6 − 2 = 4 tens. So 44.
5. What is 516 + 100?
Why: One hundred more. The 5 becomes 6. So 616.
6. What is 15 + 25 + 32?
Why: 15 + 25 = 40. Then 40 + 32 = 72.
Send it to your teacher
★
Unit wrap-up
Place Value to 1,000
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 number is 6 hundreds, 0 tens and 4 ones?
Why: 600 + 0 + 4 = 604. The 0 holds the tens place.
2. What is 275 in expanded form?
Why: 2 hundreds is 200. 7 tens is 70. 5 ones is 5. So 200 + 70 + 5.
3. Which sign goes in 348 ? 384?
Why: The hundreds tie. 4 tens is less than 8 tens. So 348 < 384.
4. Count by 10s: 460, 470, 480, ___. What comes next?
Why: 480 + 10 = 490. Only the tens digit changes.
5. Which number is even?
Why: 56 ends in 6. It makes 28 pairs with none left over. 56 is even.
6. What is 100 more than 655?
Why: 655 + 100 = 755. The hundreds digit goes from 6 to 7.
7. What is 26 + 47?
Why: 6 + 7 = 13. Trade ten ones for a ten. 2 + 4 + 1 = 7 tens. So 73.
8. What is 91 − 35?
Why: Trade: 8 tens and 11 ones. 11 − 5 = 6. 8 − 3 = 5 tens. So 56.
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.