Numbers up to 1,000,000 — compare, round, add, subtract, and solve word problems
🔢 Topic 1.1: Place Value to 1,000,000
Place Value
Click the digits to change them. See the number in standard form, expanded form, and word form. The value of each digit depends on its place!
👉 Key idea: In the number 342,715, the digit 3 is in the hundred-thousands place, so it's worth 300,000. The digit 4 is in the ten-thousands place, so it's worth 40,000. Every place is 10× bigger than the place to its right.
0
= 0
zero
Each digit's value shown above
💡 Tip: Click the ▲ / ▼ arrows next to any digit to change it. Watch how the number and its word form update instantly!
✏️ Place Value Practice
1In the number 627,415, what is the value of the digit 6?
🤔 Think about which place the 6 is in!
Hint: 627,415 → the 6 is in the hundred-thousands place. What is 6 × 100,000?
Answer: 6 × 100,000 = 600,000
2In the number 834,902, what is the value of the digit 3?
🤔 Which place is the 3 in?
Hint: 834,902 → the 3 is in the ten-thousands place. What is 3 × 10,000?
Answer: 3 × 10,000 = 30,000
3Write the number: seven hundred two thousand, four hundred sixty-eight
🤔 Remember: "thousand" separates the thousands group from the ones!
Hint: Seven hundred two = 702, then add "thousand", then four hundred sixty-eight = 468.
Answer:702,468
⚖️ Topic 1.2: Comparing & Ordering Numbers
Comparing Amounts
Drag the sliders to change two numbers. See which is greater, which is smaller, or if they're equal. Numbers are color-coded so you can compare by place value easily!
👉 Key idea: Compare digits from left to right. Start with the biggest place (hundred-thousands). The first place where the digits differ tells you which number is bigger!
5,280
=
5,280
Comparison: The numbers are equal.
📏 Ordering on a Number Line
Drag each number into the correct slot on the number line, from smallest to largest!
12,500
45,700
8,230
36,500
60,100
?
?
?
?
?
✏️ Comparing Practice
1Which is greater: 45,709 or 45,790?
🤔 Compare from left to right — which digits differ first?
Hint: 45,709 vs 45,790. The ten-thousands and thousands are the same (45,...). The hundreds digits are 7 vs 7. The tens digits: 0 vs 9!
Answer: 45,709 < 45,790 so 45,790 is greater
2Which is smaller: 302,415 or 298,999?
🤔 Start at the hundred-thousands place!
Hint: 302,415 vs 298,999. The hundred-thousands: 3 vs 2. Since 3 > 2, 302,415 is greater!
Answer:298,999 is smaller
3Order these from smallest to largest: 5,280 5,820 5,802 5,208
🤔 Compare the hundreds digits!
Hint: All start with 5,2... so compare the hundreds digits: 2, 8, 8, 2. Then tens digits for ties.
Answer: 5,208 < 5,280 < 5,802 < 5,820
🔄 Topic 1.3: Rounding
Rounding
Use the slider to pick a number, then choose which place to round to. Watch the number line show you whether to round up or down!
👉 Key idea: When rounding, look at the digit to the right of the rounding place. If it's 5 or more, round up. If it's 4 or less, round down. The "halfway" point is always in the middle!
3,475 rounded to the nearest hundred is 3,500
How it works: The digit in the hundreds place is 4. Look right to the tens place: 7 ≥ 5 → round up!
✏️ Rounding Practice
1Round 6,372 to the nearest ten.
🤔 Look at the ones digit — is it 5 or more?
Hint: 6,372 → tens digit is 7, look at ones digit 2. Since 2 < 5, round DOWN.
Answer:6,370
2Round 48,751 to the nearest thousand.
🤔 Look at the hundreds digit (the one right after thousands).
Hint: 48,751 → thousands digit is 8, look at hundreds digit 7. Since 7 ≥ 5, round UP to 49,000.
Answer:49,000
3Round 125,499 to the nearest ten-thousand.
🤔 The ten-thousands place is the 5th digit from the right. The digit after it is the thousands place.
Hint: 125,499 → ten-thousands digit is 2, look at thousands digit 5. Since 5 ≥ 5, round UP to 130,000.
Answer:130,000
➕ Topic 1.4: Multi-Digit Addition
Addition
Enter two numbers and step through the column addition process. Each step adds one column, shows any carry, and builds the sum!
👉 Key idea: Align numbers by their rightmost digit (ones place). Add each column from right to left. If a column's sum is 10 or more, carry the tens digit to the next column on the left.
3,8472,986
Step 0: Press "Next Step" to begin adding column by column!
✏️ Addition Practice
13,259 + 1,478 = ?
🤔 Stack them up and add from right to left. Don't forget the carry!
Enter two numbers and step through column subtraction. Watch the borrowing animation when a digit is too small to subtract!
👉 Key idea: Subtract each column from right to left. If the top digit is smaller than the bottom digit, borrow 1 from the next column to the left (cross it out, reduce it by 1, and add 10 to the current column).
6,5422,896
Step 0: Press "Next Step" to begin subtracting column by column!
✏️ Subtraction Practice
15,432 − 2,187 = ?
🤔 Start from the ones: 2 − 7 — need to borrow!
Hint: Borrow from tens: 12−7=5, then 2−8 (borrow from hundreds: 12−8=4), then 3−1=2, then 5−2=3 → 3,245
Answer:3,245
27,000 − 3,456 = ?
🤔 Lots of borrowing needed — zeros make it tricky!
Hint: Borrow from thousands: 10−6=4, then 9−5=4, then 9−4=5, then 6−3=3 → 3,544
Answer:3,544
39,205 − 4,718 = ?
🤔 Ones: 5−8 borrow, hundreds: 2−7 borrow from thousands...
Hint: Borrow for ones: 15−8=7, tens: 9−1=8, hundreds: 11−7=4 (borrow from thousands), thousands: 8−4=4 → 4,487
Answer:4,487
🧩 Topic 1.6: Multi-Step Word Problems
+ & − Word Problems
Read each problem, work through the steps, and use bar models to see the math. Follow along: Read → Identify → Draw → Solve → Check!
👉 Strategy: Break the problem into steps. Solve one part at a time. After each step, ask: "Do I add or subtract? What's unknown?" Bar models help you SEE which operation to use!
🏫 Problem 1: School Books
A school has 2,450 books in the library. They buy 875 new books. Then 320 books are checked out. How many books are in the library now?
1Read the problem: "How many books are in the library now?"
2We know: 2,450 books at start. 875 new books ADDED. 320 books SUBTRACTED (checked out).
3Draw bar model: Start with 2,450. Add 875 → that's the new total. Then subtract 320.
2A factory makes 4,500 toys on Monday. On Tuesday they make 1,250 more than Monday. On Wednesday they ship 3,700 toys to stores. How many toys are left at the factory?
🤔 First find Tuesday's total (Monday + 1,250), then subtract the shipment.
3Sarah is reading a book with 320 pages. She reads 45 pages on Saturday and 38 pages on Sunday. How many more pages does she need to read to finish the book?
🤔 First find total pages read, then subtract from the total!