C. Algebra · Patterns, Equations, Coding and ModellingNumber Patterns to 1000
C1.4 A1About 40 minutes
Learning goals- I can count forward and backward by 10s, 25s, 50s and 100s from different numbers up to 1000.
- I can describe what happens to the digits when I add or subtract 10 or 100.
- I can use patterns to show how numbers are related, like 3 + 4 = 7, so 300 + 400 = 700.
- I can create my own number pattern up to 1000 and describe it.
Words to know
digit
One of the symbols 0 to 9 that we use to write numbers.
place value
What a digit is worth because of where it is: hundreds, tens or ones.
hundreds
Groups of 100. In 345, the 3 means 3 hundreds, or 300.
relationship
How numbers are connected to each other.
thousand
1000, or ten hundreds.
Remember from Grade 2
In Grade 2 you found patterns on a hundred chart and skip counted by 2s, 5s, 10s and 25s up to 100. Now the numbers go all the way to 1000! Patterns help us understand these big numbers.
Counting by 100s
100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
- Only the hundreds digit changes. It goes up by 1 each time.
- 10 hundreds make one thousand (1000).
The pattern works from any number. Start at 45: 45, 145, 245, 345, 445. The tens and ones digits (45) stay the same. Only the hundreds digit grows.
Adding 10 and adding 100
Look at what happens to the digits.
| Start | + 10 | + 10 | + 10 | + 10 |
|---|
| 325 | 335 | 345 | 355 | 365 |
| Start | + 100 | + 100 | + 100 | + 100 |
|---|
| 325 | 425 | 525 | 625 | 725 |
Here is part of a chart for the numbers 401 to 430. It works just like a hundred chart.
| 401 | 402 | 403 | 404 | 405 | 406 | 407 | 408 | 409 | 410 |
|---|
| 411 | 412 | 413 | 414 | 415 | 416 | 417 | 418 | 419 | 420 |
| 421 | 422 | 423 | 424 | 425 | 426 | 427 | 428 | 429 | 430 |
Patterns that show relationships
If you know a small fact, patterns help you know bigger facts.
- 3 + 4 = 7 → 30 + 40 = 70 → 300 + 400 = 700
- 8 − 5 = 3 → 80 − 50 = 30 → 800 − 500 = 300
Why does it work? 3 hundreds + 4 hundreds = 7 hundreds, just like 3 apples + 4 apples = 7 apples.
A pattern that makes 1000
- 900 + 100 = 1000
- 800 + 200 = 1000
- 700 + 300 = 1000
- 600 + 400 = 1000
The first number goes down 100 and the second goes up 100. The total stays the same: 1000. This pattern shows that what one number loses, the other gains.
Counting by 25s and 50s
Canadian quarters are worth 25¢. Count by 25s: 25, 50, 75, 100. 4 quarters make 100¢, which is $1. Keep going: 125, 150, 175, 200. Every 4 quarters make another hundred.
Count by 50s: 50, 100, 150, 200, 250, …, 1000. Two 50s make 100.
Worked exampleExample 1: Describe the pattern
Describe this pattern: 618, 628, 638, 648, 658
- Compare each number to the next: 618 + 10 = 628, 628 + 10 = 638, and so on.
- Look at the digits: the tens digit goes 1, 2, 3, 4, 5. The hundreds (6) and ones (8) do not change.
Start at 618. Add 10 each time. Only the tens digit changes.
Worked exampleExample 2: Counting backward by 100s
Extend this pattern by 3 numbers: 970, 870, 770, …
- 970 to 870 is −100. 870 to 770 is −100.
- Keep subtracting 100: 770 − 100 = 670, 670 − 100 = 570, 570 − 100 = 470.
670, 570, 470. The hundreds digit goes down by 1 each time.
Worked exampleExample 3: Use a small fact
Use a pattern to find 500 + 400 and 900 − 600.
- 5 + 4 = 9, so 50 + 40 = 90, so 500 + 400 = 900.
- 9 − 6 = 3, so 90 − 60 = 30, so 900 − 600 = 300.
900 and 300. 5 hundreds + 4 hundreds = 9 hundreds; 9 hundreds − 6 hundreds = 3 hundreds.
Worked exampleExample 4: Create your own pattern
Create a pattern that starts at 250 and grows to 1000. Describe it.
- Choose an operation: add 250.
- 250 + 250 = 500, 500 + 250 = 750, 750 + 250 = 1000.
- Describe it: it is like counting quarters, but with hundreds: 4 jumps of 250 make 1000.
250, 500, 750, 1000. Rule: start at 250, add 250.
Just for funFunny but true: Counting from 1 to 1000 by 1s, one number every second, takes 1000 seconds. That's more than 16 minutes! Counting to 1000 by 100s takes only 10 seconds.
Look at the digits
When you describe a number pattern, say which digit changes and how. That tells you if the pattern is adding ones, tens or hundreds.
Your turn
1Count by 100s from 300 to 1000.
300, 400, 500, 600, 700, 800, 900, 1000.
2What comes next? 462, 472, 482, …
492. Add 10: the tens digit goes up by 1.
3What comes next? 159, 259, 359, …
459. Add 100: the hundreds digit goes up by 1.
4Use 2 + 6 = 8 to find 200 + 600.
800. 2 hundreds + 6 hundreds = 8 hundreds.
5Count by 50s from 600 to 800.
300. 7 + 3 = 10, so 7 hundreds + 3 hundreds = 10 hundreds = 1000.
7Describe the pattern: 840, 830, 820, 810
Start at 840. Subtract 10 each time. The tens digit goes down by 1.
Hands-on activityDigit card patterns
You need: a deck of playing cards with the 10s and the face cards (jack, queen, king) taken out, or paper cards with the digits 1 to 9, paper and a pencil.
- Draw 3 cards. Make a 3-digit number, like 4, 2, 7 → 427. (An ace is 1.)
- Write a pattern that adds 10 five times: 427, 437, 447, 457, 467, 477.
- Circle the digit that changes each time.
- Now make a pattern that adds 100 from the same number. Which digit changes now?
- Challenge: start at your number and subtract 100 until you can't anymore. How many jumps did you make?
Math talk: Tell a grown-up, "When I add 100, the ___ digit goes up by 1."
More practice: warm-up
1What is 10 more than 350?
2What is 100 more than 350?
3Count by 25s from 25 to 200.
25, 50, 75, 100, 125, 150, 175, 200.
4How many hundreds make 1000?
5Use 4 + 3 = 7 to find 400 + 300.
More practice: on your own
1Find the missing numbers: 505, 515, □, 535, □
525 and 545. The rule is add 10.
2Find the missing numbers: 1000, 900, □, 700, □
800 and 600. The rule is subtract 100.
3Extend the pattern: 900 + 100 = 1000, 800 + 200 = 1000, 700 + 300 = 1000. Write the next two lines. What stays the same?
600 + 400 = 1000 and 500 + 500 = 1000. The total stays 1000, because one number goes down 100 and the other goes up 100.
4Use a pattern to find 800 − 300. Explain.
500. 8 − 3 = 5, so 8 hundreds − 3 hundreds = 5 hundreds.
5Mira counts by 10s from 480: 480, 490, 500, 510. Why did the hundreds digit change at 500?
Because 490 + 10 = 500. 10 tens make 1 hundred, so 4 hundreds and 10 tens becomes 5 hundreds, and the tens digit goes back to 0.
Challenge
1Create a pattern that starts at 125 and adds 125. Write the first 4 numbers. Look at the last two digits. How is it like counting quarters?
125, 250, 375, 500. Look at the last two digits: 25, 50, 75, 00. That is the same pattern as counting quarters: 25¢, 50¢, 75¢, 100¢. Each jump of 125 is 1 hundred plus 25 more.
2Which number is not in this pattern? 150, 300, 450, 600, 750, 900. Choices: 450, 650, 900.
650. The pattern adds 150 each time, and it goes from 600 straight to 750.
3Start at 995 and count by 1s to 1000. Then start at 900 and count by 25s to 1000. Which pattern needs more numbers? Explain.
By 1s: 996, 997, 998, 999, 1000 is 5 jumps. By 25s: 925, 950, 975, 1000 is 4 jumps. The count by 1s needs one more jump, even though its numbers are close together, because its jumps are tiny.
Quiz
1. What comes next? 234, 334, 434, …
2. When you add 10 to a number like 352, which digit changes?
4. Which completes the pattern? 600 + 400 = 1000, 500 + 500 = 1000, 400 + □ = 1000
5. Counting by 25s: 75, 100, 125, □. What is missing?
6. Which pattern subtracts 10?
Big idea: Number patterns to 1000 show how our place-value system works (C1.4). Adding 10 changes the tens digit; adding 100 changes the hundreds digit. Patterns like 3 + 4 = 7 → 300 + 400 = 700 help children use facts they already know with bigger numbers.
Common difficulties:
- Crossing a hundred. Counting by 10s from 480: 490, then 500 (not 4100 or 4010). Talk about 10 tens making 1 hundred.
- Counting backward by 100s. Children may change the wrong digit. Ask them to say the number in hundreds, tens and ones.
- Writing 1000. Some children write 10000 or 100. Connect it to 10 hundreds.
How to help: Count by 10s and 100s in the car. Use money: 4 quarters make $1, and 10 dimes make $1. Look for large numbers in daily life (house numbers, prices, page numbers) and ask, "What is 10 more? 100 more?"