What Are We Learning Today?
Our number system is called the base-ten system. This means every position in a number is worth 10 times more than the position to its right. The digit 3 in 300 is worth much more than the digit 3 in 30 or the digit 3 in 3! Today we master the hundreds, tens, and ones places.
Key Words to Know
The Place Value Chart
Let's look at the number 347
347 = 300 + 40 + 7
Three Ways to Show a Number
| Form | What It Looks Like | Example for 256 |
|---|---|---|
| Standard Form | The regular number | 256 |
| Expanded Form | Sum of each place value | 200 + 50 + 6 |
| Word Form | Written out in words | two hundred fifty-six |
The Value of Each Digit Changes by Position
| Number | Digit 5 is in the... | Value of the 5 |
|---|---|---|
| 500 | Hundreds place | 500 |
| 50 | Tens place | 50 |
| 5 | Ones place | 5 |
| 537 | Hundreds place | 500 |
| 257 | Tens place | 50 |
| 275 | Ones place | 5 |
Try It Yourself!
- Write the number 492 in expanded form and in word form.
- What is the value of the digit 7 in each number: 700, 370, 47, 714?
- Build the number with: 5 hundreds, 3 tens, 8 ones. What is the number?
- What number has 4 hundreds, 0 tens, and 6 ones?
Remember This!
Hundreds -- Tens -- Ones: position determines value!
Expanded form = 347 = 300 + 40 + 7
The same digit in a different place has a completely different value.
Great start! Click Lesson 8.2!
What Are We Learning Today?
Today we practice reading numbers written in words and writing them as digits -- all the way up to 1,000! This includes tricky numbers like those with zeros in the middle, such as 405 or 730.
Key Words to Know
Numbers in Word Form -- The Patterns
Ones (1-19)
one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen
Tens (20-90)
twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety
Combine: twenty-one, thirty-five, forty-eight...
Hundreds (100-900)
one hundred, two hundred, three hundred...
Combine: three hundred forty-seven, five hundred twelve...
Tricky Numbers -- Zeros in the Middle!
| Standard Form | Word Form | Expanded Form |
|---|---|---|
| 405 | four hundred five | 400 + 0 + 5 = 400 + 5 |
| 730 | seven hundred thirty | 700 + 30 + 0 = 700 + 30 |
| 600 | six hundred | 600 + 0 + 0 = 600 |
| 312 | three hundred twelve | 300 + 10 + 2 |
| 1,000 | one thousand | 1,000 |
Try It Yourself!
- Write in word form: 524, 307, 890, 1,000
- Write in standard form: "six hundred forty-one," "two hundred nine," "five hundred"
- Write in expanded form: 763, 408, 550
- What number is: 800 + 0 + 3?
Remember This!
Use a hyphen for two-digit numbers in word form (twenty-four).
When a place has zero, skip it in word form but keep it in standard form!
405 = "four hundred five" -- not "four hundred zero five."
Excellent! Click Lesson 8.3!
What Are We Learning Today?
Comparing numbers means deciding which is greater, which is less, or whether they are equal. We use three special symbols: > (greater than), < (less than), and = (equal to). The key is always to compare place by place, starting from the left!
Key Words to Know
The Alligator Trick -- Remember the Symbols!
Greater Than >
8 > 5
The alligator's mouth opens toward the BIGGER number (8). The alligator always wants to eat the bigger number!
Less Than <
3 < 9
The point faces the SMALLER number (3). 3 is less than 9.
How to Compare 3-Digit Numbers -- Step by Step
| Step | What to Do | Example: 547 vs 563 |
|---|---|---|
| 1 | Compare the HUNDREDS digit first | 5 = 5 (same -- move to next place) |
| 2 | Compare the TENS digit | 4 < 6 (different! 547 is less than 563) |
| 3 | Write the comparison | 547 < 563 |
473 > 368
Hundreds: 4 > 3 -- stop here, we know!
251 < 259
Hundreds: 2=2, Tens: 5=5, Ones: 1 < 9
Ordering Numbers -- Smallest to Largest
Order these numbers from least to greatest: 472, 247, 742, 427
Compare hundreds digits first: 2 < 4 < 4 < 7. For the tie at 4 (427 and 472), compare tens: 2 < 7.
Try It Yourself!
- Write >, <, or = between each pair: 423 ___ 432 | 700 ___ 700 | 561 ___ 516
- Order from least to greatest: 834, 384, 843, 438
- Order from greatest to least: 291, 912, 129, 219
- I am a 3-digit number. My hundreds digit is greater than 5. My tens digit is less than 4. My ones digit equals my tens digit. What could I be?
Remember This!
> greater than | < less than | = equal to
Always compare left to right: hundreds first, then tens, then ones.
The alligator's mouth always opens toward the bigger number!
Well done! Click Lesson 8.4!
What Are We Learning Today?
Rounding means finding the nearest "neat" number -- the nearest 10 or the nearest 100. We round when we need a quick estimate rather than an exact answer. Rounding is used every day: "About how much will this cost?" or "Roughly how far is the trip?" are rounding questions!
Key Words to Know
The Rounding Rule
Rounding to the Nearest 10 -- Look at the ONES digit
If the ones digit is 0, 1, 2, 3, or 4 -- round DOWN (keep the tens digit the same, ones become 0)
If the ones digit is 5, 6, 7, 8, or 9 -- round UP (increase the tens digit by 1, ones become 0)
Examples: 43 → 40 | 47 → 50 | 65 → 70 | 82 → 80
Rounding to the Nearest 100 -- Look at the TENS digit
If the tens digit is 0, 1, 2, 3, or 4 -- round DOWN (keep the hundreds digit, tens and ones become 0)
If the tens digit is 5, 6, 7, 8, or 9 -- round UP (increase the hundreds digit by 1, tens and ones become 0)
Examples: 320 → 300 | 380 → 400 | 450 → 500 | 749 → 700
Using a Number Line to Round
Round 47 to the nearest 10:
47 is between 40 and 50. It is closer to 50 (only 3 away vs 7 away). So 47 rounds UP to 50.
Practice Rounding Chart
| Number | Round to nearest 10 | Round to nearest 100 |
|---|---|---|
| 234 | 230 (ones: 4, round down) | 200 (tens: 3, round down) |
| 567 | 570 (ones: 7, round up) | 600 (tens: 6, round up) |
| 450 | 450 (ones: 0, round down) | 500 (tens: 5, round up) |
| 782 | 780 (ones: 2, round down) | 800 (tens: 8, round up) |
Try It Yourself!
- Round to the nearest 10: 63, 78, 45, 91, 34
- Round to the nearest 100: 350, 420, 870, 150, 649
- A store sells 387 apples in one day. About how many apples is that, rounded to the nearest hundred?
- There are 54 students going on a field trip. About how many is that, rounded to the nearest ten?
Remember This!
To round to nearest 10: look at the ones digit.
To round to nearest 100: look at the tens digit.
Digits 0-4: round DOWN | Digits 5-9: round UP
Keep going! Click Lesson 8.5!
What Are We Learning Today?
Every whole number is either even or odd. This simple fact has powerful consequences in mathematics! Today we learn how to identify even and odd numbers and explore the patterns they create when you add, subtract, or multiply them.
Key Words to Know
Identifying Even and Odd Numbers
Even numbers (end in 0, 2, 4, 6, 8):
Odd numbers (end in 1, 3, 5, 7, 9):
Even and Odd Patterns
| Operation | Rule | Example |
|---|---|---|
| Even + Even | = Even | 4 + 6 = 10 (even) |
| Odd + Odd | = Even | 3 + 5 = 8 (even) |
| Even + Odd | = Odd | 4 + 3 = 7 (odd) |
| Even x Even | = Even | 4 x 6 = 24 (even) |
| Even x Odd | = Even | 4 x 3 = 12 (even) |
| Odd x Odd | = Odd | 3 x 5 = 15 (odd) |
Try It Yourself!
- Circle the even numbers: 47, 82, 165, 300, 991, 428, 73, 560
- Without calculating, predict whether each answer will be even or odd: 7 + 9 = ___ | 6 + 8 = ___ | 5 + 4 = ___
- Is the product of two odd numbers always odd, always even, or sometimes both? Give two examples.
- Write all the even numbers between 51 and 61.
Remember This!
EVEN = ends in 0, 2, 4, 6, 8 (can be split into two equal groups)
ODD = ends in 1, 3, 5, 7, 9 (always one left over)
Odd + Odd = Even | Even + Even = Even | Even + Odd = Odd
Almost there! Click Lesson 8.6!
What Are We Learning Today?
Numbers follow patterns -- predictable sequences where each number relates to the next by a consistent rule. Recognising number patterns is a key mathematical thinking skill. Skip counting is one of the most useful patterns -- and it connects directly to multiplication!
Key Words to Know
Skip Counting Sequences
Skip count by 2s:
Skip count by 5s:
Skip count by 100s:
Finding the Rule in a Pattern
| Pattern | Rule | Next Three Numbers |
|---|---|---|
| 3, 6, 9, 12, ___ | Add 3 each time | 15, 18, 21 |
| 100, 90, 80, 70, ___ | Subtract 10 each time | 60, 50, 40 |
| 4, 8, 12, 16, ___ | Add 4 (count by 4s) | 20, 24, 28 |
| 500, 400, 300, ___ | Subtract 100 each time | 200, 100, 0 |
| 2, 4, 8, 16, ___ | Double (multiply by 2) | 32, 64, 128 |
Skip Counting Connects to Multiplication!
Skip count by 6s:
6, 12, 18, 24, 30, 36...
These are the multiples of 6 -- the same as the 6 times table! 6x1=6, 6x2=12, 6x3=18...
Why it matters:
Skip counting IS multiplication! If you can skip count by 7s, you already know your 7 times table.
7, 14, 21, 28, 35, 42, 49, 56, 63, 70
Try It Yourself!
- Find the rule and write the next three numbers: 25, 50, 75, ___, ___, ___
- Find the rule and write the next three numbers: 200, 175, 150, ___, ___, ___
- Skip count by 8s starting from 0: 0, 8, ___, ___, ___, ___, ___, ___
- What is the pattern? 1, 2, 4, 8, 16, ___, ___. What makes this pattern different from the others?
You Finished Unit 8!
A pattern follows a consistent rule -- find the rule and you can predict what comes next!
Skip counting is the same as listing the multiples of a number.
Increasing patterns add or multiply. Decreasing patterns subtract or divide.
Incredible work! You completed all 6 lessons in Unit 8! Now take the Unit 8 Quiz!