1 · Ones, tens, hundreds
We count in groups of ten. One little cube is 1. Ten cubes in a row make a ten. Ten rows make a hundred flat.
2 · Reading a number from blocks
2 hundreds, 3 tens, and 5 ones. Say it as a number: 235. Each block goes in its own place.
3 · The place-value chart
Every digit lives in a place. In 4,286 the 4 is in the thousands place, the 2 in hundreds, the 8 in tens, and the 6 in ones.
The place tells the digit's value. That 8 is not worth 8. It is in the tens place, so it is worth 80.
4 · Expanded form
Stretch a number out into the value of each digit: 4,286 = 4,000 + 200 + 80 + 6. That is expanded form.
It works backwards too: 600 + 40 + 2 = 642.
5 · Zero holds a place
407 has 4 hundreds, 0 tens, and 7 ones. The zero keeps the 4 in the hundreds place. Without it you would have 47, a much smaller number.
6 · Numbers in words
Say the number the way you read it, one group at a time: 4,306 is "four thousand, three hundred six". A zero place is simply not said.
Watch the tens: 4,036 is "four thousand, thirty-six". The comma in the number matches the comma in the words, right after "thousand".
Tens and ones together get a hyphen: 47 is "forty-seven", 96 is "ninety-six".
7 · Comparing numbers
To compare, start from the left, the biggest place. 3,412 or 3,389? Thousands tie (3 and 3). Hundreds: 4 beats 3. So 3,412 is greater: 3,412 > 3,389.
The open side of > faces the bigger number, like a hungry mouth.
8 · Numbers on a number line
A number line puts numbers in order. Bigger is always to the right. 680 sits between 600 and 700, closer to 700.
9 · Number lines that skip
Many number lines only label some marks. Before reading one, find what one jump is worth: pick two labels next to each other and count the jumps between them.
Here 0 and 25 are 5 jumps apart, and 25 ÷ 5 = 5, so each jump is 5. The dot is 2 jumps past 25: 25, 30, 35.
10 · 10 more, 100 more, 1,000 more
Adding 10 changes the tens digit by one; adding 100 changes the hundreds digit; adding 1,000 changes the thousands digit. The other digits stay put.
Careful when a digit is a 9: 10 more than 3,995 is 4,005. The 9 tens become 10 tens, which is one more hundred, and the 9 hundreds roll over the same way.
100 less than 4,035 is 3,935: there are 0 hundreds, so borrow one thousand.
11 · Rounding to the nearest ten
Rounding means picking the closest friendly number. 47 is between 40 and 50. It is closer to 50, so 47 rounds to 50.
The rule: look at the ones digit. 5 or more, round up. 4 or less, round down. 43 → 40, 45 → 50, 47 → 50.
12 · Rounding to the nearest hundred
Now look at the tens digit. 342 → the tens digit is 4, so round down to 300. 371 → 7, round up to 400.
A number right in the middle always rounds up, so 350 rounds up to 400.
13 · Rounding bigger numbers
Same idea, look at the digit one place to the right of where you are rounding.
2,468: nearest ten → 2,470 (ones digit 8). Nearest hundred → 2,500 (tens digit 6). Nearest thousand → 2,000 (hundreds digit 4).
14 · Estimating with rounding
Round the numbers first to make estimating big sums much easier. 298 + 407: round to 300 + 400 = about 700.
Tests ask "about how many" or "closest to." That is your cue to round first.
15 · Odd and even
An even number can be split into pairs with nobody left over. An odd number always has one left over.
You only need the ones digit: 0, 2, 4, 6, 8 mean even; 1, 3, 5, 7, 9 mean odd. So 3,457 is odd and 1,004 is even.
Two rules worth knowing: odd + odd = even, and even + odd = odd.
16 · What could the number be?
A trickier question: "A number rounds to 200 at the nearest hundred. What is the smallest it could be?"
Numbers that round to 200 run from 150 up to 249 (the shaded part). So the smallest is 150, and the largest is 249.
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