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 · 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.
7 · 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.
8 · 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.
9 · 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.
Right in the middle, 350 rounds up to 400. Middle always goes up.
10 · 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).
11 · Estimating with rounding
Rounding makes hard sums easy to guess. 298 + 407: round to 300 + 400 = about 700.
Tests ask "about how many" or "closest to." That is your cue to round first.
12 · 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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