1 · Five places
Bigger numbers just need more places. 46,936 has ten thousands, thousands, hundreds, tens, ones. The comma sits after the thousands to make it easy to read.
Say it: forty-six thousand, nine hundred thirty-six.
2 · The value of a digit
In 46,936 there are two 6s. The first is in the thousands place: worth 6,000. The last is in the ones: worth 6.
The 9 is in the hundreds place, so it is worth 900. The place, not the digit, decides the value.
3 · Expanded form and words
46,936 = 40,000 + 6,000 + 900 + 30 + 6. Each digit times its place.
A zero still holds its place: 40,306 = 40,000 + 300 + 6. Words: forty thousand, three hundred six.
4 · Comparing and ordering
Start from the left. 47,311 or 46,936? Ten thousands tie (4 and 4). Thousands: 7 beats 6. So 47,311 > 46,936.
More digits always wins: 9,999 < 10,000.
5 · Halfway between
Halfway between 200 and 800: the distance is 600, half of that is 300, so 200 + 300 = 500. Or add and halve: (200 + 800) ÷ 2 = 500.
Halfway between 720 and 1,320: distance 600, half 300, 720 + 300 = 1,020.
6 · Rounding to any place
Find the place you are rounding to, then look at the digit one place to the right. 5 or more: round up. 4 or less: keep it, and everything after becomes 0.
46,936 to the nearest thousand: the hundreds digit is 9, so round up to 47,000. To the nearest hundred: tens digit 3, keep: 46,900.
7 · Rounding to the nearest ten thousand
46,936 to the nearest ten thousand: look at the thousands digit, 6. Round up: 50,000.
14,223: thousands digit 4, keep: 10,000.
8 · What could the number be?
"A number rounds to 4,000 at the nearest thousand. What is the smallest it could be?" Everything from 3,500 to 4,499 rounds to 4,000. Smallest: 3,500. Largest: 4,499.
The band always starts at the halfway point below and ends just before the halfway point above.
9 · Estimating sums and differences
2,987 + 4,120: round to 3,000 + 4,000 = about 7,000. 8,050 − 3,975: 8,000 − 4,000 = about 4,000.
Estimate first, then calculate. If your exact answer is far from the estimate, check again.
10 · Adding four-digit numbers
Same as always: ones, tens, hundreds, thousands, carrying when a column goes over 9.
2,987 + 4,120: 7 + 0 = 7. 8 + 2 = 10, write 0 carry 1. 1 + 9 + 1 = 11, write 1 carry 1. 1 + 2 + 4 = 7. Answer 7,107.
11 · Subtracting across zeros
1,000 − 265: count up instead of borrowing. 265 → 300 is 35. 300 → 1,000 is 700. Total 735.
Counting up to the next friendly number is faster than borrowing through three zeros.
12 · Multi-step number stories
"A warehouse had 1,000 items. It shipped 265, then 296 more, then received 63." 1,000 − 265 = 735. 735 − 296 = 439. 439 + 63 = 502.
One step at a time, writing each answer down. You are ready for the test! 🎉
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