1The key question: is the reference number included?
There are four expressions for describing a number range. All four boil down to just two questions: does it include the reference number, and is it the bigger side or the smaller side?
e.g. at least 12 → 12, 13, 14…
e.g. at most 12 → 12, 11, 10…
e.g. more than 12 → 13, 14, 15…
e.g. less than 12 → 11, 10, 9…
On the activity page's number line, a filled dot (●) means the reference number is included, and an empty dot (○) means it isn't.
2Rounding up always goes to the bigger side
If the digits below the place you're rounding to aren't all zero, rounding up always makes that place 1 bigger and turns everything below it to zero. Even a tiny bit over pushes it up to the next step.
Since 1234 is bigger than 1230, it always rounds up to the next ten, 1240.
3Rounding down always goes to the smaller side
Rounding down turns every digit below the place you're rounding to into zero and drops it. No matter how large the remaining part is, it just gets cut off.
The remaining 4 simply disappears, leaving 1230.
4Rounding to the nearest picks based on the halfway point
Rounding to the nearest picks whichever of the two values is closer. If it's exactly halfway (5) or more, it goes to the bigger side; if it's less than halfway, it goes to the smaller side.
Between 1230 and 1240, 1234 is closer to 1230 (since 4 is less than the halfway point, 5).
The dashed line on the activity page is exactly that halfway point. If the red dot sits left of it, it rounds down; if it sits right of it, it rounds up.
5Try this
- Round the same number to different places. Compare how the result changes when you round to the tens place versus the hundreds place.
- Find a number that lands exactly on the halfway point. Check which way it rounds when the remainder is exactly half the place value (e.g. a remainder of 5 for the tens place).
- Practice not mixing up "at least" and "more than." Keep the reference number the same and click through the four buttons in turn to see the difference between filled and empty dots.