Rounding to the nearest ten in 3rd grade

Answer. 100

The answer is 100. Since 119 is less than 150 (the halfway point between 100 and 200), 119 is closer to 100 than to 200.

1. 1Look at the number line. The point shows 119, which sits between 100 and 200.
2. 2Find the halfway point between 100 and 200. Halfway is 150.
3. 3Compare 119 to 150. Since 119 is less than 150, 119 is before the halfway point — closer to 100 than to 200.
4. 4So 119 rounds to 100.

Common mistake. A common mistake is rounding to the nearest ten (120) instead of the nearest hundred (100). Read the question carefully — it asks for the nearest 100, so the answer must be 100 or 200.

The idea underneath. To round to the nearest hundred, find the halfway point between the two hundreds (here, 150). Numbers below halfway round down to the lower hundred; numbers above halfway round up to the higher hundred. The number line makes this comparison visual.

Answer. 120

$115$ rounds to $120$ when rounding to the nearest ten. Because $115$ is exactly halfway between $110$ and $120$, the rule "$5$ rounds up" tells us to go to the higher ten, $120$.

1. 1We are rounding $115$ to the nearest ten. Look at the tens place. The tens digit is $1$, so $115$ is between $110$ and $120$.
2. 2Now look at the ones digit, which tells us which way to round. The ones digit is $5$, so $115$ is exactly halfway between $110$ and $120$.
3. 3When a number is exactly halfway, the rule "$5$ rounds up" tells us to round up. So $115$ rounds up to $120$.

Common mistake. A common mistake is rounding $115$ down to $110$. Even though $115$ sits exactly between $110$ and $120$, the rule for halfway numbers is that $5$ rounds up — so $115$ becomes $120$, not $110$.

The idea underneath. Halfway numbers like $115$ sit exactly between two tens. The "$5$ rounds up" rule gives a consistent way to decide which ten to choose: always go to the higher ten.

Answer. 40

The point at 43 is closer to 40 than to 50, so 43 rounds to 40.

1. 1The number line shows the point at 43, which sits between 40 and 50. To round to the nearest 10, find which multiple of 10 the point is closer to.
2. 2Count how many ones 43 is from each end of the number line.
3. 3The distance from 43 to 40 is 3, which is smaller than the distance from 43 to 50, which is 7. So 43 is closer to 40.

Common mistake. A common mistake is rounding up to 50 just because 43 is between two tens. But the ones digit 3 is less than 5, so 43 is actually closer to 40.

The idea underneath. When a number sits between two tens, count how far it is from each ten. The closer ten is what the number rounds to.

The answer is 451. The numbers 371, 412, and 449 all round to 400 because each one is between 350 and 450. But 451 is greater than 450, so 451 rounds to 500 instead.

1. 1To round to the nearest hundred, find which two hundreds the number sits between, then pick the closer one. For numbers near 400, the halfway marks are 350 and 450.
2. 2Check 371. It sits between 300 and 400. Because 371 is greater than 350, it is closer to 400, so 371 rounds to 400.
3. 3Check 412 and 449. Both sit between 400 and 500. Because 412 and 449 are each less than 450, both are closer to 400, so both round to 400.
4. 4Check 451. It sits between 400 and 500. But 451 is greater than 450, so 451 is closer to 500 and rounds to 500. This is the number that does NOT round to 400.
5. 5Three of the numbers (371, 412, and 449) all round to 400. Only 451 rounds to a different hundred, so 451 is the number that does not fit Sam's claim.

Common mistake. A common mistake is choosing 449 because it sits very close to 450. But 449 is less than 450, so it still rounds down to 400. Only 451, which is greater than 450, rounds up to 500.

The idea underneath. When rounding to the nearest hundred, the only thing that matters is which side of the halfway marks (the numbers ending in 50) the number sits on. A number above a halfway mark rounds up; a number below it rounds down.