Rounding hill

What the hill shows

Rounding finds the nearest ten, hundred or other benchmark. The hill makes "nearest" physical: the two tens sit in the valleys at each end, and the halfway number sits at the top. A ball placed anywhere on the hill rolls down the side it is on, toward the nearer ten.

On this page you choose to round to the nearest ten or the nearest hundred. Tap or drag on the hill to place the number, or use the + and − buttons, and use Lower and Higher (or the double arrows, which jump ten times as far) to move to other tens or hundreds. Then predict by pressing To 30 or To 40 (the buttons always show the two ends), or press Just let go. The ball rolls and the readout explains the answer. New number gives a fresh number to round.

The halfway rule

A number exactly halfway, such as 35, is just as close to 30 as to 40. A real ball might balance on top, so mathematicians agreed on a rule: halfway rounds up. The hill shows the rule on its peak, and the readout says so whenever a halfway number is rolled. That keeps the rule from feeling random, because the child can see that 35 really is a tie.

Common mix-ups

• Rounding 37 down to 30 because it is "in the thirties." The hill shows 37 is past the top, so it rolls to 40.
• Changing the ones digit and keeping the tens: rounding 37 to 37 or 38. Rounding gives a multiple of ten.
• Rounding 342 to the nearest hundred by looking at the 2. For hundreds, the tens digit decides.
• Getting stuck when rounding crosses a hundred. 395 to the nearest ten is 400, not 390 or 3,100: use the ▶▶ and Higher buttons to reach the 390s and place 395.

A 10-minute rounding routine

• Place the ball on 31, then 32, then 33, predicting each time. Ask where the ball would have to be to roll the other way.
• Place it on 35 and press Just let go. Read the halfway rule together.
• Press New number three times. The child predicts and explains before each roll.
• Switch to the nearest hundred, place 450 and then 449, and talk about why one rolls up and one rolls down.
• Finish by asking for a number that rounds to 70 and checking it on the hill.

Where it fits by grade

• Grade 3: use place value to round whole numbers to the nearest 10 or 100 (3.NBT.A.1).
• Grade 4: round multi-digit whole numbers to any place (4.NBT.A.3). The same picture works with thousands.
• England: Year 4 pupils round any number to the nearest 10, 100 or 1,000, and Year 5 extends this to 100,000.

Learning more

Rounding and place value are skills on Eurekami's skill map, and Daily Practice brings them back when they start to fade. Lessons draw diagrams live from the numbers in each question, and teachers can print rounding worksheets with answer keys.