Rounding rehearsal: 0 to 1000

• CCSS-M · 3.NBT.A.1
  Use place value understanding to round whole numbers to the nearest 10 or 100.

3.NBT.A.1 is about rounding to the nearest 10 or 100 using place value. Rounding is a number-line judgement: 480 rounds to 500 because it sits just below the 500 mark. Placing first and rounding second makes the reason visible.

With only 0 showing, the first placements are gut estimates on a very long line. That is fine; the drops turn the estimates into reasoning.

1. Start: 0 at 6.9%
2. Drop 1: 1000 at 93.1%
3. Drop 2: 500 at 50.0%
4. Drop 3: 750 at 71.6%

When to dropAfter two cards, drop 1000 to define the range. Drop 500 next to halve the line, then 750, a non-midpoint landmark, to help separate 700 and 900 in the crowded upper end.

Drop unlocks after 2 cards placed.

• 250

  at 28.4%
  A quarter of the way along, halfway between 0 and 500.
• 480

  at 48.3%
  Just short of 500. Tests placing near, but not on, the midpoint.
• 700

  at 67.2%
  Between 500 and 750, in the upper half.
• 900

  at 84.5%
  In the last tenth, between 750 and 1000.
• 150

  at 19.8%
  In the first quarter, between 0 and 250.

• Which hundred is this number nearest? How does the line show that?
• Is 480 closer to 400 or 500? Where on the line does it sit?
• Which card was hardest to tell apart from a landmark?

• Looks like
  480 placed on or just past 500.
  Means
  Rounding 480 to 500 in their head and then placing it at 500 rather than just below it.
  Respond with
  Ask whether 480 is more or less than 500, and which side of the mark that means it lives on.

Go card by card and ask what each rounds to, to the nearest 100. The positions make the answers hard to argue with.

Placing a number on a 0 to 1000 line is the same reasoning as rounding it. Where a number sits tells you which 100 it is nearest.