Counting in the hundreds

• CCSS-M · 2.NBT.A.1
  Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

2.NBT.A.1 is about understanding that the hundreds digit carries the most weight. On the line, 400 sits four fifths of the way along because it is four hundreds, and the task makes that weight visible as distance.

Children often try to count in ones or tens on a line this long. Head that off by asking them to think in hundreds first, then adjust.

1. Start: 0 at 6.9%
2. Drop 1: 500 at 93.1%
3. Drop 2: 250 at 50.0%
4. Drop 3: 100 at 24.1%

When to dropAfter two cards, drop 500 to define the range, and expect a big recalibration. Drop 250 next to halve the line, then 100 as a unit of one hundred to measure the lower numbers.

Drop unlocks after 2 cards placed.

• 150

  at 32.8%
  Between 100 and 250, in the lower part of the line.
• 300

  at 58.6%
  Just past the 250 midpoint. A little right of centre.
• 400

  at 75.9%
  In the upper part, between 250 and 500.
• 450

  at 84.5%
  Near the far end, close to 500 but not on it.

• How many hundreds is this number? Where do that many hundreds land?
• Is 450 closer to 400 or to 500?
• Which two cards are closest together? How much room between them?

• Looks like
  300 and 400 placed too close to 500.
  Means
  Compressing the larger numbers toward the end, a common magnitude error on longer lines.
  Respond with
  Use the 250 drop. If 300 is only just past 250, and 400 is well past it, the spacing usually corrects itself.

Ask whether thinking in hundreds first made the placing easier.

The same landmark reasoning that works to 100 works to 500. The hundreds digit tells you roughly where a three-digit number lives.