Landmarks to 100

• CCSS-M · 2.MD.B.6
  Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
• CCSS-M · 2.NBT.A.1
  Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

2.MD.B.6 asks children to represent whole numbers as lengths from 0 on a number line. That is precisely the placement act here. The place-value reasoning in 2.NBT.A.1 shows up when a child uses the tens digit to decide roughly where a number lands, so 45 goes near the middle because forty-something is near fifty.

Only 0 shows to begin, so the first placements are estimates. That is intended. The recalibration when 100 arrives is where the reasoning sharpens.

1. Start: 0 at 6.9%
2. Drop 1: 100 at 93.1%
3. Drop 2: 50 at 50.0%
4. Drop 3: 25 at 28.4%

When to dropAfter two cards, drop 100 to fix the far end, and watch the class pull everything left or right to fit. Drop 50 next to halve the line, which usually settles 45 and 60. Drop 25 last if the lower cards are still bunched.

Drop unlocks after 2 cards placed.

• 30

  at 32.8%
  Just under a third of the way along. Sits between 25 and 50 once those land.
• 45

  at 45.7%
  Just short of the halfway point. A good test of whether they can place near, but not on, 50.
• 60

  at 58.6%
  Just past halfway. Should sit a little to the right of the centre.
• 90

  at 84.5%
  Near the far end, in the last tenth of the line.
• 15

  at 19.8%
  Between 0 and 25. Small, in the first quarter.

• How did you use 100 to help you place that?
• Is this number more than half of 100 or less than half? Where does that put it?
• Two of our cards are close together. Which is bigger, and how much room should be between them?

• Looks like
  45 placed on or past the centre.
  Means
  Hearing forty-five as near fifty and treating near as the same as on or over.
  Respond with
  Ask whether 45 is more or less than 50, then whether it should sit left or right of the 50 mark.
• Looks like
  Even spacing of all five cards across the line.
  Means
  Placing in order without attending to the actual gaps.
  Respond with
  Point at 15 and 30, then 60 and 90, and ask if those two gaps should really be the same size.

Ask which card the class found hardest, and whether the drops changed anyone's mind, before you look at the score.

Two-digit numbers have a home on a 0 to 100 line, and landmarks like 50 and 25 make placing them far easier than counting from 0 every time.