Zooming into the tenths

• CCSS-M · 5.NBT.A.3
  Read, write, and compare decimals to thousandths.

5.NBT.A.3 comparison to thousandths is hard to do on a 0 to 1 line because the numbers crowd together. Zooming the line to 0.3 to 0.4 gives the room to compare 0.355 against 0.35 and 0.37, which is exactly the fine comparison the standard wants.

Point out that the whole line is one tenth wide. Children used to 0 to 1 need a moment to reset their sense of scale, and starting with only 0.3 showing makes that reset the first job.

1. Start: 0.3 at 8.3%
2. Drop 1: 0.4 at 91.7%
3. Drop 2: 0.35 at 50.0%

When to dropAfter two cards, drop 0.4 to close the window and fix the scale, then 0.35 to pin 0.355 just past the middle.

Drop unlocks after 2 cards placed.

• 0.32

  at 25.0%
  Two hundredths past 0.3, in the lower part of this zoomed window.
• 0.37

  at 66.7%
  Just past the 0.35 middle, toward 0.4.
• 0.355

  at 54.2%
  Just past 0.35 by half a hundredth. The thousandths card, hardest to place.
• 0.31

  at 16.7%
  One hundredth past 0.3, near the left end.
• 0.39

  at 83.3%
  Nine hundredths past 0.3, near 0.4.

• This whole line is only one tenth wide. How many hundredths fit along it?
• Where does 0.355 go, between which two hundredths?
• Is 0.37 nearer to 0.35 or to 0.4?

• Looks like
  0.355 placed well away from 0.35.
  Means
  Not seeing that 0.355 is only half a hundredth more than 0.35.
  Respond with
  Ask how many thousandths are between 0.35 and 0.36, and where 0.355 falls in that gap.

Ask what this line would look like zoomed out to 0 to 1, and where this whole window would shrink to.

When you zoom in on a single tenth, the hundredths spread out and you can see where a thousandth like 0.355 hides.